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<h2>SL Paper 2</h2><div class="specification">
<p>A student uses a load to pull a box up a ramp inclined at 30°. A string of constant length and negligible mass connects the box to the load that falls vertically. The string passes over a pulley that runs on a frictionless axle. Friction acts between the base of the box and the ramp. Air resistance is negligible.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The load has a mass of 3.5 kg and is initially 0.95 m above the floor. The mass of the box is 1.5 kg.</p>
<p>The load is released and accelerates downwards.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline <strong>two</strong> differences between the momentum of the box and the momentum of the load at the same instant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The vertical acceleration of the load downwards is 2.4 m s<sup>−2</sup>.</p>
<p>Calculate the tension in the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed of the load when it hits the floor is about 2.1 m s<sup>−1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The student then makes the ramp horizontal and applies a constant horizontal force to the box. The force is just large enough to start the box moving. The force continues to be applied after the box begins to move.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Explain, with reference to the frictional force acting, why the box accelerates once it has started to move. </p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>direction of motion is different / <em><strong>OWTTE</strong> </em>✓</p>
<p><em>mv</em> / magnitude of momentum is different «even though <em>v</em> the same» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>ma = mg − T</em> «3.5 x 2.4 = 3.5<em>g − T</em> »</p>
<p><em><strong>OR</strong></em></p>
<p><em>T </em>= 3.5(<em>g − </em>2.4) ✓</p>
<p>26 «N» ✓</p>
<p> </p>
<p><em>Accept 27 N from g = 10 m s<sup>−2</sup></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>proper use of kinematic equation ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfenced><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfenced></msqrt><mo>=</mo><mn>2</mn><mo>.</mo><mn>14</mn></math> «m s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Must see either the substituted values <strong>OR</strong> a value for v to at least three s.f. for <strong>MP2</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mfrac><mi>v</mi><mi>r</mi></mfrac></math> to give 84 «rad s<sup>−1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>025</mn></math> to give 84 «rad s<sup>−1</sup>» ✓</p>
<p> </p>
<p>quoted to 2sf only✓</p>
<p> </p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><msup><mi>u</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>s</mi><mo>⇒</mo><mn>0</mn><mo>=</mo><mn>2</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>a</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></math>» leading to <em>a </em>= 6.3 «m s<sup>-2</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi></mrow></mfenced><mi>t</mi></math> » leading to <em>t</em> = 0.33 « s » ✓</p>
<p><em><br></em><em>F</em><sub>net</sub> = « <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>6</mn><mo>.</mo><mn>3</mn></math> = » 9.45 «N» ✓</p>
<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>
<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>kinetic energy initial = work done to stop 0.5 x 1.5 x (2.1)<sup>2</sup> = <em>F</em><sub>NET</sub> x 0.35 ✓</p>
<p><em>F</em><sub>net</sub> = 9.45 «N» ✓</p>
<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>
<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>
<p> </p>
<p><em>Accept 1.95 N from g = 10 </em>m s<sup>-2</sup><em>.</em><br><em>Accept 2.42 N from u = 2.14 </em>m s<sup>-1</sup><em>.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>static coefficient of friction > dynamic/kinetic coefficient of friction / μ<sub>s</sub> > μ<sub>k</sub> ✓</p>
<p>«therefore» force of dynamic/kinetic friction will be less than the force of static friction ✓</p>
<p><br>there will be a net / unbalanced forward force once in motion «which results in acceleration»</p>
<p><em><strong>OR</strong></em></p>
<p>reference to net F = ma ✓</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many students recognized the vector nature of momentum implied in the question, although some focused on the forces acting on each object rather than discussing the momentum.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some students simply calculated the net force acting on the load and did not recognize that this was not the tension force. Many set up a net force equation but had the direction of the forces backwards. This generally resulted from sloppy problem solving.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" questions, so examiners were looking for a clear equation leading to a clear substitution of values leading to an answer that had more significant digits than the given answer. Most candidates successfully selected the correct equation and showed a proper substitution. Some candidates started with an energy approach that needed modification as it clearly led to an incorrect solution. These responses did not receive full marks.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This SL only question was generally well done. Despite some power of 10 errors, many candidates correctly reported final answer to 2 sf.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates struggled with this question. Very few drew a clear free-body diagram and many simply calculated the acceleration of the box from the given information and used this to calculate the net force on the box, confusing this with the frictional force.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was an "explain" question, so examiners were looking for a clear line of discussion starting with a comparison of the coefficients of friction, leading to a comparison of the relative magnitudes of the forces of friction and ultimately the rise of a net force leading to an acceleration. Many candidates recognized that this was a question about the comparison between static and kinetic/dynamic friction but did not clearly specify which they were referring to in their responses. Some candidates clearly did not read the stem carefully as they referred to the mass being on an incline.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Two players are playing table tennis. Player A hits the ball at a height of 0.24 m above the edge of the table, measured from the top of the table to the bottom of the ball. The initial speed of the ball is 12.0 m s<sup>−1</sup> horizontally. Assume that air resistance is negligible.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="specification">
<p>The ball bounces and then reaches a peak height of 0.18 m above the table with a horizontal speed of 10.5 m s<sup>−1</sup>. The mass of the ball is 2.7 g.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the time taken for the ball to reach the surface of the table is about 0.2 s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, a graph showing the variation with time of the vertical component of velocity <em>v</em><sub>v</sub> of the ball until it reaches the table surface. Take <em>g</em> to be +10 m s<sup>−2</sup>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.</p>
<p>Show that the ball will go over the net.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the kinetic energy of the ball immediately after the bounce.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>t</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>d</mi></mrow><mi>g</mi></mfrac></msqrt></math>=» 0.22 «s»<br><strong><em>OR</em></strong></p>
<p><em>t</em> = <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>24</mn></mrow><mrow><mn>9</mn><mo>.</mo><mn>8</mn></mrow></mfrac></msqrt></math> <strong>✓</strong> </p>
<p><em>Answer to 2 or more significant figures or formula with variables replaced by correct values.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>increasing straight line from zero up to 0.2 s in <em>x</em>-axis <strong>✓</strong></p>
<p>with gradient = 10 <strong>✓</strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1 </strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>37</mn></mrow><mn>12</mn></mfrac><mo>=</mo></math>«0.114 s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>10</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>114</mn><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>065</mn></math> m ✓</p>
<p>so (0.24 − 0.065) = 0.175 > 0.15 <em><strong>OR</strong> </em>0.065 < (0.24 − 0.15) «so it goes over the net» <strong>✓</strong></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«0.24 − 0.15 = 0.09 = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>10</mn><mo>×</mo><msup><mi>t</mi><mn>2</mn></msup></math> so» <em>t </em>= 0.134 s <strong>✓</strong></p>
<p>0.134 × 12 = 1.6 m <strong>✓</strong></p>
<p>1.6 > 1.37 «so ball passed the net already» <strong>✓</strong></p>
<p> </p>
<p><em>Allow use of g = 9.8.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1 </strong></em></p>
<p>KE = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math><em>mv</em><sup>2</sup> + <em>mgh</em> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math>0.0027 ×10.5<sup>2</sup> + 0.0027 × 9.8 × 0.18 <strong>✓</strong></p>
<p>0.15 «J» <strong>✓</strong></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>Use of <em>v</em><sub>x</sub> = 10.5 <em><strong>AND</strong></em> <em>v</em><sub>y </sub><em>= </em>1.88 to get <em>v</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>10</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>.</mo><msup><mn>88</mn><mn>2</mn></msup></msqrt></math>» = 10.67 «m s<sup>−1</sup>» <strong>✓</strong></p>
<p>KE = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> × 0.0027 × 10.67<sup>2</sup> = 0.15 «J» <strong>✓</strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Δ</mtext><mi>v</mi><mo> </mo><mo>=</mo><mo> </mo><mn>21</mn></math> «m s<sup>−1</sup>» <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>0027</mn><mo> </mo><mo>×</mo><mn>21</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>01</mn></mrow></mfrac></math></p>
<p><em><strong>OR</strong></em></p>
<p>5.67 «N» <strong>✓</strong></p>
<p>any answer to 2 significant figures «N» <strong>✓</strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of 64 m s<sup>–1</sup>. The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The student strikes the tennis ball at point P. The tennis ball is initially directed at an angle of 7.00° to the horizontal.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The following data are available.<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Height of P = 2.80 m<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Distance of student from net = 11.9 m<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Height of net = 0.910 m<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Initial speed of tennis ball = 64 m s<sup>-1</sup></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the average force exerted by the racquet on the ball.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the average power delivered to the ball during the impact.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the time it takes the tennis ball to reach the net.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the tennis ball passes over the net.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine the speed of the tennis ball as it strikes the ground.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The student models the bounce of the tennis ball to predict the angle <em>θ</em> at which the ball leaves a surface of clay and a surface of grass.</span></p>
<p><span style="background-color:#ffffff;"><img 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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">The model assumes<br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">• during contact with the surface the ball slides.<br>• the sliding time is the same for both surfaces.<br>• the sliding frictional force is greater for clay than grass.<br>• the normal reaction force is the same for both surfaces.<br></span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Predict for the student’s model, without calculation, whether θ is greater for a clay surface or for a grass surface.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F = \frac{{\Delta mv}}{{\Delta t}}/m\frac{{\Delta v}}{{\Delta t}}/\frac{{0.058 \times 64.0}}{{25 \times {{10}^{ - 3}}}}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mi>m</mi>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>0.058</mn>
<mo>×</mo>
<mn>64.0</mn>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F">
<mi>F</mi>
</math></span></span><em><span style="background-color:#ffffff;"> =</span></em><span style="background-color:#ffffff;"> 148«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{N}}">
<mrow>
<mtext>N</mtext>
</mrow>
</math></span>»≈150«<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{N}}">
<mrow>
<mtext>N</mtext>
</mrow>
</math></span></span>» ✔</span></p>
<p> </p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span style="background-color:#ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = \frac{{\frac{1}{2}m{v^2}}}{t}/\frac{{\frac{1}{2} \times 0.058 \times {{64.0}^2}}}{{25 \times {{10}^{ - 3}}}}">
<mi>P</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>t</mi>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>64.0</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <strong>✔</strong></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 4700/4800«{\text{W}}">
<mi>P</mi>
<mo>=</mo>
<mn>4700</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>4800</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>W</mtext>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<p> </p>
<p><em><strong><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">ALTERNATIVE 2</span></span></strong></em></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = {\text{average}}Fv/148 \times \frac{{64.0}}{2}">
<mi>P</mi>
<mo>=</mo>
<mrow>
<mtext>average</mtext>
</mrow>
<mi>F</mi>
<mi>v</mi>
<mrow>
<mo>/</mo>
</mrow>
<mn>148</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>64.0</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 4700/4800«{\text{W}}">
<mi>P</mi>
<mo>=</mo>
<mn>4700</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>4800</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>W</mtext>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:bold;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p> </p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">horizontal component of velocity is 64.0 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> cos7° = 63.52 «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">ms<sup>−</sup></span><sup>1</sup>» ✔</span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = « \frac{{11.9}}{{63.52}} =» 0.187/0.19 « {\text{s}}">
<mi>t</mi>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<mfrac>
<mrow>
<mn>11.9</mn>
</mrow>
<mrow>
<mn>63.52</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>0.187</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>0.19</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>s</mtext>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"> ✔</span></span></span></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Do not award BCA. Check working.<br></span></span></em></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Do not award ECF from using 64 m s<sup>-1</sup>.</span></span></em></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span style="background-color:#ffffff;"><strong>ALTERNATIVE 1</strong><br></span></em></p>
<p><em><span style="background-color:#ffffff;">u<sub>y </sub></span></em><span style="background-color:#ffffff;">= 64 </span><span style="background-color:#ffffff;">sin7</span><span style="background-color:#ffffff;">/7.80</span><em><span style="background-color:#ffffff;"> «</span></em><span style="background-color:#ffffff;">ms</span><sup><span style="background-color:#ffffff;"><span style="text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-variant:normal;font-weight:400;text-decoration:none;display:inline !important;white-space:normal;float:none;background-color:#ffffff;">−</span></span><span style="background-color:#ffffff;">1</span></sup><em><span style="background-color:#ffffff;">»</span></em><span style="background-color:#ffffff;">✔</span><em><span style="background-color:#ffffff;"><br></span></em></p>
<p><span style="background-color:#ffffff;">decrease in height = 7.80 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 0.187 + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 9.81 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 0.187<sup>2</sup>/1.63 «m» ✔<br></span></p>
<p><span style="background-color:#ffffff;">final height = «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">2.80 − 1.63</span>» = 1.1/1.2 «m» ✔<br></span></p>
<p><span style="background-color:#ffffff;">«higher than net so goes over»<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">vertical distance to fall to net <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«</span>= <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">2.80 − 0.91</span>» = 1.89 «m»✔<br></span></p>
<p><span style="background-color:#ffffff;">time to fall this distance found using <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«</span>=1.89 = 7.8<em>t</em> + <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 9.81 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span><em>t</em><sup>2</sup>»<br></span></p>
<p><span style="background-color:#ffffff;"><em>t </em>= 0.21 «s»✔<br></span></p>
<p><span style="background-color:#ffffff;">0.21 «s» > 0.187 «s» ✔<br></span></p>
<p><span style="background-color:#ffffff;">«reaches the net before it has fallen far enough so goes over»</span><em><span style="background-color:#ffffff;"><br></span></em></p>
<p><em><span style="background-color:#ffffff;">Other alternatives are possible<br></span></em></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span style="background-color:#ffffff;"><strong>ALTERNATIVE 1</strong><br></span></em></p>
<p><span style="background-color:#ffffff;">Initial KE + PE = final KE /</span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 0.058 × 64<sup>2</sup> + 0.058 × 9.81 × 2.80 = <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> 0.058 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">×</span> <em>v</em><sup>2</sup> ✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>v</em> = 64.4 «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">ms<sup>−1</sup></span>» ✔</span><span style="background-color:#ffffff;"><br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br></span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_v} = « \sqrt {{{7.8}^2} + 2 \times 9.81 \times 2.8} » = 10.8 « {\text{m}} {{\text{s}}^{ - 1}}">
<mrow>
<msub>
<mi>v</mi>
<mi>v</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<msqrt>
<mrow>
<msup>
<mrow>
<mn>7.8</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>2.8</mn>
</msqrt>
<mrow>
<mo>»</mo>
</mrow>
<mo>=</mo>
<mn>10.8</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span> </span></p>
<p><span style="background-color:#ffffff;">« <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {{{63.5}^2} + {{10.8}^2}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mn>63.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mn>10.8</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span> »</span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 64.4 « {\text{m}} {{\text{s}}^{ - 1}}">
<mi>v</mi>
<mo>=</mo>
<mn>64.4</mn>
<mrow>
<mo>«</mo>
</mrow>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></p>
<p><em><span style="background-color:#ffffff;"> </span></em></p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">so horizontal velocity component at lift off for clay is smaller ✔<br></span></p>
<p><span style="background-color:#ffffff;">normal force is the same so vertical component of velocity is the same ✔<br></span></p>
<p><span style="background-color:#ffffff;">so bounce angle on clay is greater ✔</span><em><span style="background-color:#ffffff;"><br></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>At both HL and SL many candidates scored both marks for correctly answering this. A straightforward start to the paper. For those not gaining both marks it was possible to gain some credit for calculating either the change in momentum or the acceleration. At SL some used 64 ms-1 as a value for a and continued to use this value over the next few parts to the question.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered although a significant number of candidates approached it using P = Fv but forgot to divide v by 2 to calculated the average velocity. This scored one mark out of 2.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question scored well at HL but less so at SL. One common mistake was to calculate the direct distance to the top of the net and assume that the ball travelled that distance with constant speed. At SL particularly, another was to consider the motion only when the ball is in contact with the racquet.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There were a number of approaches students could take to answer this and examiners saw examples of them all. One approach taken was to calculate the time taken to fall the distance to the top of the net and to compare this with the time calculated in bi) for the ball to reach the net. This approach, which is shown in the mark scheme, required solving a quadratic in t which is beyond the mathematical requirements of the syllabus. This mathematical technique was only required if using this approach and not required if, for example, calculating heights.</p>
<p>A common mistake was to forget that the ball has a vertical acceleration. Examiners were able to award credit/ECF for correct parts of an otherwise flawed method.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This proved difficult for candidates at both HL and SL. Many managed to calculate the final vertical component of the velocity of the ball.</p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>As the command term in this question is ‘predict’ a bald answer of clay was acceptable for one mark. This was a testing question that candidates found demanding but there were some very well-reasoned answers. The most common incorrect answer involved suggesting that the greater frictional force on the clay court left the ball with less kinetic energy and so a smaller angle. At SL many gained the answer that the angle on clay would be greater with the argument that frictional force is greater and so the distance the ball slides is less.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Airboats are used for transport across a river. To move the boat forward, air is propelled from the back of the boat by a fan blade.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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eKPHROxo+Y5n5oKZ+e+Bh1To9Hg082bEb1/P+ZFRmLpsmW6I8YymQxqtdpkAjIAPPzII7qAvHvXTrzw4gsid2RcT06dqnu+AcOG4u133tF7DxMRiYlzkInqoVAokJuTI3YbHUJxcTGcnAyzgoVGo8HHH32Mof6D4eHhgR+joxEeEaE3ncLDwwNX8vMNsj1DCRk9Wvd1TlY2lErzWaKvJUaF3H2+SSdPYVTwCC5zR0QmgwGZqAFDhg4V9US9jiItLQ3ePj6tGqOkpARR+/bhsUcfBQCcSv61VjCuJnNzQ1JSUqu2Z2hSqVTvSoJir9VsbFOmTtE7OREA5s+bB41GI1JHRER3MSATNcBvkJ/oa+a2hLldATAhPh52dnYtfnzUvn2YGBaGpKQkfLN3L1548YUGr5Rnb2+PjPT0Fm/PWPSOqppYgDc0W1tbrF6zBh9vvrtqR05WNt5Zt07EroiIKjEgEzVgSEAAigoLxW6j2cIjIuDr7y92G01SUlKCnKzsFl36OTExsXIua1ISNm7ahNVr1jRpHKlUqpv/akp8/e6emFe9qkV7FxoaipWrV+m+37l9h+7kPSIisfAkPaIGuLq6oqhQvCkWXSwtW/Q4S8uuePkfr0CtVuPqlSu4fPlP/JGTY5In7uXm5mL8hLBmPUapVOKNZcsAAP/3+ustWvEhYNhQKJVKkzpRz9PTU+97U+vPWB6dPBk/fP+97o+WH3/4gStbEJGoGJCJGqBQKJCfl4c7d26jkwgX7rjHonUf8tjb28Pe3h5e3t4AgJmznzG50KxWqyGTyZpUW71kW0Z6Ol6JjGxViHKXy6HValv8eGOwtbXVW+7t1MmTHSIgSyQSvBIZiaeerJyTvHP7Drz40ktc1YKIRMMpFh1A1L59iImJEbsNszVk6FDcKL4hdhsGUx2YHxwTipmzn8EnW7YieORI0fq5kp8PDw+PBms0Gg2WLV2K5+fORUBAAD7burXVRxgDAgKQlZnZqjGMQTgPOSEhQcRO2lZgYCBcZHcvNR535IiI3RBRR8eA3I6lpKTgyalTsSByPm6Y4YlmpsJvkB/++uua2G2IInjkSDwxY4ZRA3RSUhJkbm513idcsi0gIKDOJdtaqo+DAy5evNjqcQwtMOhu8D+wP7pDreowZeoTuq9/+P57ETshoo6OUyzaIZVKhY82bOgwJ/kY26iQEBw62DGPwHt4eiIwqPIKd02ZnjHQ16/Z28hIT4e9vb3ebSUlJTh44AAWRM7HwiVLcCr51xadxNcQe3t7ZGVlGXRMQ6h5NP34sWMIj4gQqZu2NSZ0DN5+800AlWsjq1QqTrMgIlEwILcz27dtw4ply2vdviByPhZEzhehI/OSnlX7I3cXFxfcLBFvrqophYSG5jR37dYV/fq5N3vMpJOndM+vOhi/t349wiZMMEowrubs7IwD+6ONMnZrSCQSLFyyRBcUF0TO1+2P6vAsc3ODlZVVk8fMzs7GjeJijBs/3iBH341FoVDAReaKnKxsAJXrY5vKe5+IOhYG5Hamn7u73i+YauvWv9thjkIZmlQqFfVEPVNXHZpbQqlU6i6OkZiYiPfXr4e7XI6NmzYZ/eQ0iUQCF5krNBqN0UJ4S02ZOgW7d+3U/RznZGVj44aPWj3u+AlheHvdOpMOyWETJuie6+nkZISGhorcERF1RJyD3M4EBgbix+horFv/rtittCuh48e1qxP1TIVWq4XNvffiyalT8f769fjX6tVYvWZNm63cEBQcjIKCgjbZVnPY2triy+3b9a6sZwgH9kcjNzfXoGMa2ogHHtB9Hb1/v4idEFFHxoDcDkkkEoRHROBU8q94/qUXxW6nXfD167gn6hnT8WPHkfBzPB597DF8tWtXmy9p5uXlZbKXdJZKpfhq1y5EHzqIUaND8PSsWXhi+jQ8MX2a3moPTfHE9GkIemAEJjzysMkvG+fi4qL7OicrG0qlUsRuiKij4ufF7ZitrS0WLV6MiEmTTG69V3Pj5+eHb3Z/06bb7Ny5M0pv3mzTbba1khItnp41Ex99+CFSzpxp87VvHRwdka40vUtOCykUCmRmZmLtunWtmgqiUqnw1PTpBuzMOKRSqd40sfOpqSYf6omo/eER5A5AoVC06EpjdJeLiwuuadr2o3ir7t3bfUDOyspCxKRJ+DE6GgEBAXhq+nR8/NHHbba0maurK3Jz/2iTbbWUSqWCg4NDq+dJV//hoVKpDNGWUYVNmKD7OikpScROiKijYkAmagKpVIrC69dRWloqdivtyoH90VAoFLppQT9GV64qMdR/MLZv24aSkhKjbt/Ozs7kl0NMS0vTu3hIa4RNmIC0tDSDjGVMwnnIO7fvMPr7gIioJgZkoiYKHT8ON27wgiuGotFoas2llUgkeOHFF3Aq+VcUFRVjYlgYovbtM1pAqj4qa8oB7HRyMnz9DPMJ0CB/f5xOTjbIWMbk6emp9/2ZM2dE6oSIOioGZKIm8vXzQ3FRkdhttBsFBQUICg6u8z5bW1u88OIL2LhpE5KSkjAxLAyJiYlG6eOJ6dNMemWH6P37awXGlvLy8jKLlSFsbW3xxPRpuu+XvvYatm/bhpSUFLOYIkJE5o8n6RE1UVBQEL7avgMurjKxW2kXzqemwsvLq8EahUKB1WvWQKlUYv277+L99evxSmQkAgMDG3xcczg790V2drZJnghmqPnH1YTzkE39AhwzZ83STX/Jycqu8wJIAOAic63zD62M9HQknTxV6/aFS5bghRdfMGyzRNTuMCATNVHfvn15BNmALl/Og1whb1KtQqHAhxs26C4msu3LLxE5f75BQq2TkyPy8/JaPY4xpKWlIenkKchlbgYf19QDskKhwMrVq+oNxtVysrJrXRipIW+/+SZ8/XwN+kcWEbU/DMhETWRra4vOXTqjtLQUXbt2Fbsds5eb+wfGhI5p1mMCAwMRGBiImJgYPD93LoKCgzFz1qxWBWVvHx98vnVrix9vTKeTk/HlVzsMGuYSExPx8/HjZnGFuukzZmDosGGIjYlFzKFDOGOA+dNBI0YwHBNRoxiQiZohYOgwFBYVMSAbwM7tO/DqggUtemxoaCiCg4Nx8MABPD93LqZMfQJTpk5p0VQEKysrZKSb5lrI0fv349k5cww6pqenJ5a+9hoWLV5s0HGNRaFQQKFQ4OzZ37Anah88PDxqzRlXq9W4kp+v+76Pg0Odlz/Pz8/Hhx98YPSeicj8MSATNcOIB0Zg967dsLW1E7sVs1a9akRr5tZWLw03bvx4fL71cwz1H4yFS5Zg5qyZkEgkTR5HKpXWOVdVbIaef1zN1tYWDg4OZjEPuVpJSQkO7I/Ghxs2AECtTwya+gmCQqHAG8uWQaPRGHy/ElH7wlUsiJrB29sbhdevi92G2cvNzdVbpaA1hEvDAWjR0nDjJ4SZ3CWNDbn+cU2jQkabxXrI1S5evGiw90vYhAm4cOGCQcYiovaLAZmoGfr27YvszEyx2zB72dnZcHbua9Axq5eG+3L7dt3ScDExMU16rEwmg1qtNmg/rWXI9Y9r8vXzNYv1kKudO3sWAQEBBhlrkL8/Us6kGGQsImq/GJCJmsHW1hb2vXtDe+OG2K2Ytfy8PDg5ORplbKlUitVr1mDjpk2IO3IET06d2ugayh4eHnpzWE2BIdc/rsnT09Ms1kOulpCQAG8fH4OM5eXlhaNxRwwyFhG1XwzIRM0U8uCDKC7mFfWa4s6dO3XenpaWZrDAU5/qNZRfiYzE++vX4+WXXqp3GkUfBwckJSUZtZ/mMNb842rCecimrnr+saHWqZZKpcjPz4dGozHIeETUPjEgEzWTr58virgecpPcvn27ztsT4uNhZWXVJj0EBgbiq127MOOpp/D83LlYtnRpraBsb2+Pa9eutUk/TWHM+cfVzGUesiHnH1fjPGQiagxXsSBqpiFDhmDzJ5vEbsOs5WRlt/kKCoGBgfgxOlq3NFzYhAl4ds4c2NraQqFQ4MD+6DbtpyGnk5Mx4oEHjLoNXz9fs1gP+dzZs9i5fYfuqnqG0qOHDddDJqJ6MSATNZOzszOyMzPRf6BxTqBq75RKJcZPCBNl28Kl4fbu2aNbGm7K1CkIGDbUZJY+M8b6xzWZy3rICQkJiD500KCXAlepVFj46qu85DQR1YsBmaiZJBIJ7vf2xq9Jp+B0nxQ9e/aEVffuYrdlNtRqNWQymag9SCQSTJ8xA2ETJmD3rt147NFH4eDgaBIBWaVSIScrG0P9B7fZ9sR+zvWpuf6xoQjnIXM9ZCKqCwMyUQt8vecbXLx4EYcOHsLuXTvRpXMX9LKzRy/bXga/iMitW2UGHU9sV/Lz4eHhIXYbAO4uDTdl6hQsWrgQ2VlZGDp0qKg9paWlYeGSJW1ydPPjjz5GWlqayQZkY8w/rlY9D7mjTrMoKSmpdUXCaudTUyFzc4OvLz8lo46LAZmoBSQSCXx9feHr64uFixZCpVIhOjoaMQcP4XjcEfSytUMfBwfY2duhU6eW/5jZ9+mDa5prkMncDNi9uJKSkjDx4YfFbkOPra0tnpw2zSTWBm6L+cfVTH0esiHXP66pej1kUw3IKpUKWq221u01L6td7fLlPOTm/gEAuHnzJkpKbgIAigoLkfDzzy3qYfPWLQgJCWnRY4nMHQMykQFIpVLMmTMHc+bMgUajwcmTJxEbE4t9e/bA8b77OBVD4Nq1a7C3txe7jVpcXV0Rd0T89XHbYv5xNVOfh5yQkIDI+fONMraXlxc+3bSpxUfq61syMDs7GzfqWAby4sWLuF51Fc7i4mLculW5wkvK6dPIu3y5RT0Y25xZs5GexQsjUcfEgExkYLa2tggLC0NYWBhWrV6FM2fO4GhcHPbu2QOLezrBvk8f9O7dGzb33tuk8crKSuu8ff6ixXh37VsInzzZZD8ir4sx5pQagrOzM3Zu34HVa9aI1oOx1z+uSbgesqm9h1o7/7i+AHs+NVX3dbpSie3btsHa2lpvHexr1/7SfX3AjC6oQkSGw4BMZEQSiQSBgYEIDAzE/732GpRKJY4ePYq93+xByulk9HFwRC9b2wanYtR3CWQvb28AwMSHHzFa/4amUqkQMEzcOb71kUgkcJG5inriVlusf1xT9XrIbRmQ65v/qtVqkVV1Kfes7GwEDB+GqH37UFxcrFuz+fbt2ygqqjxC25rpA9VWLFveqscTUfvEgEzUhhQKBRQKhd5UjKh9+/DTDz/A1c0Ntnb2sLO3R9euXcVu1SjUajXc5XKx26hXUHAwCgoKRAvIbTn/uFpd85A1Gg0KCgpq1TZ3/usfOTk4f+5cq/pLOnGyVY8nImoJBmQikQinYpSUlODMmTOIORSD77+L0k3FuH3rlthtGlRWZqbRTroyBGfnvjifmmrQNXebo6nzj+s7gas18183bvioNa0TdQBqxC2bjDlnZyP621lQ1Hkt4qbUGEBhHJYPfxnnFu/FnlmevCyyETAgE5kA4VSM5W8sR0pKChISEvD+O++K3ZpBXbx4EYP8/cVuo15OTo4oriNgNldT5r8KJSUlobi4GEWFRfjXypVmcQIXtX9iXdDHdNkjZPVRpIvdBgDYhGDV+br/PyHDYEAmMkHVS8ite/OtdnUhg+vXr8PV1VXUHhqa/3r5ch6OHo2DtbW17nbh/FfA+Cdw/RD1ncHHJGqJSY8+KnYLRKJhQCaiNrNz+w4sXbaswZrmzn81xglcnPdKHZ13//4IDg4Wu402Vo5iZSw2v/kG/heTB8AKnjOWYtXfH4O/oyXqnD5Rnofk7f/D8uXbcQGOeHDe8/DOq3lxp0IoYz/H2n+8g8NaAF7T8c81f8c0f8e6p0aUX8Dnk/6O9PlfYVWIYEnMwjgsH74Z8qjNmOlwovYUi2IlDm96C5HvxUBbo/dy5VZMHhuDiEObMVPRrXIztW4rR2HcSox41w17jDk9xEwwIBNRs6jVapSW1l567kp+Pm7eLNF9n3f5MrQ3ivHxRx8jN/cP3Lx5E90k3bBwwUIAhjmBi6vdeQ4AACAASURBVIiMY9Wa1ZBIJGK30bYKj+HN8DdQ8O9duLjZBRblfyJu5YuY8nxZPfOJ/0Lyey9jVupYfHbiAoY43sSFrUvweEweoLsIYRn+3LcCkzfaYFVUCj5RWKP4wg68OullqLd9ikj/nrX7sHBF0CQHrIs5h0UhIbABAJSjMPkIohSh2OPeDag5E6w8B1GL5uATu/nYc24jFNbFlb3MLsDWr1+Gv3sgInzfx774bDyl8IQFbiIjPgZncRrQ3aZBckwcMGA0HDp4OAYYkInaHZVKVeftNQNstdzcXPwumEIgtGXTJmzZtKlV/Zz+Vf/qdFxXlsi0PTN3Tge8zHRVANW6Y4FPn8ojshb3IWRlVP1zjgvP4NtNEiyImoUhjpYALOH5dCQWfHsMq3Q1Cfjo9WSEb9iDcEVl1LX2fAyLFv+EsJX7MLHO4N0N7sGhcH/rCJIXj0SIjQUADZJjEuA+aRrca9WXo/DYp1h+NATvn/gbFNYWAGyqenkSq74Zhz2zXBE0yRvr0i+jGJ6wQTFU6cCDoa44UX1beQGyz1oifH7/qlDesTEgE5kQpVJZ60SuY3FxuHjhAgDonUCWkpyM9KxMyNvRZaiJSFwDfH0x/9VXxW5DBBawGfIwnvGahVWvrAaeH4EBwx+smlpRl6pADXe87yCosbCD6wB74KygRtsXC6TWgsdawkHmDquUGCRkPAFF1ZQHvW7cAxGh2ILdh5/FyAgXWBSeQ+xeB0REudYxLaPyyK9WMRtSa8G9FnZwHdADZ79NRMbTCjjI3IHq0I1ziP3RHU988iCuzqy8bWR+IvYpgzDPv/2c99IaDMhEJiIlJQWTwyNq3Z6hVCKjnlURiIgM6X8bPux4UyuqWQfglS1fQp5wFN+9/iJWVc0XXr5kJiaHKGCtV1yG/KwMaOFecxBI5X2rAnK1eKwa63X3qLJOA3O8LVwRNKkvVm05jIy/PQ0H4fSK+qSsRFi/lbVv9wUAC9j4j0Y4NiM7vwzlyMLvE0djkSfQH4eRnV+IjPgYZDw6B/42nF8BMCATmYzqK4gREYnhy692mNwlx9uahaM/Hn7UHw8/Oh/lecn4/quPsHzWSuDQZszUWx696ihwrRGKoUr/Q/8mq6ex+cSKqqkSTVU5zWLAP2OQkBEK13qnVwg2M2MLfl4dUv/0CJv+GPNoPt6L/x3DcRS35YGwtrHDmEdLEKu6DNf0fLjLnWr8IdBx8c8EIiKiDu7jzZsQGBgodhsmxcLRH+HPTke41R9IV9U8K676iGwGsvMFq1aUFyD7rLpGTRxikzWCx5ajMG4FBnqvQFxhef3bdw9EhG8+0s8eq5xeEVzX9AoAsIV/aAiw9wiS9cZTI27ZKAxcFodCAJVHtx2Q8XsMvv8WVeNZQyqXIOrzd/BFg9voeLgfiIiIOrCFS5boXWq8YypHcfIHmOg9Fx8k5aEyZpYhLzkeyfDHEI86jsva+GHS3BKsemUd4vLKABTiwhfrsS5FW6PGHl+9+QGilIWV21F+h7VvxmHEv5/FyIaOKletZvHVq0vxlSIUQfVOr6iaP+36Pda+9R2UxeUACqHc9wHW7vXHqpeCqo4qV538t/NDfIxRVeNVHgnHkRgca3AbHQ8DMpGJ6G7ND7aIqG2tXL0KL7z4gthtmAALWPvPxPoNwbjyxhh4yNwgl3li3DYbLIhaifD76jpZryf8532I3dNKsHa4J+Sy8Vh3bRieCXXUr5m/BdEL7fFjuC/kMnf4hf8Iu4Wb8VaESyMhrGqaBawwYFJgg9MrYB2AyK93YYHdj5jc3x1ymS8m/2Bfq/fKo9JWsBogq1rKreoot1UTttHB3FNRUVFR1x1ymRsm1nHCEInvvffa1+WHqZJSqUTY2HHNegxXsSCilvryqx2cVkEdklzmhvSshs/74d8KREREHYRFJwvY9+nNcEzUCAZkM6RUKlFSUnnBB5VKpbswhEajgVKwHJhSqYRGo6lVV1JSYpS66p6EdRqNxuB11T3VrFOpVAava2jfGrruHK8qR0RG5tN/APZ8+y3DMVEjuMybmfn52DFcSEtF+kUl/Ab7487t21Cp/oRGrYab3B23yspQVlqGq1euoP/AATib8hsAYIDvQF2dwtMTJSXaRuvcFXKUlpbiVtkt2NnboVOnTnp1ubkqXCsogLtCjs6du+Cva9dw9coV+AzoX2/dPffcg6LColp17goFNBoNet57L+6U34GlpWW9dXfu3EYni064lJEBd4UcxUXFuHLlCnz6++jVlZWVwbJLF11d+kWlrqezKb/Bz98fRUVFjdYBgJvcHbdv3YaVRIJ0pRJu7v306oSvwe1bt1F68yauXrmiG893sD/KG3ithNslIjKGea/Ox5y5czvuOsdEzcAjyGbm+jUNPL180MvWFmd+TYa0rwv6ODgAAGx72cHLpz/+unYNFRUVcJH1Qy/byivi9HZwhMytcq5q9x49Gqzz8PQEAHTq3AVePv1x7do1nD+XWqvOy6e/rs5FJsO1a9dQXl4OF1k/uMhkdda5ucv16hT3319Z18cBXj79kZ2VhZys7Fp19/v46Oruc3ZB5qVLqKiogNzDE9obN1B+506tur6uMr266t6lfV1wv48PziQn16qr3rfCuup9K/fwREZGBu7cuVOrTvgayD08dfu2ui6lkddKOB4RkSE5OjlhT9Q+/OOVVxiOiZqIR5DNzMTwCCSdPIHi4mKMHjsOl1V/4mJaGh4IGY3u1t0RFxuLrt26YWzYBL260pulSElObrSuorwCSSdOYOCgQbhPKq2s69oVI0c/WKvuZPzPddZd/P135P35Z6N1uTk5yMzIwAOjR6Nzp844duQwZO7u8PD0rFV3MS2tVp2Xtw/ijx9DBYDQh8IarDuZmIDSsjKEPhSmt886d9avq36OY8Y/VGvfxh48CBeZrNG6uNhY9HF0hO8g/2a/VkREhmDRyQLld8p51JiohRiQzUzSyRO4ptEgZMwY/KlSIe3cOQwNDETXbl0RFxuLLl26YOToB/HLqZO6ugJ1AVKSf0XA8OEN1hUVFiHp5An4Dh4MW1vbGnUn9OtOJMK1Xz/0cXDQqzufmgpVTjZGNVKXeekSLv5+HqNDx6KosAgJJ47BtV8/uMvlOBp7WK/u99TK53ir7JauzsvbBwnHj+PO7duN1p06eQJarRajx4Tq1ZVXVODYkcO6OuG+UOWqdHVdu3VF7MGD6Ovq2mhdXGws7Hv3hu8gf726pr5W8ceOQXvjhthvMyIyc3+LiMDzL7wAhULReDER1cKAbGau5OVhaFAQsjKzoPw9DQpPT3TpYomYn36CZVdL+PkPx7Ejh1FUWIihQUG4kp+PlOTkOuuOxx1B4fXrGBoUBLVajdNJSZD27YvuVt316k7EH0eBukCvrpedHaRSZ726lDOnkZud3WjdubO/IfvSJQwaPLhW3dHYWJSVleGBYaN1dQpPT9y6fRu/njypq4uLjcGN4mI8ENJw3dHDsSguKqpVd4+FBeKPxt2tO3IExYWV+0J54QKyquqq91lT67p37w63fu56dc15rRiOiag1/PwHYcGiRTwJj6iVuA6ymUlLTYX2RjH6ufdDYFAQftofjYKCAowZG4pOnTrhiy1bMemxyejZqxeif/gR/dz7YdTo0fju230oKCjAQxMnoPzOnTrrgoKDcfLkSSgvXNSre/yJqejVsxe+i4qCnZ0dRoaMwrlz56C8cBFjx4/DPffco6u7z+k+7Nq5E3Z2dggdNxbJycm6ui+3fg4AiJj8KOTuckTv3w8AenUTH34YhUVF+HrnTox9aDzkcjmOxR0FAIwZG4rTp0/r6soryrFl86cY+9B4eHt7I+bgoVp1Y8ePQ7du3fB91HcY4DtQr2506BiknDmD43FH8djUqehh00O3LwKGDtWry8rMxA9R3zVYFzzyAdwsKcEXW7biienTIbGS6Oqa+lqlnU/DNY0GTcV1kIkIqPx/dfJjjzEYEzVBU9ZBZkA2Q+Z6oZCmvCE7ujGjRyM7M6vJ9QzIRB3bvFfn46GwME6lIGqGpuQRTrEgMiGBQUHNCshE1PGMHjMGU598AsHBwTz5jshIGJCJTIiXl5fYLRCRCYqY/CgeCguDv78/bLkkJJHRMSATmRBra2uxWyAiE/BAyCiEhoai/4AB8PDw4JFiojbGgExkQqov5kJEHcfD4X/D/fd7wcnJEd4+PpxPTGQCGJCJTIiHhwf6ODjgSn6+2K0QkQGMnzABXbp0hrW1Nby8vGBtbY0+Dg6wt7eHnZ0dp0sQmSgGZCITIpFIsG79u3jqyWlit0LUbjk6OcF30CC926pDrFBAQEC9Y8jc3GBlZaV3m5WVFaRSqeEaJSLRMCCbocNHjordQouZc+9t6ZMtW5tUJ5e5NbmWiAynQPMXCjR/1br9wsV0EbohIkOzELsBIiIiIiJTwoBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTQIQLyj1H7xG6BiKhDeG72LLFbICJqtQ4RkImIiIiImooBmYiIiIhIgAGZiIiIiEiAAZmIiIiISIABmYiIiIhIgAGZiIiIiEiAAZmIiIiISIABmYiIiIhI4J6KioqKuu6Qy9zauhciIiIiIqNLz8ps8P56A3J7Ipe5NbojyPj4Ohge9ymZGr4niag94BQLIiIiIiIBBmQiIiIiIgEGZCIiIiIiAQZkIiIiIiIBBmQiIiIiIgEGZCIiIiIiAQZkIiIiIiIBBmQiIiIiIgEGZCIiIiIiAQZkIiIiIiIBBmQiIiIiIgEGZCIiIiIiAQZkIiIiIiIBBmQiIiIiIgEGZCIiIiIiAQZkIiIiIiIBEw/I5SiMW4GBshn4XHnT+JsrjMNybx9M2noB5cbfGrUD5XmJ+GBOIOQyN8jDt0JptDeOGnHLRjWyjabUGGpb1OHw/0ci6kA6i91AW0jPyhS7BUJ7fB1uIuOnD/He1ecRfWkWFCL8udn+9imZLJsQrDqf2mgZ35NE1B6Y+BFkIlNWDFX6H2I3QURERAZmJgG5COnxX2J5mA/kMjcMnPMBDisL9UvK85C871085+1W+XG3LBDPvXsIyuKqDwML47DcexSW74vH4XfnYmB1zfuJyKv388JCXNj6IgZ6v4jPLxTWV9SBVH70PnDOGrxdNa1g4LI4FAK193/YMnwep0Rx9UN1+/8YopaFV9Z4z8X6WEFNZSGUsR/ojbMtOc/0PtItv4DPw0dhzrYcIGUlwvqNwvI4NYAy5CXvw/rqaRe13q9V04a8lyEq6ae7dd5z8UFSE55nWToSvliGiXW9x+vss5Gfi+qaL4Vj/oAzeWU1BjKT14UMoJ6fc+EUi/IL+Dx8bNV7XqAwDsu9BVPiipWC/299MHHZDiQL31uFcVjuHYjn1q6pem+Nqj0mEZEIzCQg/4avdl3BmC2nkZ6Vgq9HnEdk+ApE/Vn9H+1fSH7vZcz6oTcWnMpAelYGzhxaAoeDS7D4G6Xgl3gOvnp9K1JHrMKZrAycOfAy8PEcvPhFXXPqypAX9wFefQtY8O2bmOlp00bP1fRpY06heMYeXMw6i4N/HwKbqv0/ZaMW0w5fqNz/6+9H/EtPY/G+HP39H7kOp0M/wsWsDJz5dhTO/0NYU4Y/963A5LfVmBiVohvn2IyX8X7yX2I93bpZeGJm1FFsnuEC+K5A9KWjWBVii+LkjXh2xgH0WnQA6VmZSD/3E1Y5xuC5hXv15/Nqt2P5xiyMWH0U6Vkp+HFxZ2x6fCG+bGyufdq32J05Gp9eykT6uc0ITn0Dkxd9hz/rTKpN+bmoqjnqjJUnLiA96wAW9DqJz2LyBOOY0etCBlP751zAwhVBkxwQFXMOdw8dlKMw+QiiFKEIcu8GlOcgatEcrCuYiD3nMpCelYh35Mcxa/ZGJOv9UZeHw4dR+X/Hua/x8hDbtnqKRET1MpOA7I+/r3kZIY6WAGzg+fRrWDUqGVsPZlb+ki88g283qRE+4yF4WlsAsIC1YgTGDO6Bs98mIkP3f7EVBixeiJcDHGEBC1h7PoRpj9rXqAGAUuTFrcWzL+ViCsNxbVZ+CPF3hAWs4ehojXLlPqx6D4LXyALWnlPwz38Px8+vf4pjhdU71wqe85ZhYch9Vfu/qmbL4cr9X5iAj15PRviSfyBcYVM1zmNYtFiC/63cZwYnjGnwy95v8MejUzGp+j1jrcDoUD9YpcQgIUMYfoOxYMksDKl+Tz86FeFWp7EvPrvho7JeL2DVotFwtABg7YOn/rUEI45+g0MZdQTrpvxcFJ7Bt5sk+r08HYkFvlaCccz9daEWqfFzrq8b3IND4b73CJJ1P98aJMckwH1SINwtylF47FMsPxqCRYv/BoW1BXTvLcstWKV34AKwGhwMf0dLwLoPHK3N5NcSEbVr5vE/kVV/+MkFIdWiD7yH9b37S94mBKvOH8XK+3Pww759iNq3F58ve7by4+8WKPv5XcydtQOWiyPxFMNxbQo3SHW/xMpRrMpERs3XCJZw9PGFuzYD2fnVR/rt4T/IDdY1a1JikJChrTz6pO0LudRabxwHmXsdAdMU2SNk9VH89q/7kf79PkTt24eorW/gyVlfQGugLVgNHgC5IEBYOHphmOJ83cG60Z+LqiN+cIerg+Xdx1nYwXWAvX6NWb8u1CJ6P+e1WbgHIkIRh92Hc6sOVJxD7F4HRAS7wgIaJMfEQVtzDAs7uA6ofeDCXe6EmhGciEhM5hGQG1U5V9hv+FP46BcNAAvYPboKn8xwacFYWlyI0WDgjKHIeOtjfP9nzbmYpK8M+VkZDQTAP5CuKq733trisWqsl27+rlzmDn8DBkzjKkfxhW14rn8gpmz4BX8BgF043vn0aVg19lCjaOznor7XzhpSed8at5nz60JGYeGKoEl9cXDLYWSU15heUS1lJcL6uQneNwEtPnBBRNSW2sUyb+XKvfi/f17BM3vjEenfs+pWNeL2tmQ0Kwz451tY87QEwwumYvmGBIxeHQIeR65P1ZHEeu+veeSxEVZPY/OJFQixMcO/3cqV2LP4Hajm7saZ+QFVR8TKURj3g0jtNPZzUd9rV8fqHOb8upCRVE6zGPDPGCRkhMI1JgHuk6bBXfAWsZqxBT/z/08iMkPm8dtO72N6AOXZSPj2PAZUzXWr8yP+8gJkn23F2dAWzhgzdxr6bvsAn/FEpAZYwFrqBnftOZxJF670UYa81BRkWAk/vlfjXFaBYCrATWTEx+CsbyiC3K1g4z8a4YhDbLJGME71qg8rEFdo4pNdiy8jXdmjxjSSxo6wN4/2bBbyhQtQZCRiX4p31cfaQk35ubCo2uc1f77qqjHj14WMxsI9EBG++Ug/e0wwvQIAbOEfGgLozVEGdCtkVK9+Q0RkoswjICMe697cil/yygAU4sIX67GubDaWP6aoPNnLYxBG4ODduXDFShx+722sS2lNLLGAtf9TWDUP+N/SL2ucdU1CFooILJ8H/G/ph4jLK0PlVIPd+OfrJzDi389ipO6ooxZn33obHybloRzlKL7wDda+VYK/r4iovMiGjR8mzbXHV29+gChlYeU4yu+w9s24GuOYKOt+GDKqDFG7fq5aVaIQythNWPtWvOG2kbIRa/9XtTRhcSq+fHMLyubNw2RFtxqFTfy5sPHDpLklWPXKuqrXrurnq1aNGb8uZDxVq1l89epSfKU3vcICNkMexjOu32PtW99VLStYCOW+D7B2rz9WvRTEo8pEZNLM4zeb1WNYMPUOPnnQE3KZLx7/2RefbXke/lUnf1jcNwFvfD4Tt18fBQ+ZG+RD38Jvbs/h60+fhpUyE6oWh9ue8Jv6FMZl78DmmFyu+VqvnvCf9yF2P2+FHQ96Qi5zh1/k7wje8AXeinARvMms4PmoH+5snASPqpqR2z7EK7qP/3vCf/4WRC+0x4/hvpXjhP8Iu4Wba4xjoixc8MiKdzD31psY2c8Nctl4rP2tL1749iM8adXcudh1s3rieTyOzzCunxvk/ecgfuB/8em8gDpPcGraz0XVazetBGuHe0IuG49114bhmVBHwUhm/rqQEVVNs4BV1Sd6grusAxD59S4ssPsRk/u7Qy7zxeQf7LEgaiXC77Osd0QiIlNwT0VFRYXYTVAHUBiH5cNfxrnFe7FnlidDFREREZks5hQiIiIiIoEOEZDlMjexWyAyCr63ydTwPUlE7UG7WOaNzIBNCFadTxW7CyIiIqJGdYgjyERERERETcWATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkwIBMRERERCTAgExEREREJMCATEREREQkcE9FRUVFXXfIZW5t3QsRERERkdGlZ2U2eH/nhu6cGB5h0GbE8mPUvnbzXAAgPKL9PBdqnedmz8InW7aK3QaRDt+TRGTqnps9q9EaTrEgIiIiIhJgQCYiIiIiEmBAJiIiIiISYEAmIiIiIhJgQCYiIiIiEmBAJiIiIiISYEAmIiIiIhLoEAG5Pa2BTERkyrgGMhG1Bx0iIBMRERERNRUDMhERERGRAAMyEREREZEAAzIRERERkQADMhERERGRAAMyEREREZEAAzIRERERkQADMhERERGRAAMyEREREZEAAzIRERERkQADMhERERGRAAMyEREREZEAAzIRERERkQADMhERERGRQGexGyCiu9LOn0fUt9/iUrqyzvuDR46sddvnWz4zyLatuneHs7OzQcaqS8+evWBz771GG793b3tYWnY12vhERNRxMCATmQi1Wo13177VYE38sWN636dnZUIuczNmW1Slrj9ODMnD09NoY3frJkEfBwejjW9jY4MePXoYbXwiorbGgExkIpQXL4jdAjWg5h8n5ja+OfP194e1tbXRxucfJ0RUEwMyERGZtJTkZKOO35H/OLGzt8fYhx7Cg2NCxW6FyKTwJD0iIqIOqkCtxs5t23DayH+EEJkbHkEmMnERkx+D36BB9d7/z9Vr2rCbpistLcWmjz+C+upVsVshokb8lnIGg/z9xW6DyGQwIBOZuAkPP1zvfXKZGz7ZsrUNu2meRyImYcumT8Rug4gacfnPy2K3QGRSOMWCiIiog6tvaUmijooBmcjMPTd7ltgtEFE7oFKpxG6ByGRwigVRFXMLmsJ+n5s9y6SnWhCR6buSnw+pVCp2G0QmgQGZqIrYATMxIR5bNm0StQci6riuXdOI3QKRyeAUCyIiIsIfOTlit0BkMhiQiYiIqENfMIWoJgZkIiIiAgAUFRWJ3QKRSWBAJiIiIgBAYWGh2C0QmQQGZCIiIgIA5GRnid0CkUlgQCYiIiIAQG5urtgtEJkEBmQiIiICULkWMhExIBMREVGVlORksVsgMgkMyERERKSjVqvFboFIdAzIREREpFNYeF3sFohEx4DcAahUKvx3zRqx2yAiIjOQn5cndgtEoussdgNkPEVFRdj7zde8OhIRETWZRqMRuwUi0TEgt0NlZaX4+fhx7Ny2TexWiIjIzKivXhW7BSLRMSC3M5cuZWDTRx+hoI6TLJ6bPUuEjszLJ1u2it0CEZGo4o8dw8zZz4jdBpGoGJDbmd69++B+b+86p1Uw/BERUVOUlZXC0rKr2G0QiYYn6bUzPXr0wMzZz2DF6jXoJ1eI3Q4REZmhq1e51Bt1bAzI7ZRUKsX/LV2KF//xCuzs7cVuh4iIzAivqEcdHadYtHOD/P3h098Hhw4eFLsVaqfKykpx9aoaOdlZGDxkCD+WJWoHbt4sEbsFIlExIHcAlpZdMfHhR8Rug9qB6jB84fffkZ6uRGZGBgquXoVVd2tobxQj7vBhLFi8mCGZyMzl5uaK3QKRqBiQiahO9YXhLpaWuFVWplervVEMACgsLMTVq2pIpVIxWiYiA9HeuCF2C0SiYkAmIhQVFeHq1SvIyszCubO/4VJ6OrQ3btQZhmt+T0TtD5d6o46OAZmog2EYJiIiahgDMlE7VlcYvnXrFoDa4ZdhmIiE1Go17Dv0Kki3oVGexAUMRKCih8i9FOK3rSvxv6zxWPHGOEi5BpnRMSATtUNFRUV44/XXUFYVehl+iai5SktLxW5BXNpUfP/2XuClAQgUuxfYYOCsdfhE7DY6EP4NQtQObf3sU9woLsatsjKGYyJqkcLr18VugUg0PIJsZkpLS6FSqdC1a1fY29tDpVIBqLwwiFqtRmlpKWxsbABUrijQtWtX2Nj00F0VSVjXu7c9SkvLWl1X3YOwzsbGBl27Wra6rrCwSPecqutqPveW1gn3UVP3pTH3uSHxDHQiaq2//romdguiKVcdxJplO/AHAKx/BfGu06qmNlROuzj6w9eI/u0vAK4IfvJRhD4wAFKJBaqnQnyCSXjFIwPbNx3BZfSEzyNP4bGwQVU1NZVBdfAd/OfPMLw1yxdWutsL8dvWfyPqvpexdNy9OFdrioUWqtMH8M3HUUgtAyAdhSdmhiNEYQuL8j9w6F//wYmg17B0XN/Ko6F13aZNwefzo3HfG69irNTSyHvVvDAgm5kTPx/H7+dTAQB/5ubiPmdnWFhYICcrCz1tbWFjY4Nbt24h//Jl9HV1xZ07d2rV2ffuDavu3XV10r59UVFRUauuj6MjunXrhlu3buFKYS+WIgAADpdJREFUfj7uk0p1dY73SdG5cye9upKSEty5fRvdra11dQ5OTujSpYteXU5WFux694aVlRUqKiqQd/kyHJ2c7vbXpw+srKxq1ZVotZBYWTVYV6LVQqPR4D6pFBYWFlD98Qds7e0hkUj09pH2xg2or16Fs4sLLCwsUFxUDKvuVrX2pfbGDd14de7zXrawudemwX1ZXFyMThYWkFhZ1arLzcnR9ZCTlSXmW4uIiKpYSMdh+YcO+Hz+F8BLKzDT1wZAOW4qv8d7/z4DeeRyfDzfDhYlWTj08Xr85/fHsfLvwbCryr9lR7/AdosXMe/TmbAtrarZdFOv5i5LOPn4w2HPGaRPGYCBVlUF2kycTuyJ4W84wAI3azzmNgoSPsd/9lth+hsbME/aDTdzD2Pjqv/h+sJXMUnhAO8gF3ydkIbLoX0htQDKL6fhRLYWf6D6tnJolWeQBCc814txsCZOsTAzMnc5+g8cCPXVq+gnl8N3kD969bKFnX1v3O/lBXe5Alfy8uA9YCC8fHz06rp27QYHJycMGjJEr85nwAC9ups3b6Kviyt8Bw3S1fn6++vVDRo8WK+ur4srNGo1PO6/X6/Of0iAXl11rwoPD12d94CBetsdNHhwrbr8vDw4u7g2WCdXeOCaRgPv/gPgO8gfWq0WMnd3DB0eWGsfXdNo0N/XD76D/FFYWAhbO9s692X1eHXt8z5OTggYPqzBfdm1azd06dIFfoMH11kn9/DQPSdLS/71TkRksspVOL79EPDINDzua1cZoCQyjHn6cdyfuhc/nC28WysNw1OP+8LWQlhzHMmX657yZuHkheFOaTitLK7eWGV4dfKHt1Mdvxu0qfjh83QEPD4JgVIrABbo5jwSj022RPT2BKjKK0N338uXUXCzHEA5bqqvAAP7w0l3221cy78MBPpBbsU4WBP3iJlx7uuMuNhYdOnSBbJ+7sjNycHZlDPw7t8fEokVjh05DNd+/WrVZWZkIDvzEvz8/XH71u1665JOnsA1jQZyT0+9uj59+tRbp72hxYn4nxEwfDh69upVb92VvHxdr9V1vezs0KdPnwbrYg8eRF9XV/RuoE743F1lMpxMTIBWq4VbA/vIVSZD/PFjuHP7drP2ZW5ODlLP/YZBjezLi7//3qx9PiggoFXvjedmz9L9y1AqDfSOIyIiAMBNDf68LEE/dyd0E9xs0csFnk4lyMm/jvKq2yzl/XCfYDpFZU0OTqTm62r0WDjAO6gnko6eRUE5ABQj/XQaHIK84FQrqVWF57LeuM9e2Eln9HJwgmV2Ms5fLoNFLwe44Leq0F2M9NOX4BIyDiOqg3h5Ps4n/IWAQW6CaR1UjcfUzUx1sBo5+kFkXrqE31PPYWhgIMorKnQBzF0ux9HYw3p1ygu/IyQ0FMXFN3Di5+N11v1yqjKohYwZg6LCIiSdSGy0rkBdgJTkXxEwfDh62NjUW/enSoW0c5W9du3WVfc8/AcPabCuOhx7efvUWyd87l7ePjh14gS0Wi1GjwlFVualeusSjh/Hndu3MXL0g/XW1bUvL/5+HqNDxza4L8+npkKVk41RY8Y0eZ8XFhY2/gZowCdbtuq+fvPfaxiSif6/vfuPifq+4zj+ktLjRzyV844DTvklWMRfhdWqUO3WVaW2rGqibtFG6QLtfrXZsmzrsq3r1m1Zt2XLlmwZ/mHXZetSmri6DfvLJq3lR9uJ4ETgDhD52SsH1EDGjynuD+D61QIiFb/H8Xz844V7872X3/jHK+f7PgfcQMM9XjUPSfHjPntR3vZuDWjhNK8+umbx/AlVdKzTlijjesVEalX0vQIVfeznaSN/RCYpY+Otesl7QcPDkrclWRl74qVEqdx7QZfsNSrvWKEHU+dPM3NwoyDPMgP9/XI6Y1RTXa3Geo8W2WwaGBhU5ckShUdEat68eXrzjTc0NDioBGeSTldVqaXpnGJcLnV+0KnKk/9WeESkbrkl9Iq50hNvqae7+2NzkZGRE851tHfoTFWlFtls6uvrU8V772loaEjJrhSVlbytbp9PMS6XPG63mhoa/HPlJSW6JTRUrqVLrzk39ncqLzmhLl+XXEuW6Py5Jrlra7TIZtOHH36o2upq/1zpiRPq6R6Z89TVTTj35vHX1dfXp4TEJNXVnFW92z3te3n13KmKk2pvaZnWvQQABKaQKKfiJ9yEC5UzznbFO8vXff3YFdqQ8HeVV7+vLOfIesUT461XjLF8Rl/99UMf7SyPkyklY4W8R2rUni6VX4rWw+ELFJWxQl2nfOpxdsgbG6vF4SwTjIeCPMtk3LFOw8OXFGWzaeNd2frA61VLc7P2HTyovt5eNTY0aHturhwOh46/9rqSEhOUc982NTWdV7fP55/zuN3anpsrq9Wq01VVSk27TUlJif65z+/fr/7+fv9caGioPG63f+5s9VkN9Pcrr+ARdXf55HG7tWvPXl28+D/V1dYqOSVFSUmJeveddzXfatXWbTnyet9X5ckK7dq9R5Ywi6rPnFFScrJccXGqrKz0z5071yh3Ta0O5udroL9f1WfOaPny5YqOjlZlZaUiIiKUl5+v1tZWtbW2+ufKS8u0bv2dinO5dKqiYty5nu5uVZ2q1L05OXI4HHr3nXcUZbNpQ1aWvFO4l5s/ffeE93zsXjqio3X/A/f77+Xe/fs1MIV7uXX7dr1aXGz2PzEAwHjCbYqL7dfbDR0aWLvAX4aHe5pV1xGheOdC/7u9Q01e9QxLY9115ANy8dqQP8k7wiEjH6x7qb1ele01cmbdM856hSSFKDL1dq3Tczrl6dOatQvGkui/VX/Wt34vFYwW53B7rJwdDXqv7IKUtU+xISGSPVaLy4r1F1/3JK8BCvIsE+dy6cEdO6Y0u+7O9YbHGyac27T57inNbd2W84nn7n8g1//4ns/e63+cvWmz//EdV+3iTjR3NeNcVvZdE84ZMxjv0WSmOvdJ7mVZacmUXgMAcLP0qtl7QZf6b9XFCJc27duit3/6VxUte0z71o6cYnH8uSLVrtytp1YvkDS6Kne+WC8eXaKHPpcu22CTjr/wii7mFmjTpEepja1ZPKc/KU27n56kTEcuU/a2hXqm6IiW23droytcA21lKio6rbQD39aq0WY+8uG/F1VUnPzR9aKcipdHJdVp2v2FyVY45jYKMhCEbs/8lJrPn+dLQgBMW3xCotkRzBWZqnsPZKvw0Pf1pdLRc5BTc/X4d6P15j9/rEd/M3YOcp6e2LT6yuPbXGu1Yvhl/eCLz2hICcreV6DH77ntmisYI2sWFrVogtMr/OYrZdc39WTSK3rxR1/W4SFJljW679FvaG9G9EelN8Sp9KxkqSNWzrGj3CKTlLFxsUqarvUacxsFGQhC23JyZLNF6T+nT8vjdqurs1PhEREa6O83OxoAzBKRcmUd0FNZBww/C5UtNVs7v56tnZP9aqhLK3fkaeuu63zJkKXa8sNCbfnYE+N91XSkXBk79fgfJ0tikWvrd1S49VrXwtUoyECQWnfnev9qyNDQoDo7fWpsqJfH7VZLc7PaWloozQAmNPYNocBcREEG5gCLJUwul0sul+uKPem2tja1t7XK4/HIU1dHaQbgZ7VazY4AmIaCDMxhY6XZ+CHEtrY2feD1qqbmrBrr69Xc1KT5Vqv6entNTArgZkpOSTU7wizF+kKwoCADuMJYac7IzPT/bKqleWhwUGFhYTc7MoAbLDYu1uwIgKkoyHNEb28v/12GaZtqaT7w8MOy2+0mJgVwI9gdDrMjAKaiIM8BZaUlOnrkiH72i1+aHQVBZLzSDCA42Gw2syMApqIgB7HGxga98Pzf1FjvMTsKAGAWccbEmB0BMBUFOQj5fD796x9HVfLWW2ZHAQDMQgsWLDQ7AmAqCnKQOVVRoT/87rfjPleQd/Amp5l9Cg8/a3YEADAdnyXAXEdBDjIrV61UXn6+jh45oi6f74rnKH8AgGvhiDeAghx0LJYwbczK1qrVa/TysWK9duyY2ZEAALMIR7wBUojZATAzrFardu/Zqyef/onWcsoAAGCKlsbHmx0BMB3vIAc5l8ulr3ztMdWcPWt2FADALBAVxRFvAO8gzxEr0tPNjgAAmAWinU6zIwCmoyADAAA/h4MTLAAKMgAAkCQttttlsYSZHQMwHQUZAABIktJYxwMkUZABAMAoTrAARlCQAQCAJE6wAMZQkAEAgCROsADGUJABAICkkbPzAVCQAQCApOSUVLMjAAGDggwAALQsNcXsCEDAoCADAAAtWbLE7AhAwAg1OwAQKAryDpodYdoKDz9rdgQAs5wzJsbsCEDAoCADo8wumWWlJTp86NCU5wsPP6uCvIOm5wYQHByOaLMjAAGDFQtgFqMcA7hRrFar2RGAgEFBBgJcl89ndoRpa2ttNTsCgCnI3rzZ7AhAQGHFAghwv3rm58rdsdPsGNetrbVVrx4rNjsGgCmwOxxmRwACCgUZCHC+zk4dPlRodgwAQWqx3a71GzaaHQMIKBRkAABugsV2u9LS02fs+naHQzab7bp/b9XqNewfA1ehIAMBYtGiKLMjYA4I1JI2Vc6YGIWFhc/Y9fmqZQASBRkIGMtSlmltZqaqKirMjjLjklNSFRsXO2PXXxofr4iIiBm7PiUNAIIbBRkIEBZLmPIfeUTVZ6o1MNB/zfn4hMQZyxIWFia73T5j1wcAIJBRkIEAYrGEKSMz0+wYAADMaZyDDAAAABhQkAEAAAADCjIAAABgQEEGAAAADCjIAAAAgAEFGQAAADCgIAMAAAAGFGQAAADAgIIMAAAAGFCQAQAAAAMKMgAAAGBAQQYAAAAMKMgAAACAAQUZAAAAMKAgAwAAAAYUZAAAAMCAggwAAAAYUJABAAAAAwoyAAAAYEBBBgAAAAwoyAAAAIABBRkAAAAwmHf58uXL4z2Rkph0s7MAAAAAM66+6dykz09YkAEAAIC5iBULAAAAwICCDAAAABhQkAEAAAADCjIAAABg8H9SM5jY2hWNeQAAAABJRU5ErkJggg=="></p>
<p>An airboat has a fan blade of radius 1.8 m. This fan can propel air with a maximum speed relative to the boat of 20 m s<sup>−1</sup>. The density of air is 1.2 kg m<sup>−3</sup>.</p>
</div>
<div class="specification">
<p>In a test the airboat is tied to the river bank with a rope normal to the bank. The fan propels the air at its maximum speed. There is no wind.</p>
</div>
<div class="specification">
<p>The rope is untied and the airboat moves away from the bank. The variation with time <em>t</em> of the speed <em>v</em> of the airboat is shown for the motion.<br><br></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why a force acts on the airboat due to the fan blade.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that a mass of about 240 kg of air moves through the fan every second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the tension in the rope is about 5 kN.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the distance the airboat travels to reach its maximum speed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the mass of the airboat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The fan is rotating at 120 revolutions every minute. Calculate the centripetal acceleration of the tip of a fan blade.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>there is a force «by the fan» on the air / air is accelerated «to the rear» ✓</p>
<p>by Newton 3 ✓</p>
<p>there is an «equal and» opposite force on the boat ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>air gains momentum «backward» ✓</p>
<p>by conservation of momentum / force is rate of change in momentum ✓</p>
<p>boat gains momentum in the opposite direction ✓</p>
<p> </p>
<p><em>Accept a reference to Newton’s third law, e.g. N’3, or any correct statement of it for <strong>MP2</strong> in <strong>ALT 1</strong>.</em></p>
<p><em>Allow any reasonable choice of object where the force of the air is acting on, e.g., fan or blades.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><msup><mi>R</mi><mn>2</mn></msup></math> <em><strong>OR</strong></em> «mass of air through system per unit time =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>v</mi><mi>ρ</mi></math> seen ✓</p>
<p>244 «kg s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Accept use of Energy of air per second = 0.5 ρΑv<sup>3</sup> = 0.5 mv<sup>2</sup> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«force = Momentum change per sec = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>v</mi><mn>2</mn></msup><mi>ρ</mi></math> = » 244 x 20 <em><strong>OR</strong> </em>4.9 «kN» ✓</p>
<p> </p>
<p><em>Allow use of 240</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that area under the graph is distance covered ✓</p>
<p>«Distance =» 480 - 560 «m» ✓</p>
<p> </p>
<p><em>Accept graphical evidence or calculation of correct geometric areas for <strong>MP1</strong>.</em></p>
<p><em><strong>MP2</strong> is numerical value within range.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculation of acceleration as gradient at <em>t</em> = 0 «= 1 m s<sup>-2</sup>» ✓</p>
<p>use of <em>F=ma <strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4900</mn><mn>1</mn></mfrac></math> </strong></em>seen ✓</p>
<p>4900 «kg» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be shown on the graph.</em></p>
<p><em>Allow an acceleration in the range 1 – 1.1 for <strong>MP2</strong> and consistent answer for <strong>MP3</strong></em></p>
<p><em>Allow ECF from <strong>MP1</strong>.</em></p>
<p><em>Allow use of average acceleration = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>40</mn></mfrac></math></em></p>
<p><em>or assumption of constant force to obtain 11000 «kg» for <strong>[2]</strong></em></p>
<p><em>Allow use of 4800 or 5000 for <strong>MP2</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATE 1</em></strong></p>
<p>« <em>ω</em> = » 4<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> rad s<sup>−1</sup> ✓</p>
<p>« <em>a = r ω</em><sup>2</sup>= » 280 « m s<sup>−2</sup> » ✓</p>
<p> </p>
<p><em><strong>ALTERNATE 2</strong></em></p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi><mi>r</mi></mrow><mi>T</mi></mfrac></math> » = 22.6 m s<sup>−1</sup> ✓</p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>r</mi></mfrac></math>»= 280 « m s<sup>−2</sup> » ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> for wrong ω (120 gives 2.6 x 10<sup>4 </sup></em>« m s<sup>−2</sup> »<em>)</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> for wrong T (2 s gives 18 </em>« m s<sup>−2</sup> »<em>)</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority succeeded in making use of Newton's third law to explain the force on the boat. The question was quite well answered but sequencing of answers was not always ideal. There were some confusions about the air hitting the bank and bouncing off to hit the boat. A small number thought that the wind blowing the fan caused the force on the boat.</p>
<p>bi) This was generally well answered with candidates either starting from the wind turbine formula given in the data booklet or with the mass of the air being found using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi><mi>A</mi><mi>v</mi></math>.</p>
<p>1bii) Well answered by most candidates. Some creative work to end up with 240 was found in scripts.</p>
<p>1ci) Many candidates gained credit here for recognising that the resistive force eventually equalled the drag force and most were able to go on to link this to e.g. zero acceleration. Some had not read the question properly and assumed that the rope was still tied. There was one group of answers that stated something along the lines of "as there is no rope there is nothing to stop the boat so it can go at max speed.</p>
<p>1cii) A slight majority did not realise that they had to find the area under the velocity-time graph, trying equations of motion for non-linear acceleration. Those that attempted to calculate the area under the graph always succeeded in answering within the range.</p>
<p>1ciii) Use of the average gradient was common here for the acceleration. However, there also were answers that attempted to calculate the mass via a kinetic energy calculation that made all sorts of incorrect assumptions. Use of average acceleration taken from the gradient of the secant was also common.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A girl on a sledge is moving down a snow slope at a uniform speed.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The sledge, without the girl on it, now travels up a snow slope that makes an angle of 6.5˚ to the horizontal. At the start of the slope, the speed of the sledge is 4.2 m s<sup>–1</sup>. The coefficient of dynamic friction of the sledge on the snow is 0.11.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the free-body diagram for the sledge at the position shown on the snow slope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s<sup>–1</sup>. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the acceleration of the sledge is about –2 m s<sup>–2</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coefficient of static friction between the sledge and the snow is 0.14. Outline, with a calculation, the subsequent motion of the sledge. </p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>arrow vertically downwards labelled weight «of sledge and/or girl»/<em>W</em>/mg/gravitational force/<em>F</em><sub>g</sub>/<em>F</em><sub>gravitational</sub> <em><strong>AND</strong> </em>arrow perpendicular to the snow slope labelled reaction force/<em>R</em>/normal contact force/N/<em>F</em><sub>N</sub></p>
<p>friction force/<em>F</em>/<em>f</em> acting up slope «perpendicular to reaction force»</p>
<p><em>Do not allow G/g/“gravity”.</em></p>
<p><em>Do not award MP1 if a “driving force” is included.</em></p>
<p><em>Allow components of weight if correctly labelled.</em></p>
<p><em>Ignore point of application or shape of object.</em></p>
<p><em>Ignore “air resistance”.</em></p>
<p><em>Ignore any reference to “push of feet on sledge”.</em></p>
<p><em>Do not award MP2 for forces on sledge on horizontal ground</em></p>
<p><em>The arrows should contact the object</em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gravitational force/weight from the Earth «downwards»</p>
<p>reaction force from the sledge/snow/ground «upwards»</p>
<p>no vertical acceleration/remains in contact with the ground/does not move vertically as there is no resultant vertical force</p>
<p><em>Allow naming of forces as in (a)</em></p>
<p><em>Allow vertical forces are balanced/equal in magnitude/cancel out</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mention of conservation of momentum</p>
<p><em><strong>OR</strong></em></p>
<p>5.5 x 4.2 = (55 + 5.5) «v»</p>
<p>0.38 «m s<sup>–1</sup>»</p>
<p><em>Allow p=p′ or other algebraically equivalent statement</em></p>
<p><em>Award <strong>[0]</strong> for answers based on energy</em></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>same change in momentum/impulse</p>
<p>the time taken «to stop» would be greater «with the snow»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F = \frac{{\Delta p}}{{\Delta t}}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> therefore<em> F</em> is smaller «with the snow»</p>
<p><em><strong>OR</strong></em></p>
<p>force is proportional to rate of change of momentum therefore <em>F</em> is smaller «with the snow»</p>
<p><em>Allow reverse argument for ice</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«friction force down slope» = <em>μmg</em> cos(6.5) = «5.9 N»</p>
<p>«component of weight down slope» = <em>mg</em> sin(6.5) «= 6.1 N»</p>
<p>«so <em>a</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{F}{m}">
<mfrac>
<mi>F</mi>
<mi>m</mi>
</mfrac>
</math></span>» acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{5.5}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mn>5.5</mn>
</mrow>
</mfrac>
</math></span> = 2.2 «m s<sup>–2</sup>»</p>
<p><em>Ignore negative signs </em></p>
<p><em>Allow use of g = 10 m s<sup>–2</sup></em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct use of kinematics equation</p>
<p>distance = 4.4 <em><strong>or</strong> </em>4.0 «m»</p>
<p><em><strong>Alternative 2</strong></em></p>
<p>KE lost=work done against friction + GPE</p>
<p>distance = 4.4 <em><strong>or</strong> </em>4.0 «m»</p>
<p><em>Allow ECF from (e)(i)</em></p>
<p><em>Allow <strong>[1 max]</strong> for GPE missing leading to 8.2 «m»</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculates a maximum value for the frictional force = «<em>μR=</em>» 7.5 «N»</p>
<p>sledge will not move as the maximum static friction force is greater than the component of weight down the slope</p>
<p><em>Allow correct conclusion from incorrect MP1</em></p>
<p><em>Allow 7.5 > 6.1 so will not move</em></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is 19 m s<sup>−1</sup> and the ball does not rotate. Air resistance is negligible and there is no wind.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In practice, air resistance affects the ball. Outline the effect that air resistance has on the vertical acceleration of the ball. Take the direction of the acceleration due to gravity to be positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>40</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The radius of the ball is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mtext>m</mtext></math>. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Δ</mtext><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn><mo> </mo><mtext mathvariant="bold-italic">OR </mtext><mi>a</mi><mo> </mo><mo>=</mo><mfrac><mn>19</mn><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>F</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac><mo>»</mo><mn>160</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong> if 19 sin22 <strong>OR</strong> 19 cos22 used.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>horizontal speed =</mtext><mo> </mo><mn>19</mn><mo>×</mo><mi>cos</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mn>17</mn><mo>.</mo><mn>6</mn><msup><mtext> m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>time</mtext><mo>=</mo><mo>«</mo><mfrac><mtext>distance</mtext><mtext>speed</mtext></mfrac><mo>=</mo><mfrac><mn>11</mn><mrow><mn>19</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>22</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>62</mn><mo> </mo><mo>«</mo><mtext>s</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>initial vertical speed</mtext><mo>=</mo><mn>19</mn><mo>×</mo><mi>sin</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>7</mn><mo>.</mo><mn>12</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>624</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>624</mn><mn>2</mn></msup><mo>=</mo><mo>»</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>«</mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p>ball does not hit wall <em><strong>OR</strong> </em>2.5 «m» > 2.4 «m» <strong>✓</strong></p>
<p><em><br>Allow <strong>ECF</strong> from (b)(i) and from <strong>MP1</strong> </em></p>
<p><em>Allow g = 10 m s<sup>−2</sup></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>air resistance opposes «direction of» motion<br><em><strong>OR</strong></em><br>air resistance opposes velocity <strong>✓</strong></p>
<p>on the way up «vertical» acceleration is increased <em><strong>OR</strong> </em>greater than g <strong>✓</strong></p>
<p>on the way down «vertical» acceleration is decreased <em><strong>OR</strong> </em>smaller than g <strong>✓</strong></p>
<p><em><br>Allow deceleration/acceleration but meaning must be clear</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><strong>✓</strong></p>
<p><em><br>Unit must be seen for mark</em></p>
<p><em>Accept Hz</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>π</mi><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The graph shows the variation with time<em> t</em> of the horizontal force <em>F</em> exerted on a tennis ball by a racket.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" src="data:image/png;base64,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" width="457" height="356"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The tennis ball was stationary at the instant when it was hit. The mass of the tennis ball is 5.8 × 10<sup>–2</sup> kg. The area under the curve is 0.84 N s.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the speed of the ball as it leaves the racket.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the average force exerted on the ball by the racket is about 50 N.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Draw a graph to show the variation with<em> t</em> of the horizontal speed <em>v</em> of the ball while it was in contact with the racket. Numbers are <strong>not</strong> required on the axes.</span></p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">links 0.84 to Δ<em>p</em> ✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo></math>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>84</mn></mrow><mrow><mn>5</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac><mo>=</mo></math>» 14.5 «m s<sup>–1</sup>»✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of Δ<em>t = </em><span style="background-color: #ffffff;">«</span>(28 – 12) × 10<sup>–3 </sup>=<span style="background-color: #ffffff;">»</span> 16 × 10<sup>–3</sup> <span style="background-color: #ffffff;">«</span>s<span style="background-color: #ffffff;">» <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>F</mi><mo>¯</mo></mover></math> =«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>∆</mo><mi>p</mi></mrow><mrow><mo>∆</mo><mi>t</mi></mrow></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>84</mn></mrow><mrow><mn>16</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac></math> <em><strong>OR</strong></em> 53 «N» ✔</span></span></p>
<p><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">NOTE: Accept a time interval from 14 to 16 </span></span></em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">ms</span></span><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"> <br>Allow ECF from incorrect time interval</span></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>k </sub><em>= <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> × </em>5.8 × 10<sup>–2 </sup>× 14.5<sup>2 </sup>✔</p>
<p><em style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">E</em><sub style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 11.6px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">k</sub> = <em>W <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></em></p>
<p><span style="font-size: 14px;"><em><span style="text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;">s = </span></em><span style="text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;"><span style="background-color: #ffffff;">«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>W</mi><mi>F</mi></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>5</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>×</mo><mn>14</mn><mo>.</mo><msup><mn>5</mn><mn>2</mn></msup></mstyle><mn>53</mn></mfrac><mo>=</mo></math>» 0.12 « m » ✔</span></span></span></p>
<p> </p>
<p><em>Allow ECF from (a) and (b)</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><em>Award <strong>[2]</strong> max for a calculation without reference to work done, eg: average velocity × time</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" width="370" height="241"></p>
<p><span style="background-color: #ffffff;">graph must show increasing speed from an initial of zero all the time ✔<br>overall correct curvature ✔</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">An electron is placed at a distance of 0.40 m from a fixed point charge of –6.0 mC.</span></p>
<p style="text-align: center;"> </p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10<sup>8</sup> N C<sup>–1</sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the magnitude of the initial acceleration of the electron.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Describe the subsequent motion of the electron.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>×</mo><mi>q</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>37</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo> </mo><msup><mi mathvariant="normal">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> </strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><em>NOTE: <span style="background-color: #ffffff;">Ignore any negative sign.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>q</mi><mo>×</mo><mi>E</mi><mo> </mo></math><em><strong> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo>»</mo></math> </strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>5</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>19</mn></msup><mo>«</mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></strong></p>
<p><em><span style="background-color: #ffffff;">NOTE: Ignore any negative sign. <br>Award <strong>[1]</strong> for a calculation leading to </span></em><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>«</mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math></span><em><span style="background-color: #ffffff;"><br>Award <strong>[2]</strong> for bald correct answer</span></em></p>
<p> </p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">the electron moves away from the point charge/to the right «along the line joining them» ✔<br>decreasing acceleration ✔<br>increasing speed ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from MP1 if a candidate mistakenly evaluates the force as attractive so concludes that the acceleration will increase</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.</p>
</div>
<div class="specification">
<p>A mass of 0.86 kg of water remains after it has boiled for 200 s.</p>
</div>
<div class="specification">
<p>The electric heater has two identical resistors connected in parallel.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The molar mass of water is 18 g mol<sup>−1</sup>. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> assumption of the kinetic model of an ideal gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the temperature of water remains at 100 °C during this time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.</p>
<p>Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.</p>
<p style="padding-left:180px;">Specific heat capacity of pasta = 1.8 kJ kg<sup>−1</sup> K<sup>−1</sup><br>Specific heat capacity of water = 4.2 kJ kg<sup>−1</sup> K<sup>−1</sup></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that each resistor has a resistance of about 30 Ω.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power transferred by the heater when both switches are closed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>k</sub> = « <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>373</mn><mo>)</mo></math>» = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>21</mn></mrow></msup></math> «J» <strong>✓</strong></p>
<p><em>v = </em>«<em><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>×</mo><mn>373</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn></mrow></mfrac></msqrt></math></em>»<em> = </em>720 «m s<sup>−1</sup>» <strong>✓</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>particles can be considered points «without dimensions» <strong>✓</strong></p>
<p>no intermolecular forces/no forces between particles «except during collisions»<strong>✓</strong></p>
<p>the volume of a particle is negligible compared to volume of gas <strong>✓</strong></p>
<p>collisions between particles are elastic <strong>✓</strong></p>
<p>time between particle collisions are greater than time of collision <strong>✓</strong></p>
<p>no intermolecular PE/no PE between particles <strong>✓</strong></p>
<p> </p>
<p><em>Accept reference to atoms/molecules for “particle”</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>mL = P</em> t» so «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfrac><mrow><mn>1600</mn><mo>×</mo><mn>200</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow></mfrac></math>» = 2.3 x 10<sup>6</sup> «J kg<sup>-1</sup>» <strong>✓</strong></p>
<p>J kg<sup>−1 </sup><strong>✓</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«all» of the energy added is used to increase the «intermolecular» potential energy of the particles/break «intermolecular» bonds/<strong>OWTTE</strong> <strong>✓</strong></p>
<p><em>Accept reference to atoms/molecules for “particle”</em> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of mcΔT <strong>✓</strong></p>
<p>0.86 × 4200 × (100 – <em>T</em>) = 0.3 × 1800 × (<em>T</em> +10) <strong>✓</strong></p>
<p><em>T</em><sub>eq</sub> = 85.69«°C» ≅ 86«°C» <strong>✓</strong></p>
<p><em>Accept T<sub>eq</sub> in Kelvin (359 K).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>R</mi></mfrac><mo> </mo><mi>so</mi><mo> </mo><mfrac><msup><mn>220</mn><mn>2</mn></msup><mn>1600</mn></mfrac><mo> </mo><mi>so</mi><mo> </mo><mi>R</mi><mo>=</mo><mn>30</mn><mo>.</mo><mn>25</mn></math> «Ω» <strong>✓</strong></p>
<p><em>Must see either the substituted values <strong>OR</strong> a value for R to at least three s.f.</em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of parallel resistors addition so <em>R</em><sub>eq</sub> = 15 «Ω» <strong>✓</strong></p>
<p><em>P</em> = 3200 «W» <strong>✓</strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A girl rides a bicycle that is powered by an electric motor. A battery transfers energy to the electric motor. The emf of the battery is 16 V and it can deliver a charge of 43 kC when discharging completely from a full charge.</p>
<p>The maximum speed of the girl on a horizontal road is 7.0 m s<sup>–1</sup> with energy from the battery alone. The maximum distance that the girl can travel under these conditions is 20 km.</p>
</div>
<div class="specification">
<p>The bicycle and the girl have a total mass of 66 kg. The girl rides up a slope that is at an angle of 3.0° to the horizontal.</p>
<p style="text-align: center;"><img 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VHdDZOsImniRwysmUiABNyDAIWPe8wzR0kCDkVg586dSExIzNW2x7TTytA5NBQeHmWRnJxs+hralteO33/H2bNn1fuwsDDMnjsHiRcuZBNL2mmvgf0e1fNnq5QPSIAEXIoAhY9LTScHQwLOQeDTTz5BcIj54+vWjKBazZpIv3Il2xaWlJUtL9+AANx7Tyd9G6tHz57o3bcvLsTHZxM/6vi7jw96P9zLKO6XNf1gHhIgAecjQOHjfHPGHpOAUxOQlZhdf/xptW2PucHKSk29BneqLS9D42Utr4gZcVooNjxvvfmWevz6tNfxSO/eOB8Tk81GSGx+0tLSMH7cOK0KfpIACbgogRJTp06d6qJj47BIgAQckMCHCz/EmTMx8M2Kop7XLko4ilKlS6ktrJKlSkHEkGEqUbIkPL298cfOnYiLi0PHezqqrypVq2DNylWQMqVLl9aLiMPDQwcOonLlypDo7UwkQAKuSaDYrVu3brnm0DgqEiABRyOQnp6ONq1aoVqNWtmEiq19jfz3FKa8+gpKlSyJF557Hp4+Puq0lmk9YgQtW1z16tXDF0uXoGzZssqep1+fPkhJTkFAUJDu/FAMoGNjYvDr9m0Q2yAmEiAB1yPArS7Xm1OOiAQclsCuXbuUYbLp6oytHb5586YKY9GiRQvce9996uRWiWLFzBowi8FzcPnyOP7PP+jd67Ydj4iazT/9BM3Xz5XUVNUF6VdgcDBEFIlIYyIBEnA9AhQ+rjenHBEJOCyBZUuX2nSE3dJAJEBpsxZ3IzAwUGURIfPzr1vRtn07xMfG4vq1a0ZF1Wmv4GCcPXdeiR+xM5KVH83Xj4gmzdOz2PukXknTRZJRRbwhARJwegIUPk4/hRwACTgHAYmM/vPmLfkyatZGmpyUiGeGD9du1acImQ/mzcNHHy/GpeRks6s/AYGBOB8bh/s7ddaPr4uvHxFNTz79NC6cP387sntgIGLOxKBbl67Ytm0bV3+MSPOGBJybAIWPc88fe08CTkPghx9+UOEiTONs5WUAEq29cqVKZou2adMGu/buUas/sWfPQtvG0jL7+fvD28/PSPyIaHp+9PPYsvUXhJQPRvz58yhWogSiIyMxYdx4NKhbD2+/9Vau8b20NvhJAiTguARo3Oy4c8OekYBLEWjbqjVuZNxEpSpV8mXYnHblCk6dPIGraWlo0rSpsvHp0LEDZOXGNEkg0icGD8allEvKt4+hbZEcg5dwFsu+WoGGWZ6etfLvzJyJzz75FJ8tWYK6deti159/YsfOHfjpx81YvfYbfYtNy89PEiAB5yFA4eM8c8WekoDTEhCbmk4dOiIjK2xEcEgI/AMCbfbcLADi42JxM+MmKoSFqW0pOdaeevkSihUrho6dOuHhXg+jUaNGyoZHA7Zo0WK8PX06/MuVM9pqE/Ejtj1Tpk5Fo8aNEHn6NDIzMxFaoQLWfvMN2rZthxYtW6JF06ZaVRg7YTyGjxih3/OCBEjAuQhQ+DjXfLG3JOCUBL788kvM+2AePDw8lPGxodNBEUGeXl7w9vZB8RIlVB7DQcoR8xvXr+P69evKU3Pc+XMIr1Ezm2iSfJdSUnAl9TLizp/HPfd2Rs+HH4ac/BIjaBFfI4ePUNtV4tzwZkaGyp95MwPVqldHgzvvRO06d8Dbywt79+zBwYMHkZ6eliWyKuKvPXtVt/r2748Zb84w7CKvSYAEnIgAhY8TTRa7SgLOSmDY00/j7Nnz+mqLnMpKTk5CSlKS2bATOY2zePHiqFu/gRJLlvLJcXfVRlKiOvYuJ8DEGLp58+ZYunQZZr39thI+s+fORafOnfVqkpKSsGP7dvz880/45++/lRi7dCkF5cuHICoqEkkJidi4+Uez22p6JbwgARJwaAIUPg49PewcCTg/AfGHI8bBTVu0VNtRpiO6evUqrqan4/r1axD7nYyMDNMs8PLyRomSJZQQOXLwAJq1bJUtj6UHmghKT7uCmOhotRLUoEEDLJy/ANeuXsVLU6agadOmOBMdjVnvzERM9BlVVaUqldX1A9264ofvN6hnwSHl8fPWrUbbaJba5XMSIAHHJEDh45jzwl6RgMsQEAPjh7p2Q+OmzfI9JhFG0VGRuKNeRJ7q0kSQHIeXk2HNW7ZAcHCwOrpesmRJtGrTGu/PmWtU9659e9Gn1yOIioxUz5cs/xItW7Y0ysMbEiAB5yHA4+zOM1fsKQk4LQEfX1+79D0lORl+fv55rkuO0vsHBCC8eg00aX43Ll5MxE+btygD5oj6ETh65IhR3U89M0zZB02Z+qp+Em382LE4cOCAUT7ekAAJOA8Brvg4z1yxpyTglARkxWfAo/1Rs3adfPVfVmsO7tuHug0aZDOAzk/FUq/E/Ro/cQL8/f0RHh6OSpUqZdvOklNp2qpP+44d8fGnn+SnWZYlARIoIgJc8Ski8GyWBNyJgBgk5yUlJyVBTmtJSrh4AV4+3nYVPVKvrAKVCwrGWzNmQJwfij8gcWhommTVp0yZMurxHzt24MWJE+nR2RQS70nACQjk7aeREwyMXSQBEnAMArJ6knDhQp46I8feT504rsTP2eho3Lp1CwkXL0IMou2ZZPvralo6YmJiLFbboUMHXMuKASafX3+1EmtWr7aYny9IgAQckwCFj2POC3tFAi5DQFZP6kZEqOPltg5KnBRKOnn8HwwfNQrzFsxHhw7tcOVyCo4dPqS2qMShoRg9y5ZVfpKnt7fNxd+dNdvmMixAAiRQtAQofIqWP1snAbcgMHzkCLVVlZfB1qpzB66lp6NevbrqNNXLkybhxy1bVGDRd+fOQffu3RESEox9u/7E7p07EHvurC6IRBSJP5/chJGIJnGS6OnpabaLYqfUt08f3cBZyyROFXfu3Knd8pMESMAJCNC42QkmiV0kAWcnIL582rRqhSrh1fNkoyPC5UxUJNZv+B5hWatA5phIBPiEhARcvHhRbVslJyfj7em3vSxXr1Ub5YKCzBVTYTDq1KmN+QsWGL2X+qZMnoKfN2/WbY2MMgCgobMpEd6TgGMToPBx7Plh70jAZQhI2Iq5785BjVq18zQmse0pXgz4Zt1as8bH5ip9Z+Y7+Gr5coRVrmLR07PYCx36ax9+3b5NF1Ui1P773ntYtPBDc9UaPSvrWRZr1q2jN2cjKrwhAcclwK0ux50b9owEXIrAgAEDUKNmDbW6kpeByWpNSkoKpr0+zariiz5ahFUrV0JWeiQWmLkkoufU8X/w8eefKdEjgmfZ0qVodXcLq0SP1Jmelo65c+byhJc5wHxGAg5IgCs+Djgp7BIJuCoBCRTa/cEHUT6kQrYgo9aM2dDnTp8+fSwW2b17N/4z5AnUrlsvm12OVkgTPe/Pn4f27dtj69atmDb1NcTHxykxo+Wz9jMgMBCbtmxWDg+tLcN8JEAChU+AwqfwmbNFEnBrAiJ+2rdug4g7G1pcickJkCZYlny5DA0bNsyWVVZt2rVug5AKFfWgqKaZtDpE9FSsWBGTXn4Zh/YfsGjHY1hefPn4+PmiTBkPnD1zO66X9n7w0KGY8soU7ZafJEACDkiAW10OOCnsEgm4MgExTpatpdOnTubJH4+Hh4ey2Rk6ZAjE+Ng0ffD+ByhZqlSuoufV11/Dyq9WonvXbti3e4+R6ClVqhTu79oVEpdLc1oo7ci1+PBZ/c036NO3r2nT+PyTT7jllY0KH5CAYxGg8HGs+WBvSMAtCMjWkqy2iH2NrL7YmsThoI+PH0aOGGEkNOTY+bIlS1C5arjZKqWtk//8jTbt2mLqlCnYtGGDkeARQ+XqNWvg2w3fY978eZjz7ru600KpUESPiCERb/c/cD/Kmhx/l5hkOTlBNNspPiQBEihUAhQ+hYqbjZEACWgEDMWP+NqxNYlzw+ioaMgKj5ZemTIF5YKDVRgK7Zn2mZaWhr8PH1Len3/c+EM2Ox4RLa9Mnap8BEnYCrH5ke0vw2QYmV3ySDR3wyTjkK08JhIgAcclQBsfx50b9owE3ILAr7/+iv8MHoJad9S12eBZjJ2PHjqIeQtv+98ZO/oFVY8puLjY84g+fRqlSpdWjgoN38v21UM9e2DCxIm6YbJmJ5RksJU24aUX8fSwYYZF1WrT4Mcfx7EjRyHhNSQ1adYUK1etMsrHGxIgAcchQOHjOHPBnpCA2xLQTnvJ9pUWpsJaGLJ9JX54KletAi9vXyPbHnF8ePzYUaPtLK1eETx31KuLt2bOzOaDR460S9BSOaouSU5s/bZ9m0X/QSNHjFTbZpJXtr/WrFubrU6tXX6SAAkULQEKn6Llz9ZJgASyCIj4GTd2LCJPRyobHYmabm0S54Yx0VGo37CR2uYSMSTG06kWttD8/P0xbfob6NqtW7YmxGC6U4eOemwxETJijyRBSi0lsS3q1aOHLpQ63XcvPvzoI6Pshl6l4+PijN7Vi4hQ4TJy8kptVIA3JEACeSZA4ZNndCxIAiRgbwKyxSQOCrds3qxObskJLmtT5L+nkJl5S2VPvHhB2fKYlhXj5ccefxzPPf+8xdUbaV9OZ2nJnIjR3hl+GpaTdtauX4/4+Hhs+/13bNywAdGRUYbZLV4PGzEcjZs0QevWrS320WJhviABEsiVAIVProiYgQRIoLAJrFq1CtNfn4YKYZWstvsRe58Tfx8zG5BUjqc3aNQQ02fMyHELynTlRgTMDyLCcogPprGRFZ32bdroqz7iLVq22vKTxk2ciL79+uq2R/mpi2VJgARuE6Dw4XcCCZCAQxIQETKw/wC1dSXH063Z+pItrmOHDiIjI0MfU07bWnqmrIv/PDEUv/7yi/549NixGPXsKP0+pwtZrRr21NPYsW2bUbYq4VXRt9+jaNioIYKCgswKL9nmk8Cqhw8dwnfr12P3n7uM6hABNHjIYK4AGVHhDQnkjQCFT964sRQJkEAhEBAxMfyZZ7Bn124V3NRSzC3Drih7n6hIlChZItdtLcNyBw4cwGP9B+ins0Qwbdu5wyqxISLtlcmTswmWXr17Y+asdwybsepa6vtpy0+Y9fbben4RUHPee8+st2o9Ey9IgARyJUDhkysiZiABEihqAi2bNUdiUhIqVamC8iGhuXbn8IEDWPDRQrRp0ybXvFoGMWiOioxUt7I1tmDRRzkaNGvldu7ciUH9B2i3CKtUCWdjYvT7Q8eOWiWe9AIGF7J99vHixfhw/u3j+vJKVn+eGf6MQS5ekgAJ2EKADgxtocW8JEACRUJgzPhxuJmRgXNnzuDvI4dz9fYskdxl5cfaJFHcJTiplsQeKKdTXFq+hQsWGomehYsX4Ztv12mv1eea1auN7m25CQwMxPgJE7B63VrIio8kWQWSdplIgATyRoDCJ2/cWIoESKAQCTz40EPKP8+NGzeUwbD47YmPi7VLD2Q7bcYb03WjZDFoFiPo3JL4+tG2okSU/Lp9Gzp37qwMkSVYqZZmzXzHKKyG9tyWTwnG+vWaNbi/axdVjOLHFnrMSwLGBEoa3/KOBEiABGwnIOJBYlQdPXJEFT5+/DhSUlL0ipo1awYvb29UrVrVrHGvnjGHi+Dywcq3jpzeknQ+JgaJFy/ijoj62UpdvZoO8Y1jTVowf77us0fyy3F3CUeRU5LtrVcn347CLqJnybJlRie/Ro4aqR+JlzAWsuoz8LHHcqoy13ey+jNr9myVb9OGjbro4rZXruiYgQSMCNDGxwgHb0iABKwlIPYn+/btwzdr1kB+EduSxFdNm7Zt0ahRo1ztX0RUSVgIiaBumnz9/FCnnrHAkVWhowcP4ujxv02zZ7uXMTRvcpf+3BqDZjmB1b71bdshc6JHq+zd2bMxPyuOWG6en7Uy1nwKD3H0qDE3jB9mTXnmIQF3J0Dh4+7fARw/CdhIQMTCyq9W6isOpsWb3d0cNWrWNHq8Y/t2sw78RDg8P3o07rv/frMCKCfRU8ajLMIqV4bY8xim5KQk5cVZQkwEBAQYvsp2bRhqQkJYvPPubLPenA0LSkR4TXRs3PyjxdUhQ1El22dvvw4w9aYAAByySURBVPNOrnUbtpPTtdTdu1cvxVQYyjaYrAgxkQAJ5E6Awid3RsxBAiQAKDsV2bLRtng0KGJ3ct9996mtpZy2iETEyBaY+KqRk0qGnozll/fLkycrGxmtXnOiRyKoFy9eHCnJycqvT4PGTSAnsAyT2P5cv3YNdevVw0eLjMNGGOaTI+Pdu3bT43hZE1x03dq1kECokmbPnYMePXsaVpnt2nDVp2p4OH7a+n8fQdky2/hAjt8/0uN2+zzpZSM8ZndrAhQ+bj39HDwJWEdARMKwp54yEivyy/ah7g8Z2bZYV9vtXGIn8/1332HFsi/1Yo8OHIBJkyere9PtLRE9323cgAP792P82LEAiuHOxk30strFyeP/oF3HTlj39UoMfepJvDxpkvbK6PO+zp3x78lT6pms9qz9br3F1RvJJEKsW5cuioGsai3/6iuj+szdGK76SBvzPlxo1Wkxc3WZe/bOzJn6UXcxrrbGw7S5eviMBNyJAE91udNsc6wkkAcCIlC63HufLnpEnOzat1f5ksnPL9qWLVvijenT1VFtERKSRAR1uf8BPNq3r5FNj6zGiOiR9jrecw9KlCgJS84MMzMzsem7b+Ht64tPFi1G65atcPr0aaORb926FWeiovVnjw4cmKPokYw/btqkM3hu9Gi9bE4Xsv00Isvz87Vr1zBt6ms5Zbf53X+efFIvs/7b9fo1L0iABCwToPCxzIZvSMDtCciRbUPnfOKnRsSKPe1J5Kj2J599phzzCfCY6GgcOXRYsRfbGBE9n3/xhb6aUbZsWQwZ+oTFubl16xbadrwHdzZqrLw9S6iL/n376fll5Wb8mLH6FpesJMkprNzSiuXLVRYRaSLarE1DnnhCHcWX/BK0VISkvZLMg6y8SZIj7jI2JhIggZwJUPjkzIdvScBtCZge2db81BQEEBEzEosqvHo1o+q79+ypRI+8N0z33Xe/4a3R9aXkZGzeuAH/njgBT28vlAsOVl9aJrFTSkpMVLey/fTy5Em5Cjk5yaXFz7J2tUdrT4mTCePVbXpaGl6fOlV7ZZdP2W7U0vbt27VLfpIACVggQOFjAQwfk4A7ExDDWW2lJ6cj2/ZipBkyR/5rvCW1c8cOs02U8SiTa9DSGxnX1bH2IwcP4qmnn1L1iM2NoXF2WOVK6NO3r9k2DB9uNQhcKkfwbU29HnlEX/WJORMDsZmyV5LtP22r8K99++xVLeshAZclQOHjslPLgZFA3giIOHjh+edV4cIUPZqfHlmFGfnss6p9Ofk1/Y03sg2kXLlyuBgfn+254YOECxchzg7LlCkNcaAoaaZB0E9lbLzg/zGwDMuaXh87dkw9Evsm09Un07zm7qXMOINVn7dmvGkuW56fiWdrSYYxvfJcGQuSgIsToPBx8Qnm8EjAVgJyBFs7aj79zTd12xpb67Emv4gs09NbcvLphbFjdNsVMXjesmWLUXWyfRQYFKTb6Ri9zLoR+6DX3piGNevWqTHIKsv36/9vAPxQzx65GjRr9WonzzQBpT235dNw1WfHtm12XfWp36CB3hXZlmMiARKwTIDCxzIbviEBtyMgW1zaL3nxrmyLEa+tsOQX9P2d79VPb4mRsdgRacFBxeZH28KZ8cYb2Qx3mzZriqtmjHl9/PxUV9LT0iGCQPMtJKss8kyStDUhyyg4t36LONNSeDVjGyTtuTWfhqs+4l3anqs+QQZOHNPS0qzpDvOQgNsSoPBx26nnwEkgO4G3soJzyhbXqKztpuy58v9ERM+DXbrqRsbi3E87rq7VLkLh9axtLlmBkuPkhklCXqRevmz4SF2XLl1afxaZdYxdjq/v+vNP9VxWgqwxaNYqSUhI0C7h6empX+flwnDVZ8/u3bDX6oyhWwEtXlpe+scyJOAOBCh83GGWOUYSsIKArPZoJ5ckjERebFmsaEb9shfRI8E7JRn66DEtL6s1Ylcj6b25c41WfSIiInDjxnXTIkb358/HqjLiP0dOVEkqXz7EKoNmo4qybvIrfITp8JEjVG0lS5aEodG0ufb4jARIwP4EKHzsz5Q1koBTEtBWVGS1R2JnFUTSVnpE9Ihx8f1du5o9rm7YtnbqSlZ99u/fr7+qXLky4s6f1++1C3FgqKULFy6oyOjx8XHqkYS3WJhDGAutnKVPe4jB3n36qEj1EnZDM5q21B6fk4A7EZDTnWKLJ1+mdn325FDSnpWxLhIgAeckID9wtBNBffs9WiCrPaai5/EnhmDiiy/mCkwcHIqtj6xGSYgLze7IkhNFidielLU9dezYUaz5+mvdtueee+/VbX5ybdhMBtn2stSumexmH0n5NevWYtFHH+GJoUPN5uFDEnA1AmIrp20ba9uxErsvJSUFp06e1FebJfafBBeuVKkymjRpku//b+Y4UviYo8JnJOBmBOQHkJY6de6kXdrtU5whjhj2jNreUk4Dp0zGwMces7p+Oa4twkcMryWWl7by0q5jByQkJGULX1HGwwPXrl7Frp1/GLUx7Y1pRvdFdVOjRg28ZXC0vqj6wXZJwB4E5I8aMaqXL82ubvfu3arqHdu366dEtW3runXrwtvbG2KnJ4b5soVsaKdmjz7lVAeFT050+I4E3ISAREyXJNtc2ikoew1dDIufHHI7xITynZOHQJ3N775b7454J/by8kJ8XBySEpOUDY9h3C6J42WaJGzFgMcH5emvR/EZpKWLFy/anY9Wd34+DY2k60VE5KcqliUBIwKas0353pf/c6mpqfoWrXYCVH5utGrdWpXTXD7IFrUImjFjx+bp/51RJ+x8k/0nhJ0bYHUkQAKOT0CzNdF+eNmrx4aiR46Qr1z9da7CQbbdYmJioP2g1ZbDtT59vHixWgKvXbs2uj3YDR8v/hjlDI5za6tBWn75DAkNRUhIiDKstvUvS8OtrX9PndK32gzrL+rr6Oj/B1zNrwF2UY+F7RcOAe3/mbQWFRWFK6mpkMMAMTFnkJSUhE0bNqqOyDZzjZo14efnB/k/Jys1g4cMUe8MV18Lp9f2aYXCxz4cWQsJODUBWY6WJEvQ9kq7du3SV3pE9BgeV9d+6JqKG+0vSFkS137Qasvhx/85jn179uDBBx/Ut8nEbuCt6TMQXr2G3u3iJUog8+ZN/V4uMm5mYMiQIVi8eDFGjRpl9M6aG+mP9G3Hjh1629aUK6w8B/YfUE3JX962CrvC6iPbKTwCebGnqVAhFDVr1YS21T1v/vzC63Aht0ThU8jA2RwJOCIBzVOz/DVnjyQ/eIc9eTs+ltR3d8sW+HLZMmXImJO4yekvyNp1aivho61OSb2yGiPGzHJKTMSVJA8PDyOPzrK99nCvXup5YECAio6uGUirAlb8I8v30m/5K1jGZrgKZEXxAs+y8qsVqo0uXbsWeFtsoGgJaKLGWexpipaW+dYpfMxz4VMScEsCXnYSPhs3bND99MjWU7169dCseXNlyGgqbrTVHwFuuMUly+6SIiNP4/LlVOzPCsC5aeMP2Ll9B6IiI9X7kqVKITk5SRc+8lB85GRkZKhnS5Ytw4oVyzFyxAi8MGYMIrPKqcJW/tM0K9aXZP/9t9/Qo2dPK0sWfDbxv6QJV1kdY3JeApqRsLYS6gr2NI44GxQ+jjgr7BMJODmBn3/+WR+BCJv/zpmLgMBAVAyriCOHDuvvtIuq1cJx7do1xJ7L7pdHy6N9JiUm6h6f5VnGjRu4EBeHmxk3UawYUDGsErx8fJCSlAQPjzL45ptv9DAcInzykmT7SI7ZyorPiuXLHUr4rFq5Ug1JtrnyEjk+LzxYxnYCmpGwu9nT2E6q4EtQ+BQ8Y7ZAAk5DQAwc7ZEMnQhq9ZkKFu25fEadvr16Y/gsp2sJO1E+JERliY+Lh7ePD+5u2QpnY2Jw7MghlPX0hJe3DzIyMrFp4/+NNC9euKBOhOVUt6V3jw0apISPHKuX4/m2bpdZqjc/z+WXqbZ1WFD+l/LTP3coa7hiaa1/Gneyp3HE7wEKH0ecFfaJBJycwKeffYbXp76mtpWa391cjUZOXoljMrHBkRNWtqa5c+Zi04YN6N2vL/7z5JOq+KVLlzB44CA80PUhFCteDLVq10Hju+7Cjes34Ofvj08+WoikxNuxth7t3x979u7Fww8/bGvTKr8IHc2R4qSXXsL3Gzfq/oTyVKEdCn3+2Wd6LX379dWveWEfArSnsQ9HR6uFwsfRZoT9IYEiIKBt4xg6MsxvN0Y99yzOnDmjOzSTug/s32/WS6t2gkva1PzQiP8cQyNiET2SRIBovobWrl2LKuHhSvSsXLYUlapWwUM9euldf6Dbg9jw7To8OewpRNSvr3yQ5OfU03OjR2NQ/wHKpuaD99/H+AkT9LYK+0Jc+murPbPnzjFiVdh9ccb28mtPM3zECJ6gc8aJFxtAJ+03u00CJGBHAuHh4aq2fXv32q1WES3yJSEnLCVTuwcx5tRWMbRf6mK7cqdBHSKgZKtJPL4uXrQYx/8+hjbtOyjR07hJU6OmqoZXQ6OmTbFi+QqIk8aZs2YZvbf1RkSXdrRdQnyIMXFRbHnJL+1nsk7NySpUQcVWs5WPo+Q3/b6y1T+NIzrdcxS2rtCPYrdu3brlCgPhGEiABPJOQFYPtF+ku/btdajVA9lu+G79erz+6lQ1wNfemIZz586po/Gbf9wCCTx682YG+g0YpK7NUdi5Yxv+2rMb733wPjp37mwui9XPpD+9e/XST1L9un1bof7lL6Jn0MCBevsbN/+or4BZPQgnzZhXexo5rVi1alU16kqVKhX5FqWT4neZblP4uMxUciAkkHcC8su0fes2qoKFixflWxzkvSfmS06eNElt68jqxvKvvtIz1QyvhlEvjMOKZV+gcpVwdLjHcpyxE8f/wc+bN6FFq1YQe5i77rpL2RzpldlwISsKXe69T5WQFSk5Mp+fLTRrmzYVPUuWf1kkK07W9teWfHm1pxEjd1n9k6RtgdrSLvO6HwEKH/ebc46YBMwS6N+vnwoEaiouzGYuxIfyC7F5k7tUi7LaYxjctFuXbggoVw4hoRXww/pvUa/Bnah9xx2oWDFM5VeBE69cUYbOsjIkp7q2/bYVp0+dVO/l9Neo55/DsGHDbB6RbLeJvY+WClqEiNga9tRT+krPuIkT8czwZ7TmHfpTBJvMha3+acKrVVPxngo7iKVDw2Tn8k2AwiffCFkBCbgGAcPtLkfaPlm4YCFmZUUyN92Gk62P7777Dhu+34C/jx1D6uXLKF26DFKSk1C3fgNEnf4Xfv4BOH82Rp8kEUoStNTT01sZRderewfen/eB/t6WC1PxM2zEcIx69lm7b6WsW7sWY0e/oHfNkUSPtfY0YmPVp18/3ebLkhG7PkhekEABEaDwKSCwrJYEnI2AiIhuXbqoFQUx4H1j+vQiH4Lhao81fZLgitu2bcOyJUsg8atkpaDTfQ/Ay8sbpUqXUsfcZVBXrqTi3LmzOLBvL3r37YtXp76a57GarsTI1tf0N9+0yxaU1P3K5MlqJU7rYEGvLGnt5GRPYxjEUk4EipuCSpUqQ/zTWLKnke1KCW7J7SiNMD+LigCFT1GRZ7sk4IAEDFcWCusXbE4Y3pk5E3J6SpK1q1CycrV3zx4s/eILpKelIyCwHDzKeiD1cio8vTzh4VEWt25l4pE+vTFgwIA82/kY9lsE2ruzZ+vHy+WdbBmK76C27drZZCwugmP//v3479y5RoJHBMbLkybZxZYoJ3uaUydP6u2K2JQkwWsljlt+7GkofAy/Y3hdlAQofIqSPtsmAQcjYLjqIysXX69ZY9MvbXsOR2JQPdLjdkws2UKyxmeOlHnyiaFGIS20PoVWrICvVq2yi3DQ6jT9lK0vU8EieUS0tGrVCtVr1FCGuLISJUf9JTaZJC3g5O7du43Ek7yTeXh+9Girw2TkZE+zY/t2taIndbZq3Vq1LQFYJRW0Pc2ypUuVeHKkOGdq4PzH7QhQ+LjdlHPAJJAzAUPBIb+w582fn3OBAnhreHrJFgEm5bp3exDXr19Tqz0RDeojtEIFNG7cBDVr1Sy002oigJYuWaJCXOQVj7ZiJD56JNCrJEv2NPJO83sk5WrUrAlrnELmtW95KSeriZIofPJCj2XsSYDCx540WRcJuAgBQ4PiwjaklVWnoUOG6Nstq9et1Q1ircEr4sDU67M15QoijwixPbt3w9xKjrn27u/aFWXLeiAiIkKdgEpJSUFO9jRSh2Yk7Oj+aUT4iINKw1N55hjwGQkUNAEKn4ImzPpJwAkJiPgYN3asvmJRWOJHhMKM6dP1diUUg7OvEBja08jJpsuXL+Pw4dsR6s9EReNI1rWpPY2hkbArGASLIBWv3I5gNO+E/yXZZTsSYMgKO8JkVSTgKgRka2XW7NlqOJs2bFTHyQ8dOqieadsu9h6r/GI09VPj6KJHhJol/zSW7GnESLhho0a6rU9hOD6091yxPhJwZgJc8XHm2WPfSaCACZiu/Ii9zZz33rNp6ym3LkobP27a5HB+avJqT6MZCTvKdltu/AvrvYjEcWPGGHneLqy22Q4JGBKg8DGkwWsSIIFsBESYfP7Z57oTQckg2zL28Mli7hRUQR+jl/Fop6mOHjmixiuBT13JnibbJDrIAwkxcjLytIP0ht1wVwIUPu468xw3CdhIQE57vfD883rIBCkup74eGzQIderUsfrYu/zlv/WXX1Tg0d1/7tJ7YQ8/NYb2NJGnb/+C1URNTv5pXM2eRofqYBcUPg42IW7aHQofN514DpsE8kJAVkvWrF6NVydPyVZchEuDBncq772aozvNP41kFgGyccMGI+Ekz+X49XOjR+fq6djUnkbKymkpSZbsaeSd1hfGe1KoivQfET6Hjh3Vj+cXaWfYuNsSoPBx26nnwEkg7wQ0u5wVy5frx85trU1bLWrZsmU2/zRy7PnYsWOqypz809CexlbqRZuf3puLlj9bv02AwoffCSRAAvkiICsx4qtGVnT27d1rUQiJM8HKlSvD28cXGRk3IOJJToxJEhFkGO9JnjmLf5p8wXOzwhQ+bjbhDjpcHmd30Ilht0jA0QkY2tNIX2vXrq26LF6DzdnTmAtiWRReoR2dK/tHAiRQsAQofAqWL2snAackYKs9jRbEsk3btvRP45QzXjidFvEbFRXFCO2Fg5utWCDArS4LYPiYBFyVgKl/mpzsaYSBaRBL+qdxgu+M1BP4edFMjH5vC9IAeHYeg7kTB+OeWr45dj4zdje+/OANTF168Ha+ugMxZUQv3N+tCUKL336UGbsT8yaPwXtbgHvGvIvXR7XU3+VYOQDG68qNEN8XBgGu+BQGZbZBAoVAwJx/mvPnYxETc8ZsvCctiKV4EhafPJImTZ7MEzeFMFcF2kRmNNaNfxIflXsBqw9/iFreqTixdjZG3/sEDq75GKOb+JtvPjMa618bh+XlhmHlH6vQJBSI3f0JXhn8Ak76rMa0DkEALuK3Dz5CwmOrcXyxJ/bPGY95v9XKeme+Wj4lAUcjQOHjaDPC/pCAGQKG9jTW+KfR7GkkInmnzp1UjbSnMQPW5R5l4tJvH2PKrx3w3z+6o5a3LNP4olb3Aej7aS/MXrMfQ5t0gLl1n8xTP+OzjZXRd3MvNAktrciENhuC8RO24ZEthzG+Qwf4XjqMn76vgk4TQiE112xcERu1dy7HkgNyVQIUPq46sxyX0xDQ7GkMfd7k5J+G9jROM7VF0NHi8O3wGg4etbXpTKSePY1TnjVQNeS26LldQ2mEhNcAZv6CfRPaoYNvfXTq9jm27otFuw6eOPnXOXTpXN+skDLXA/GptO3338294jMSKDQCFD6FhpoNuSMBzZ7m4sWLiI+Lg7X2NH369oU43BszdqzVHpHdkS/HbAWBzFjs+WAWZp+4D9MWtLIgUq4jLvIU0lDDfIVppxAVdx3wDUK7UU/j0ORHUHtIlo1PO9kCsy4FBQWp0CDW5WYuEigYAhQ+BcOVtbo4AUN7GjmlciU1FbSncfFJd7rhXcWJz55El6nbAYQqQ+S7s7awsg8lFWdPngEsCR+DAsVDW+LZxTvxrMEzXpKAMxGg8HGm2WJfC4WAZk8jjZkGsczJPw3taQpletiI1QQ8UGvIUpwcAmTG/oTXn3gS9x2bjh/m9UTFrBNaVlfFjCTgQgQofFxoMjmU3AlYY08jtUj0cUm0p8mdKXM4PoHioR0xZmJvrBnyNTafegCDa3mYdNobYTUrmzzjLQm4JgEKH9ecV7cclTX2NFXCq6JV69aKj+afhvY0bvnt4qaDPoOTZ1OBbMLnthGzpyUq2YyeLWXM+bn4gJKAskwkUJQEKHyKkj7btoqAtfY0EuVbwiXQP41VWJnJJQlk2fXMrIHFf7yKDr4me1qeHdCpSaCZkReHd1g11EjbkmXErK0IZRk91+qMMHU03kxRGx4FBgYiOjLKhhLMSgL2J0DPzfZnyhptIGCtPY1pEEsvb29UrVpVtVSrVi0bWmRWEnBxAqm7MbfPOBztNx/vDomANzQbn9dxzuBZNgri+HBkP0y5MRKr5g5AHe+MLAeGyxEyX3NgmK2UzQ9qhlfDycjTNpdjARKwFwEKH3uRZD3ZCOTVnkZ8fcixVznOHRYWlq1ePiABEsiZQGbsPqxfvgBTskJWQEJPTByMRzrUUkII0E58nUH/zzRRk4nUE79h9edzME0LWeHZGaNmDMej3f8fsiLnlnN/S+GTOyPmKFgCFD4Fy9dla9dETU7+aczZ04RXq6YEDeM9uey3BgdGAjkSoPDJEQ9fFgIBCp9CgOxsTWhGwjn5pzG1p5Ex1ouIUEOtVKkS4z0526SzvyRQSAQofAoJNJuxSIDCxyIa13thaCSck38a2tO43txzRCTgKAQofBxlJty3HzzV5SJzrxkJ5xTvSYZK/zQuMuEcBgk4KQHZApefV3LCi4kEioIAhU9RULexzbza09A/jY2gmZ0ESKDACYgfrYSEBAqfAifNBiwRoPCxRKaQnufFnsbb2xuDhwxRPZw0eTLtaQpprtgMCZAACZCA8xOg8CmgOcyrPY1hvKdZs2dT1BTQ/LBaEiABEiAB9yRA4ZOHec+vPY00Sad7eQDPIiRAAiRAAiSQTwIUPiYA82tPM3zECDrdM2HKWxIgARIgARJwFAJuJXzya08zZuxYGuQ5yncu+0ECJEACJEACeSDgEsInJ3uapKQkbNqwUaEx9U9De5o8fMewCAmQAAmQAAk4MQGHFz452dOcOnkSu//cpfBb8k8jL+fNn+/EU8SukwAJkAAJkAAJ2ItAkXpu1lZqzMV72rF9O6Ijo4zGaSpuDCN0G2XkDQmQAAmQgEMSmDtnLh7u9TCqVq3qkP1jpxyLQEEEqy5S4SOGxAu4GuNY32XsDQmQAAkUIIHU1FR4eHigZEmH33AoQAqs2loCdevWxcDHHrM2u1X5ilT4WNVDZiIBEiABEiABEiABOxEobqd6WA0JkAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODwBCh+HnyJ2kARIgARIgARIwF4EKHzsRZL1kAAJkAAJkAAJODyB/wHexVTzQjheHQAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>The bicycle has a meter that displays the current and the terminal potential difference (pd) for the battery when the motor is running. The diagram shows the meter readings at one instant. The emf of the cell is 16 V.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The battery is made from an arrangement of 10 identical cells as shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the time taken for the battery to discharge is about 3 × 10<sup>3</sup> s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the average power output of the battery is about 240 W.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the component of weight for the bicycle and girl acting down the slope.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).</p>
<p>Calculate the maximum speed of the bicycle and the girl up the slope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On another journey up the slope, the girl carries an additional mass. Explain whether carrying this mass will change the maximum distance that the bicycle can travel along the slope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the internal resistance of the battery.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the emf of <strong>one</strong> cell.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the internal resistance of <strong>one</strong> cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>time taken <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.0 \times {{10}^4}}}{7}">
<mfrac>
<mrow>
<mn>2.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
<mn>7</mn>
</mfrac>
</math></span></span>«= 2860 s» = 2900«s» ✔</p>
<p><em>Must see at least two s.f.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of E = qV <em><strong>OR</strong></em> energy = 4.3 × 10<sup>3</sup> × 16 «= 6.88 × 10<sup>5</sup> J» ✔</p>
<p>power = 241 «W» ✔</p>
<p><em>Accept 229 W − 241 W depending on the exact value of t used from ai.</em></p>
<p><em>Must see at least three s.f</em>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of power = force × speed <em><strong>OR</strong></em> <em>force × distance</em> = <em>power × time</em> ✔</p>
<p>«34N» ✔</p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p><em>Accept 34 N – 36 N.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>66 g sin(3°) = 34 «N» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total force 34 + 34 = 68 «N» ✔<br>3.5 «ms<sup>-1</sup>»✔</p>
<p><em>If you suspect that the incorrect reference in this question caused confusion for a particular candidate, please refer the response to the PE.</em></p>
<p><em>Look for ECF from aiii and bi.</em></p>
<p><em>Accept 3.4 − 3.5 «ms<sup>-1</sup>».</em></p>
<p><em>Award <strong>[0]</strong> for solutions involving use of KE.</em></p>
<p><em>Award <strong>[0]</strong> for v = 7 ms<sup>-1</sup>.</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«maximum» distance will decrease <em><strong>OWTTE</strong></em> ✔</p>
<p>because opposing/resistive force has increased<br><em><strong>OR</strong></em><br>because more energy is transferred to GPE<br><em><strong>OR</strong></em><br>because velocity has decreased<br><em><strong>OR</strong></em><br>increased mass means more work required «to move up the hill» ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>V dropped across battery <em><strong>OR</strong></em> R<sub>circuit</sub> = 1.85 Ω ✔</p>
<p>so internal resistance = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4.0}{6.5}">
<mfrac>
<mn>4.0</mn>
<mn>6.5</mn>
</mfrac>
</math></span> = 0.62«Ω» ✔</p>
<p><em>For MP1 allow use of internal resistance equations that leads to 16V − 12V (=4V).</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{16}{5}">
<mfrac>
<mn>16</mn>
<mn>5</mn>
</mfrac>
</math></span> = 3.2 «V» ✔</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em>:</p>
<p>2.5<em>r</em> = 0.62 ✔</p>
<p><em>r</em> = 0.25 «Ω» ✔</p>
<p><em><strong>ALTERNATIVE 2</strong></em>:</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{0.62}{5}">
<mfrac>
<mn>0.62</mn>
<mn>5</mn>
</mfrac>
</math></span> = 0.124 «Ω» ✔</p>
<p><em>r</em> = 2(0.124)= 0.248 «Ω» ✔</p>
<p><em>Allow ECF from (d) and/or e(i)</em>.</p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well answered. Candidates should be reminded on questions where a given value is being calculated that they should include an unrounded answer. This whole question set was a blend of electricity and mechanics concepts, and it was clear that some candidates struggled with applying the correct concepts in the various sub-questions.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. They either simply calculated the weight, used the cosine rather than the sine function, or failed to multiply by the acceleration due to gravity. Candidates need to be able to apply free-body diagram skills in a variety of “real world” situations.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was well answered in general, with the vast majority of candidates specifying that the maximum distance would decrease. This is an “explain” command term, so the examiners were looking for a detailed reason why the distance would decrease for the second marking point. Unfortunately, some candidates simply wrote that because the mass increased so did the weight without making it clear why this would change the maximum distance.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The air in a kitchen has pressure 1.0 × 10<sup>5</sup> Pa and temperature 22°C. A refrigerator of internal volume 0.36 m<sup>3</sup> is installed in the kitchen.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The refrigerator door is closed. The air in the refrigerator is cooled to 5.0°C and the number of air molecules in the refrigerator stays the same.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">With the door open the air in the refrigerator is initially at the same temperature and pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Determine the pressure of the air inside the refrigerator.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The door of the refrigerator has an area of 0.72 m<sup>2</sup>. Show that the minimum force needed to open the refrigerator door is about 4 kN.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Comment on the magnitude of the force in (b)(ii).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mi>V</mi></mrow><mrow><mi>k</mi><mi>T</mi></mrow></mfrac></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>36</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>295</mn></mrow></mfrac></math> ✔</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup></math> ✔</p>
<p><em>NOTE: Allow <strong>[1 max]</strong> for substitution with T in Celsius.</em><br><em>Allow <strong>[1 max]</strong> for a final answer of n = 14.7 or 15</em><br><em>Award <strong>[2]</strong> for bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>p</mi><mi>T</mi></mfrac></math> = constant <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac></math> <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>N</mi><mi>k</mi><mi>T</mi></mrow><mi>V</mi></mfrac></math> ✔<br><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></math>« Pa »✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from (a) <br>Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>A</mi><mo>×</mo><mo>∆</mo><mi>p</mi></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>72</mn><mo>×</mo><mfenced><mrow><mn>1</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>94</mn></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo> </mo></math><em><strong>OR </strong></em>4.3 × 10<sup>3</sup> « N »✔</p>
<p><em>NOTE: <span style="background-color: #ffffff;">Allow ECF from (b)(i)<br>Allow ECF from MP1</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">force is «very» large ✔</span></p>
<p><span style="background-color: #ffffff;">there must be a mechanism that makes this force smaller<br><em><strong>OR</strong></em><br>assumption used to calculate the force/pressure is unrealistic ✔</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<br><hr><br><div class="specification">
<p>An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.44.22.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/01"></p>
<p>The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.</p>
</div>
<div class="specification">
<p>At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.</p>
</div>
<div class="specification">
<p>For the rope and block, describe the energy changes that take place</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At position B the rope starts to extend. Calculate the speed of the block at position B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude of the average resultant force acting on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the magnitude of the average force exerted by the rope on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between B and C.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of conservation of energy</p>
<p><strong><em>OR</em></strong></p>
<p><em>v</em><sup>2</sup> = <em>u</em><sup>2</sup> + 2<em>as</em></p>
<p> </p>
<p><em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 60.0 \times 9.81} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>60.0</mn>
<mo>×</mo>
<mn>9.81</mn>
</msqrt>
</math></span><strong>»</strong> = 34.3 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of impulse <em>F</em><sub>ave</sub> × Δ<em>t</em> = Δ<em>p</em></p>
<p><strong><em>OR</em></strong></p>
<p>use of <em>F</em> = <em>ma</em> with average acceleration</p>
<p><strong><em>OR</em></strong></p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{80.0 \times 34.3}}{{0.759}}">
<mfrac>
<mrow>
<mn>80.0</mn>
<mo>×</mo>
<mn>34.3</mn>
</mrow>
<mrow>
<mn>0.759</mn>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<p>3620<strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (a).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>upwards</p>
<p>clearly longer than weight</p>
<p> </p>
<p><em>For second marking point allow ECF from (b)(i) providing line is upwards.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3620 + 80.0 × 9.81</p>
<p>4400 <strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (b)(i).</em></p>
<p><strong><em>[</em></strong><strong><em>2 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential energy (of block) into kinetic energy (of block)</p>
<p> </p>
<p><em>Must</em><em> see names of energy (gravitational potential energy and kinetic energy) – Allow for reasonable variations of terminology (eg energy of motion for KE).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential and kinetic energy of block into elastic potential energy of rope</p>
<p> </p>
<p><em>See note for 1(c)(i) for naming convention.</em></p>
<p><em>Must see either the block or the rope (or both) mentioned in connection with the appropriate energies.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>k can be determined using EPE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kx</em><sup>2</sup></p>
<p>correct statement or equation showing</p>
<p>GPE at A = EPE at C</p>
<p><strong><em>OR</em></strong></p>
<p>(GPE + KE) at B = EPE at C</p>
<p> </p>
<p><em>Candidate must clearly indicate the energy associated with either position A or B for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A small metal pendulum bob of mass 75 g is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible. The bob is then displaced to the left.</p>
<p>At time <em>t</em> = 0 the bob is moving horizontally to the right at 0.8 m s<sup>–1</sup>. It collides with a small stationary object also of mass 75 g. Both objects then move together with motion that is simple harmonic.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the combined masses immediately after the collision.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the collision is inelastic.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the changes in gravitational potential energy of the oscillating system from <em>t</em> = 0 as it oscillates through one cycle of its motion.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0.40 «m s<sup>−1</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial energy 24 mJ and final energy 12 mJ ✔</p>
<p>energy is lost/unequal /change in energy is 12 mJ ✔</p>
<p>inelastic collisions occur when energy is lost ✔<br><br></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>maximum GPE at extremes, minimum in centre ✔</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This straightforward question had surprisingly poorly answers. Candidate answers tended to be overly vague, such as “as the bob went higher the GPE increased and as it fell the GPE decreased.” Candidates needed to specify when GPE would be at maximum and minimum values. Some candidates mistakenly assumed that at t=0 the pendulum bob was at maximum height despite being told otherwise in the question stem.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.</p>
<p style="text-align: center;"><img 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"></p>
<p>The mass of ions ejected each second is 6.6 × 10<sup>–6 </sup>kg and the speed of each ion is 5.2 × 10<sup>4</sup> m s<sup>–1</sup>. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.</p>
</div>
<div class="specification">
<p>An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.</p>
</div>
<div class="specification">
<p>In practice, the ions leave the spacecraft at a range of angles as shown.</p>
<p style="text-align: center;"><img 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W+6w9qay+2OVrNMTldOG3G5W9VlclY13z4aF4eI/TAwIrVyGWJZITIOnQaChqGfvJHKjqvYvWI90sQhYAXK8j/DnKkHEPDhePR0ewxufr0R7PIj9iZlq5ZFPsKNE9uxdGEqytUkGkE+YBxCW/8Tq9ZkKMspfsXRpBTktZuMyGHeaNJzPKJ6HUfk4u2qIWLq6y+xYlE8MGMGhno1AsStfUehVVIM1mb+Kv4xVNzIxq49F+AtlVG3KZ3IjNRRKq/56YqWnq1UF/5AWdl/NX/kc70ElA/Vcq9O8JECWcVyqviSaqegjCmjt9EaLqpGA8p1nVl6CD8DTy/J8WwEef9h6H9lH1JO3hVlKn7Nwt7k5nhrSGe4QWWbi9xA7EwmDucq69WgkJ6fJR2VI3Rab7mijreRduhc5XSOrgQtO3R/5O/6CGgx1leAr1mKgPLB8m7wAmQ//R6yaDj5p8NY9nQ2pvcbh1gaHlMf2fhgxWE8MXanOORccDwazx6Yj5lbTinfHMtOYev0Jcj2/BCnxSHpfGTNb4y9Ycu03k7U4vjEMAGZN8Zs3oqJzb7G0A6qOIAOYfi62TgkLHkVz6r/D+qIkSO8cXnF3+HpIUfnwUfgs34HVoY8rxyuc+uBaUmL4PfDdAS0pTiCXlic1QyjEtdgpEtl8zL3PlgcvxkjK+KU5dr2w6qKEdgbPwl+FMwoex7Bq3YgLuAXLOnmrWwr+Gs0m7QV22Z0VQUqNoB74FxsSx6BihX98IJHG7zQLQ4VozZrlKlsU31mpI7q8uoTlXPzaBWC2r6EMfuK+S1NzcbAieIOruRpvPFWKSbFslT5oRYXXCD31AxeranqI9wsKdZwWquWL88rwU0FIHs2AMOHQPVAVq3K8XoNAzs3qaxkVOxMbXWUxKvydIj5RlR5R9oOQNSZSpdbKsmf9SPAqxvqx8+Ete/i5M4tON5rPr6VhgLhji7TlyPu1lCEL0vFwJQ30UJs8XmMnP8Ogr2UC6mUw4hPICnzPK7P6Ar59fM4crEVQvzlGg+NRfhajJA3ocpOIkrm7ofgWVsQPEufwdJ6wifg6T8EY8NGYaa+YuJQ5yhEpY9ClM7vgReGaF2RuXdFaHQaQqO1Lld+cfVCYFi0+K/you4ZDa3qbw9QrXSoIt9wHU0dlbE0YVoNknOzNP08lmpd5S8GCciaobVvcyDPUAnpTfm6oQJmuN4ALTzkcKkmSsbF1wMtRMe4Kfz6BgJTM5A7pwWupFyA7+BIyNVOMwCKnUkJg5fmNU2tNWbaNC8bd+6PyINbMZZGzvQe1TlgeivwRQMEDHWfgeJ82WwESs/hcPJtyF9pp5wrVDekGsrVmadW/yyeaJeRPdMevdr9iDWJ3+Bk5jdVMvpp1+VvTIAJGEOgsLAQuv/u3q3rsLnyIas3voRiWdAKni1djVHLhGWkKadifH/+lvZoUNl1FBVCY2RCVRaZ+Ff8PqSe8UGIf2tVkFs1tmnEztRN8ep0PIHYID8MTsjX1r1uDXEtFQF2EmzkVlDcLMG56kbKtILkalDatStmfpGKuC6/I23FXIT366STSriG+vyzFoEHDx4gLTVV6xp/cS4C165dQ1C//ggdOQqTJ05U/+sVEKC1FJXSbR87dswIODK4dRmO2T104kvEWJZ9aGUwdsQI0fUp4uaH0HmdkbUwChtO3FA+bGkVxrsLsLs1xcV4VUa7u3XG4AnN8cW67cjr1Bc91PE5MrgZEztTVz3demDKh910dMxH2kfR+BjjtHWsqQ0xRqGhslR5GdRxmDXVc6Lf2Umwkc6WtfBAB4256SpqVQkCqlJC+wINSYe8haj08yj66Rj2xgbi5spxGPrRUcNBPdoS+JuKQPL+/Thx4oQBHlKyo6Rqhj4NVOXLdkOgZcuW6NW7N+7cvo0rl0vU/x6Ua+986de1Czp37mycXRSRH6sTXzLzEvw3pmLPLCm+xDhRpivlBu+wFdi/0R+3FvcR41k8OyxEUcBypH8xTRkXo26sCTr/4zX4wh39x/1Ne6rBqNgZtaBanjTAsyHLdHRUxgmpY3eMlSgG+Q7FIzFPwmTsL9bJ/WCsHEcupy9XM1+zDIEKrRz4yvz36hz9ahU08+JL+wRo5s2ngg+EgvjRgrzdYiHjnqEM5JpylMJTU1KE8vJydUt8UpXA6dOnhd69egl37typ+iNfcSoCBQUFQod2PoKc9unQ86+zb0e+T5zqjnAOY3kkwWY8wKboMmYCuh1ZgaUfH1Mtk6PEJpGYntQcby8JMRwApGODcmllMCJT81Xr5GmZXBYOn4KWx3/9+g0MDArioXQdftJXmm+eNWMGYtatQ9OmTaXL/OmkBLy8vOD5gpde6xs2bIi9+/fxfaKXDl+0ZwLsJNhM7yk36lmbthz+tz5SLZPrjneLXkHcwXjM9NNYWlSDzjKvUdiUPA7NvgpDZ3GJkBydxWVyMVg8SLUkD8DkKZOxecsWcSh95IgRRs6l1tC4A/0cGRGB8eHh6NSpkwNZxabUhQAFLEYsWoTrv/6KBg1Vc9gqQY8//jiWRr0PciL4YAKORuB/aMDE0Yxie2pPgIKt4mJjIff0xNiwMKf/g7crKQk5OTnYsHFj7WFyDYchQP9fJO3ciYsXLmDGzJno//e/4x9Br+JKSeV64pGhoxEVXWU9qcMwYEOcmwA7Cc7d/1Wspyj+dbGxGD7iDQwfMdwph0/prXHShAnYl5zslPZXuSmc7AKtZsnOzsa2LVtEy6fPnInu3burKWRmZuKdqVNBQYsUqJi4YwcaN26s/p1PmIAjEWAnwZF600S20B/JxIRErF6xAmtiY8S3J2f5I0i2U5wGxSHwNIOJbig7EUN9f+Bf/xKd5B7+/nh9+HCD90BXv5fw3//+F1+lfwNa+cAHE3BUAuwkOGrPmsAuCtxbu2YNcrKz8cHy5VpvUyYQb5MiaN75uedaifEaNqkgK2VyAnSf792zV3SK58yfjz59+9Q43fbDDz/gqaeeqrGcyZVlgUzAwgTYSbAwcHtsjobfF0dEiKq/Hx3tsH8YaarlwIEDWL1mDQ8f2+ONWkud6b5OTUlB+jffOPX0Wi2xcXEnI8BOgpN1eH3MpSCuRQsWgIZi350926Hm66U4hJ27dvHwcX1uEjuoS/fx1199JY6QScGIzjKdZgfdwyraGAF2EmysQ2xdHWnedvbMWaCh2bFhY+3+rVuKQ3CWKRVbv8fMoR/18enTp8UVPCRfNxjRHG2yTCbgCATYSXCEXrSCDdI87t49n4tLw4JDQqyghWmaXLVypSho7rx5phHIUmyGgOTU0oqdmoIRbUZpVoQJ2BABdhJsqDPsURUapk9MSEBxUZFdvp0dOnRIXOq2PSHB7kdE7PH+MZfOkhNLK3SMDUY0ly4slwnYMwF2Euy592xId3tMxkQ7+/XyD8CR7CyOQ7Che6k+qnAwYn3ocV0mUJUAOwlVmfCVehCwl2RMNAz9VlgYxk+YgL59+9bDYq5qCwQ4GNEWeoF1cEQC7CQ4Yq9a2SZ6ANcnGRP9wR8zcpSVreDmzUWgqOSySUTTfVZdZkSTNMJCmICTE2AnwclvAHOaX5dkTOQg0DJLc2Y8lNr4Oj2d4xDMeQPoke3p0Qb1dRLovvr30aNGZUbUowJfYgJMoBYE2EmoBSwuWjcCNE9sTDIm2lRp29atMGeuAopDGDN6tLj7Je/aV7f+rE+t+jgJHIxYH/JclwnUjQA7CXXjxrXqQEB6g9eXjOmTTZ/gSGYGVq9da9YgQnJEXF1dYc9LNuuA3q6rSCtoKD04bd0d9OqrDpXIy647h5V3eALsJDh8F9uWgdK6dSkZ04g3RmDrli0oKSnhdMi21VVW14acStqm+e6dO3hj5Ein2mjM6vBZASagIsBOAt8KViFAQ8f0Vv/Jho3o+JfO2B4fz/EBVukJyzZa03SD5ER+vns3mjZrhtAxY5xiYzHL9gK3xgSMJ/CY8UW5JBMwHQF6GFy6dAlvjB6Nhw//EJcjcqpc0/G1N0lSvAFl8KTpKEfeSMze+ob1dW4C7CQ4d/9bxXopeJDml0eHhoo60NByXGysuPHO2LAwh91p0irAbbhRKfnR5o2bxMyI+5KTOd7AhvuLVXM+Ajzd4Hx9blWLz5w5g1kzZsDQZkr2kozJqhDtuHFpukGKN7h44YK490f/v/+dp5vsuF9ZdcclwE6C4/atzVlGDwZKkrRz92fVzjPTVER9kjHZnOGskEiAphTSv/lGXObazseH4w34vmACdkCAnQQ76CRHUJE2UvowOrpWORDoobJ2zRrQ0jdDIw+OwMbRbaDRoy/27hX7cfiIN/DaoNfMuszV0XmyfUzAkgTYSbAkbSdti3IgUEBaXZMkGZuMyUnx2qTZ5OBRVkRapUAH7ZHh7+8P33Y+9c64aJMGs1JMwEEJyBzULjbLBgjQtAE5CHl5Z0EpkFu2bFknrSgz4u49e8StqCdNmICIRYtADyE66C21f9++oLlu+qSgSD7qRoCcsfoe1B+rVq7Ey34voaCgQFylQH1Hm2g1bty4vuK5PhNgAhYmwCMJFgbuLM2RgzBn9mzR3NVr1pjsAUFyD/zrXzhw4ACioqPRJ7A37peWqrE+2aQJso7lmKw9tWAHPsnMzMSs6TPw2GOP4be7d7E1IR6BgYFGWUz9Qc7AsZxj4mgRxRoMHjIEfn5+elcpSIGLRgnnQkyACVidADsJVu8Cx1OA3vIjIyLg69sRk6dMNpuB9OYb1K+/lvyGDRsi9at/8hJKLSqGv1Bf0Vu/5tHYpTGOZGVpPeRphKa8vFz8V3L5sugY5J46hRPf/4A3Ro9CYO/eaNeuXY2jRewkaJLmcyZg+wQ4T4Lt95FdaSjlQKAANXM6CBIUcgoePnwofUWDhg3h4uKi/s4n1RO4c+cOyCl4UP5AXZDOdR2Hrq+8DLmnp1ima9euCPjrXxEyeHCtnbH67gCpVpJPmAATsAgBdhIsgtk5GpEchIUREeIctLmtpliF9h19kXvipLqpl7u9UuPbrLown4gOlaJCoUWisYsLktNSa+0AaAnhL0yACTgEAXYSHKIbrW+EsTkQTK1p4o4d+Pbbb3Ho4CH07dcXAwYMMHUTDi2PgknfHBeGpB078aC8HI8//jhChtR+hMBYSDzdYCwpLscEbIMAxyTYRj/YtRbkICxasACbt2zht0877UlalUCxBk+3aFFtoqv6msdOgn6CNArXtGlTDrjVj4evWpEAOwlWhO8ITdc3B4IjMGAbjCfAToJ+Vi936YK7t+8geMhg9OnTB926d9cKHNVfi68yAfMT4OkG8zN22BakHAi8KY/DdjEbZiECtBLoSEYG0pJTxH/UrF/XLggODhZXjtQ1x4iF1OdmHJgAOwkO3LnmMs1cORDMpS/LZQK2TqB9h/aik6CpJwXk0j9awdOy1XMYFByC8eHjeUpCExKfm50AZ1w0O2LHakByEDw8PGDKJEmORan21lC+AtoBk+I7iLGjHrwEUn/PduzUSf8PgLjE96eiYsRv2+bQ94ZBAPyDVQnwSIJV8dtX4xRcNefdd9ErsLdFciDYF526a0sZD8PDxokC6K2RlnXSqg1OY1x3pvZQk5zBX375BRfOnxedQ5lMBoVCezkq2UH3RGCfPli9ZjXfE/bQsQ6mIwcuOliHmsscKQfCjJkzERwSYq5mnFIu7TlBb4qax6qYtRg8eLDmJYc4d9bARRop+vnnn8UVJCdOnBB3xLxackXMVilmqnzuObWjqNvRcRs+xqsDB+pe5u9MwCIEeCTBIpjtuxH6w/68R2vertlM3ajrIFAzN2/cNFNrLNbcBPQ5BNRmD39/MXX1wH/8A1OmTq2S9Ouppk3FvTMk/dp6yhGfmFilnPQ7fzIBSxBgJ8ESlB2gjZh169CpmnlTBzDRaibQw0DTUaDh5eefb2U1fbhh4wnQCNvVq1fxU3ExLl68iM93fSY61OQQUPrq14cPx7uzZxu1nJHiEmiFAyW0Chv/FqbPmMHTC8Z3BZc0E3FdfTgAACAASURBVAF2EswE1tHEsoNgvh6lt8WQ1wahYaOGuPf77wgZMoSHl82Hu86SaUOx27dvazkEtKeF30sv4YUXXqiVQ6BPCVrhQJtmxcStM3oXTn1y+BoTMCUBjkkwJU0HleWs88iW7k56CNHmVLwm3tLktduTAgqvXLmCosIi5OWdxb++SYemQ+DTvj2ee+45k77pU7v0jzIv8sEEbIUAOwm20hM2rAc7CTbcOaxavQhQ/ADthEkrDAoKCsQ3edr++u+vBolbnXt6eaJ169acbrxelLmyPRNgJ8Gee89CurOTYCHQTtCMNe8lih+g6QLao0LfCoO2cjmaN2/ODoET3IdsovEE2EkwnpXTlrTmH3anhe6ghlvqXqKpG5ouuHnjht6AQo82bdCqVSse2nfQ+4zNMh0BdhJMx9JhJVnqD7vDAmTD1ARMfS/pTheUlJSI8QM0XUBZQSmg0BzxA2qD+IQJODgBdhIcvINNYZ6p/7CbQieWYZ8E6nMv6a4uyMnOhmZCIp4usM97grW2bQLsJNh2/9iEdvX5w24TBrASdkXA0OiA5uoCni6wqy5lZe2YADsJdtx5llKdnQRLkXaudjSXGuqLHaB0xS3c3Xl1gXPdFmytjRFwKCeBdtDz9vbmYCQT32TsJJgYqJOJ03QGJodPEPcr0JwqeO65VnjmGXcxdqBZs2b8/6+T3R9srm0TcIiMi7SLXtTSZbhSUoL0gwf4j4xt33OsnYUJ0NK/FR99hGPZOejTry/emT7d5AmbpCkCWmJ46+ZNMefAvXv3xDTFZO4bo0eBnAE6KFWxvr0LLIyFm2MCTMAIAnY9kiA5B79eu4b/+7//E80lJ8HLy8sI07mIsQR4JMFYUrZXjt7iA7r3ENM9S9q19vDA4cwM6Wu1n9IoABUqLy8XcwzQOSUeIieguKgIlHyINgCj/QqefPJJcUXBn11dxWkC3ayEfC9Vi5t/ZAI2R8AuRxL0OQc2R5YVYgI2QOD06dNaDgKpdOP6dXyy6RM88YSrmENAV01pKkC6TqMA0kGbFtER8Ne/iomHOI20RIY/mYBjErArJ4GdA8e8Cdkq8xKgXSUfPnxYpRFXV1eMDQurct3YXQurVDTiQlHJZSNKcREmwARshYDdTDfQvGov/wBb4WYRPWzlDyoPEVuku83SCE0X9PQPwG9376rl+3Xtgr1ffKH+zidMgAkwAUME7MZJIAMoOGrDxxuw9/PdeFD+QK9NHJOgF0u9LrKTUC98Vq9M/99s+fRTnP7xNDr/pTOmz5hh0t0La2Mg30u1oVXbsn+gMCEcQSvl2Hp8CQLdZLUVwOXVBBQozVyGgLBizD64FWO9YKdsFSgrPIytSXcxcMkIeNXhlrArJ0Hqv+qcBXYSJEqm++Q/7KZj6eyS+F5y9jvAXuzXdRIa2YviOnreRmbEUITnjUN6SlidnIQ6+BU6OljhK+23Hrk4EkeysjD2rbfQ2KWxFbTgJpkAE2ACTIAJODYBu3QSpC7RdRak6/zp2AQoPmX2u+/izTFj8OnmzaB5dz6YABOg6YZQePosQWapQoWjFIWZCYgMag8axfH0CEZkQiYKy6Tf6U2zFzyDP0Hmic8qy/lMQOzhQpSpoerKaY+BEQnILCxVl6h6QkPdmUiMCFa13QaeQRFIzJTkarT9/SeY6EP6Kcsk5d6AUkN6o1+CjqT39tWqMr0QmXlbbE5x4wSS1PL166S4kYu0mAnoKNqvjwEAxQ3kpsaodegYvg4HfvxVwyQdtqWZiPRpj8HbD+PkzggMVMnuGL4e32kxIQYHERveXWkbcU3eLnLuGJEJw/R02enaJnGpZKFUVsVUvAduKUcRkq4CZ5YhqK1uWQ3zqjm1aydBsktyFn7IPQVal82H4xKgqaZBA/+BtOQU5Pw7CyuXf4SZM2bYrcFkz66kJPEfnfPBBExHoBT5CfMxdGo2nn7/MApKLqPg+Ht4OmsBgl7fgFy1owDgzHqsSnPBm1/koagkH1kbPXBw/HvYmvs7PUFRlpuImVO/h2fsMVBAddFPBzH3TykIn5OMQsnf0FW87BS2Tl+CbM8PcZrqkNz5jbE3bBn2F/5RWfrMCkzfAkz8Lh9FJWeQPulP2D1kGuLEtqViZ5GW447ZPxSj4Hg8xnVpCsWvqXj7b9Nx9On3kPUTyT+GtZ7fY3rwEqT9+khZsewE4sbNwtd/egsHxDLEYDr+tOddzNxySuUE/Y7cddMwfPPvGJh2BkUlxciZ3wZnDuSgXGpe72c58t6PQ9oTY7BHZJKNuJaHMHF6opqt4tcvMS94MS4EbFUy+GEmnvpmC3ZfrE6yAmX5n+Hd4AXIlmz76TCWPZ2N6f3GIVaLi17FVBebIzB6P7aGPg90WoL0n44gKrB5dRX0/uYQToJkGTkLjRvz1IPEwxE/c3Nzq6z7z8nKAo0u2NtBuxr2CeyNJRGR4r+X/V4CXXPkw1ZW7DgyY7VtpblIWnkaAR9GYlpXd9Afe5l7d7yzdjlGXvkEUfsKVW/rAFyGYe68QfBypVIN4O7nDz+XSzhy9iYUeITrZ79Hvtcr6OHlphQvexaBy9JQlGZ4nltx/TyOXGwFf385XMVaDeAeuAhflyRhrJfGHL9LCKLefwtd3BsAcINXyDuYG3ob25NPa7xpP4/g0AHwdpVB5t4WbV3v4ujGGBzwmoS5b3eHu/gkc4N3WBTihuQicmMOSqFA6cmvsP1KIEaFvaIqQwz8MXqED/Izz+M6OTilp5Gy5TZGzn8HwaJ9Mrh6DcLc+cPgooap/8QldBbmhngr7ZO5w693Z7hc/B5518lJuS3qmNVrPpa+2V5ZxrU9xhL/agXfxcmdW3Cc6km2ydzRZfpyxIXexsfLUg07ZvrVrNdVu8qTUC9LubJDEPjfssoBUMmgRo3s0zFcHxeH+6XaA44fREdjUUSEZJpRnxfOn6+2nE/79gZ/5+ykBtHY+Q8KlOZmIK1cjtntnxYdBLVBrs/A0wtIK7qOMjRTX9Y60SrjhWc6vgLvpfHY8aUX+qACLfsGqBwKrVpaX2TPtEevdquwJvEbtO/bCGUtAxAoORmaJb06wUd0EKSLrmjp2QrlKzOQOy8AftJlzc/SczicfBUuQzzQQutVV7NuTwQGLsPZCzR0n4W072ikToHfTyYiKuks0Kmv+F3JqRVmt1S6MspmZHBt2QZyFGu2WsO5VCcTRdfKgBak423I57VTOyiiAJFtNV6CaJueelDahuTLuFamQIsatDHVz+wkmIoky7EIgb/27Ikn3Ny0Hq5e3i+YfC8CSxjzn1v/qdLM+bxzSExIqHK9ugu0WyIlRtJ3lJWVGZT322+/4V/fpKur/f3VIDz11FPq1MpPt2ghZlXUTa2srlCHE17dUAdodaryCDdLiqsdLi/PK8FNRQcjpMvg6jcNew52wuHsdKxaugv5VKvdaETOH4uhgV6qkQIdUa5dMfOLVHQ+9G+krVijGmLviJFLZ+HNYT3hpf+WrRRSXowrNx/pdxJUpcqTxsEvqbKK+sxFrjwtO4/EmeGIOlQK79DZmNilKZr0jcJez5UYvpIetn8ANXBSy7TQieJmCc5VNxthBBdTqspOgilpsiyzE6Appb379+GjD5eLewnQW/KcuXPM3q45Guj6clec+P57LdEjR48CZTy0xiFNdVy5cgU0YpP173+L+zN8vusz9d4MlJaZmJvScbCGrY7fZgO08JDDpZo3YRdf5Vu4cRN1NATfE8H0LywaFAz4z92bEBkWjqKE/Ybnul29EBhC/95CFAUHfrkbnywch6FF8ciKrsFBcZGjdYsGgEEFXeC7NBn7w7y1R0rUnUvBhssRldMNa3JWIPhZms6gg4L7fgZAjkTNnFSVLPYha+GBDi7AOUMt1sjFUMW6XWcnoW7cuJYVCdAQ+bb47VbUwDRN006I+fn5OHzgoCiwT/9+4u6IppFeeynS1IP0KUmI/uADMebj6tWr+Km4GLExMeIIBO3pENi7N2gko2XLllJx/rQJAjK4+fVGsMsBfH/+FsZ4PV/5IC27jqJCQD74Gf0jAEboL3P3Q/D40Ti5ZRrOldyBAs0r5RuqT3P2IWMw6mQqvtMcxShUDp97qZM/leFa0c9wGRIOP/U1HaFuHdBnSHOkfX8RN970xrPqKYffkRszHsMzX0N6yj9EOfDqqz2doSjHvTuqwEZInFRTBOpYCQXKrl2uxsXS0UffV0lHcVrHG6poDkDkXw746qtEYRmGbFNyIXtauj6mmg7JNCDEdJfVaE0nsj6SpCUxCcrADEU+EoPbo/qlIvVpT7OuaqnKkj3qoBBFYQIGe9Rt2YimZJOel+UjTb3kJxSJmlHCJm2IhZmbAAXZbv70U+RdvABamUPnthp4S05A9+7dMTo0FBs2bhR1pi2fiwqLMGb0aIwcMQKHDh0Ss6KamxvLN5KAmx9C53VG1sIobDihWlJIw+/vLsDu1pMROcyr5ge72JRq+V/QEqSpl/eVovC7DOSiP8L6t9ErR/n3MxiRqfmqVQTK2IDDp4D+4/4GufT0Kd+HVSu/VC3LpBUZkZie7IeoqT0qH6xVTG6OnlNnIeDICiz9+BhuiCssSlGYGoPIdcDbS0LgJWsKv76BcDmTgl1Hf1UGaSpu4OTHUYhMv1Ep0a0Hpnzoh7SpkUjMpxgh0vNLrFqxr9rpmkoBhs5UOibHYJXEgP5+r4zB7uqmE9AUXcZMQDcd20QuSc1VtgEyeXeEdLqNtKRvkS+uVCH712MVLXlUH6o4BvH7Hygr+6/6F2NPpG4ytrxly8m8MTbtPM5GB1Zzs5hKpbs4mRiNj09XrrmXeYUhpaRuy0ZMpZW2nD9QuC8Ks5PbYk0OLRfSiRLWLszf7IQAOQY0jWJPB+ncqVMnTJ4yGd9lZuK9hQtFh4FWaNAOk9LUha5NvLpBl4g5v1O0/wrs3+iPW4v74AVay99hIYoCliP9i2nwE1cyGNN+I3i9uRp7JzXB18GdVDkPOmHoV00wMWk+XlMP42vLknmNwqbkcWj2VRg6i3kE5Ogc/DWaTYrB4kEaIxvtBmO432WselkOT49OeD3LB7FpyzSmB7TlSt9kzw7CyrTl8L/1EQLaUv4DlU7JGzDdrwmt5YBbzylIiPLFiTB/lf2RyHpuNLbHjtZYudAAz4Ysw/71PsgeTPbJ0Xn6j/CbNM7gy76kQ02fSh3frmTw8mpc7jUWb3eqJnARMrh6j8JaLdu6492iVxB3MB4zRdvIPC8MXR2Lt7ABAzsQuzHYcb8P5i7211CrEeQDxiH00SoEtX0JY/YVV65o0ShV3amNpWWmkYT6pZCsztjqf7Nm29VrVvkrefSWz83OwWaVPcBn1ROgXA//PnoU62Jj0cPfX9xlUnf6onoJ/KvzELCHv7lm6A0aIR/8Nopm7TYcy2GGZusq0qojCdqZsLpjYsxXOH1DmiuiUR/N6QYpw1TdM2+JWbX0ZsdS3aw6mamqTjfQMJRmBjFDWbBCEZ95VCMTGNl2UCPLmYHuKitEZkJl9i6t7GQii5cQtDQbKN+B8I5yC03DGNCVLzMBPQRoRCQ4JARfp6eDghwnTZggjixIWTHJ4eSDCTgHAXqu9ELH8CTVdAA902i6YzXWPBqEwV3sY/TQek6CmAkrHJ/eGYj954pRVPIvzG1zGQcPacwV6b2T6ph5S3EVadMGY/hnf8LEg5RV6wy+CLiAmWJ2LjcjMlPVJgtWNj5YcRhPjN0pZicrOB6NZw/M18jwpccwcanOm5ie9RyWHaephHxkvf8csqeGYETMCZSJUy+nkL7UH3B5E1vPFltoGkapK2UF5IMJGEuApiPIWdiXnCxWGRgUJMYsGFufyzEB+yfQHD3fjkFU+yN4XZwOaAPPtoPxacVAJMRPqsV0j5VJCFY5KoR7GYsF33aLhYx7FRoa/EfIWNRTkA+KFwrocsUlIWGQj+C7KEO4J6jqtO4pRGT8x3Ad9S9KWcq6glBREC+E6Na9lyFEtPMRQuIvCRWCTtvUvFYdlbzJKcI1TZW16tVWR0lZicdMIfXaQ+kiaaDk1Hq0kFDwQBCEB0JB/GhBXoWbRhUznP7yyy/CG8OHC5s2bjKDdBbpDAQKCgqEqVOmCPLWHgKd88EEmIB9ELDSSMJd5B7KRLlXG7TUCp7RjMQ00nuSMm+p1vxW1lJl3krOQG5pOYqzDyEPreCpmVXLLRBRF84jxeA620ppkLJgvaKTPUvKgqVaxqNRQ+NUZZfBMhIP3cxjUgavn5UZvDQkWvKUItu3JyQgL+8sVq1cyRsqWRK+g7RFcQm0KoIOmoKgkSlpCsJBTGQzmIBDErCOk6C4gyt5yl28TEVVzLyl3uWLIl3bKefvTdSAsVmw6tRcjTxuq9Yi10m6SSrR8PHqNWvE5DpzZs/mP/Amoep8Qmh1A01BXLx4ETQFcebMGeeDwBYzATsiYB0nQdYMrX1rvxuVYa6UeetbcZczcYcycccx2hXsMoouLEOgoYQchgVW+UXKglXlB+mClAVL+l6bzxp5NEcHj2Z61yLXppn6liVHgRLr+Pp2BDkK9ripUn0ZcP36E6DgRrqPYtatw6wZM3h0qv5IWQITMBsB6zgJUCW5qDL8rsooVRtzVdmpiinzltaWpZR5ayg8gykxUyPI/fvCFzrD9qrVE8oyNTRqsB0pC5bu1EkN8rR+lnicwQXN1R2U1EPM+qUzTaJV1/JfaG18jx49xCQ67ChYnr89t6i5uoHyLNAqiCeecBNHFY4dO2bPprHuTMAhCVjJSaAkF+MR1esApr/7WTXZooxhbkzmLcpO1R8zxjbB7hWbkSk+iB/hxtF92HvmRVUGK814CH2ZqYzLgmWMxlXLyODWZThm9ziOyMXbcVLUT7maYs7UfWg1YwaGqtOFVq1tjSuUee+D5ctFR4GHjK3RA3VrkzZ16uLnp0qI0waj3hhZN0EmqkWjU+R0bt6yBXGxsYhYtIizNpqILYthAqYgYCUngbJFPY/gVTsQq14e0h0zT3pj4oxutbar5sxb1N6zCFyyGXtHPcCqbt7w9PBGwIoHGKnOzlVTZiojs2DVWntVBdpnPHYH4gJ+wRJRPzk6z7wE/42p2DOra51zrNdVHWPqUZpechSGBoeA3wKNIWb9MoODg/H73d/Uivxw/DgWLlig/m6tEwpspOBY2gdi2JAhvFzSWh3B7TIBHQI2lnFRRzv+ahcEaMqB8vcvjIhA3760RzsftkpAc7hf0rFBgwYY8vow8QFNW07/2dUVrVu3NstOj8Zk76SUzosjIiD39MSiiAib3c9C4sefTMCRCbCT4Mi9a0HbJEdh+Ig3xOFjCzbNTdWCgLfcExUVFVo12nrKsWHTJlw4f168XlBQYHCLaEulWKblkcn792Pb1q1igCPFL/DBBJiA5Qmwk2B55g7bIv1hp1UPtPphbNhYfgO0wZ5OSEhA9NJlWprt2b8PL730ktY16QvtxfDzzz/jXF4ecnJyxC2iJ02dgoC//hWdO3c2ex9TvAutgAh69VW8/c47Zm9Psps/mQATUBJgJ4HvBJMSkBwFEkp5FSgwjQ/bIkBbOu/9/HM0bNgIs96dhbZyudEKktOQm5uLFMp1cOECaOTotUGvgRJumeuge+rj9euR/s03PKpgLsgslwkYIMBOggEwfLl+BGi7YMrQGBUdbXfbINfPcuepTQ4DPbhpSsDYHR+NiUkwRFAaVRgfHo4hQ4eyA2oIFF9nAiYkYL3VDSY0gkXZHgFa1kbTDhSpzrkUbK9/TKERJUWipbCaOz6acwkjxSVI2RrfCgvj+8oUncgymEANBNhJqAEQ/1x3AuQoSLkU2FGoO0dbr0lTSprbQ7/s9xLSUlPNoraUrXH8hAno5R9gtnbMojwLZQJ2SICnG+yw0+xNZcqhMGbkKOzc/RkotwIfjk2ApiHWrlkDSty0cNEirXiF+kw36FIjx/PDDz7AU089hXdnz+ZpLV1A/J0JmIAAjySYACKLqJ4AOQbpBw9g0YIFnHSpelQO8av0tt+/f38xf4Zmoi3aT8VUBwVL0s6SUgImzXZM1QbLYQLOTuBPS5cuXersEGplf1k+0t4fj3+8tRBxsSfx5MAA/Pl0AtZnP4menZrjf2olzESFywrx3YatyG7eBR2bPQbQnhQhvfDm+fYY/TcPNDRRM/UR06xZM/Tt1w9vT52KBw/+QJeuXeojjuvaAYEXX3xRDGikJYxNmjQBfTfH0bFjR3U7t27dgp+fHx5//HFzNMUymYDTEeCRhFp1+R8o3BeF2cltsSYnH0UlSRjb4gJ2vLMRZ7Tz09RKav0KK1B6Mgkz1+VBrYLMG2PTzuNsdCDc6ifcpLXpzY8Cz2jVA61+4MPxCVDypZ27duHz3bvFPteX8dEUFKgdCqCkg4MaTUGUZTABJQF2Eup0J7jhSdfH6lTT2SvRUDTlTyBHYZo4qvDA2ZGI9lMugJSUFPFB6mjD5uQc0r4M1OfmPCiAcu68eaCgRkoTbq7gSXPawLKZgM0REKo97gkFGfFCxAAfQd7aQ5C39hFeXRQvZBTcU9a6lyFEtPMRQrYdEr5fFy74qsvsEk5df6gh+aFw/VSKEDO+m0qOhyAfsEhIyCgQ7muUEgQqt6uyvXbhQswh7TIV138Qdi4apF8fSVbFdeHUjkXCq6I+HoLv+DjhsI7Ory76WK2P76IMgSyquH5KSF0r2UH2DhIi4jOEgvsVglBxSUgYJHGg3zwE37AJwrh2ynORT7vFQsa9CkmLyk+J09r9wgG1fGJJnP4jFByKEyao5PiO3ySc0GKn2wcaOgkVwr2MxSruKp3IFpWukl2iIvcLhIz4SiZV+Es6bjsknDDErtKiep+Vl5cLmzZuEqZOmSLQuTMfZP/rw4ap/9940dNLWB+33uGQ3LlzR7Tx4MGDZrftl19+Ee+tRQsXCtQuH0yACdSNAAxXqxDun4oTXm03WUi4pHIKKq4JGYsHCfJB8UIBPQvFBws9nLoJE9blCNfp2v1LQio9xAfECafo4SpIcsKFuB+uC8pH6EPheka08GrrIULMqd9UKjwUrqXMFHzpwZxySbhP9S7tFCa06yZMSbki1qu4liJMaafRlnBPuBQ/WfBtN1NIvaZySiquCKmTuwnyAYuFVNEx0Ckj6SzZVXFTKCi+Jwj3fxBiBvSstEN0Gg4JSwb8RXh17Q8qZ+aBUBA/WpBrOgPSwzX+kso2PUSlNtW2kUNCssnp0LDn/jkhYXw3wXdyinBNBCXpXsmu4nqOEEfOlgZfpaMwWkgoeKBsXNdJkOSqHZCHwvUfNgkT2vlU2qZHR0Hqb3Vbemyr5yVyFN4YPlygP+rOetBDU+mEazicrT0c0nkiO3v36iXk5OSYvbvJ+UrauVNs7/Tp02ZvjxtgAo5IoJrphke4fvZ75Hu9gh5eqplt2m55WRqK0sLgpVHTJWg+lr7dHe50zdUbwfNmYeSVfUg5eRfAXZxM3oefh4zG2K7uUFZrAPeewzC802UcOXsTChpfUVzGwfgDQOgszA3xhitoa+YBGDWkAQ7Ef4dixW0c3RiDA16TMFdqC27wDotC3JBcRG7MQSmJKf4OCekNMHL+OwgW9XaD95ARCMYBJBy4rGwLgMuQERjs7QbInoZXW1eUnvwK268EYlTYK0o7aHdpd3+MHuGD/MzzuC4qWb+BIBe1bSS7EwJfag500rDHVY4eAXKUH/kRBWUKoDQXSStPI+DDSExTsZO5d8c7a5dj5JVPELWvUG2PYc0oZmEv1uR0Q9T7b6GLewMADeDedSJWbxyGn9etw/7CP9TVNXWEzB1+vTvD5eL3yLv+SF3GlCeUS+GNkSPF4WFnzaXwv2VlVZA+1bQpaCmhox20umHzli3iklhz9zdNP1Cyp5h168T9H3YlJTkaTraHCZidgMajXretBnim4yvwPhOPHV9mIzP1KArpwVXlcIH8lXbqB6v4s+sz8PS6jbRD51CK5giMPoKz0X64mflPcZ4wLXU7IgcOQdSZh2ppiuJjSD0DyD2fgav6qrKu6JSUncPh5Ktw8fVACy2tXdHSsxXKkzOQW1qO4uxDyEMreLaslAK3QERdOI+UMG+Vk6JuQHUig1vgMpy9sARdbmapdExGYsQIBC3N1i1soe8KlOZmIK1cjlfaP62tt8gXKC66jqqPF1317iL3UCbKvTrBR3QQpN9lcG3ZBnL8jKJrhqQYU0aSV/dPSsQjJV1ytPl4Y6j4tG+Phg2116C4ublp5RcwRo69lBGDGXd/ZjHHUMrUSBtUURyMuZ0Te+kH1pMJGENA63GrXUEGV79p2HMwCl1+T8eqmWMR1EEOz6AIJGYWGvFwAsrzSnBToUBZfhIm+nRCUNhWnPydHI3/hz6x2xHZydgHXaVm5Unj4OfRBhQlrfzXzjQP8rLzSAz3R+d+U/CpOAIiQ5O+Udi71B8ovIxreh2kSr1qPnPRcYBqqvEIN0uKUV5NMSXfagrQT4o7uJJ3u5pCt3Gu5I4RIxLViDDBT5RLgd74nDGXAj00N2z+BE+4KUfsaOvmHbsc861XWt1A/U17MFAyJAraNPdBAbOUU0Ff7gZzt83ymYA9E6ghRF8GV6+eCKZ/YdFQ3MjFP3dvQmRYOIoS9iPKr3rTxbd+FGL/vOU43isGRzeE4FnJLSnNRGRhOeBbvQztX13guzQZ+w2OCPyBQu0KRn6jpY3LEZXTDWtyViD4WRqSp+M2MiN+BmD8Lnmqiib4aIAWHnK4oNigrKqjKnqKypqhtW9zIE/Pb+Kl5ujg0QwyXDdUwGLX6Y2PlstRZPqMmTPFVL8Wa9zKDQUGBuLHs2esrIVlm6epgPv3y8TtxekBbomDRq1o5GbShAniDpa8pbklqHMb9kygBidB2zSZux+Cx4/GyS3TlG+fopNQrhr29q5ck192HUWFzRE8qwPcys6hqBCQD9aeklCU/Y47GuJlOr7w8QAADORJREFU8u4I6QSsEYfQJVl/oDAhHEFLgciDH6HPkOZI+/4ibrzpXels4HfkxozH8MzXkJ4SBrl/X/giXjmE7tVI2QIlFxo8BFGYi/RED41WpdMyXCv6GfDqqz0kryjHvTvmmYuXWjb8KYObX28EuxzA9+dvYYzX85VTDiJfYqqcmjE0WaCU3RR+fQPhknwGF248gpfaAVKg7NplFKMVQjSnZgwrZJFfaLkcOQqUl3/2zFkWaZMbsR4BekjPmT1bXPpJ8SmWOKScCh9ER4tt66aOtoQO3AYTsBcC1TgJqgf0HjnWxM1WBQGWovC7DOSiPyb2b6N++yxPisGqLs9gPgUc0rD9uwuQ1ms+vu3ZHJB1EB/uu/fsw9EBcxHo3gCKG8ewYfEKHCgHXCRSsjb4+6xR2BsWg7V9X8DiwGeBG9nYtecCvGdsxlCv5+AydRYC+q7A0o9b4H0xeLEUhakxiFwHvJ0cogymlPfHjLEpCF+xGX1epPaAG0f3Ye+ZF1VlTkstanyqHqRJKdh1tL/YtkxxAyc/jkJk+g0NJTWqSKdifEBDnKPv5WUoa+QKV2m0RCpT1083P4TO64zXF0ZhQ8soZfCiiu/u1pOxd5gXZBTgKcYW0IiDAuVl5WikhkoNy+DWZThm9whH5OLtaBlNwYuPoSz/M8yZug+tZiRgKDlTFPVpIwc5CqZM32sjZrEaeghQcCHlzaAESJ5enujbt6+eUqa/RO1Gf/CBGH9EI1cUE8P7ipieM0u0fwLVPM4awevN1dg7qQm+Du6kmv/vhKFfNcHEpPl4Tf1G6gLv0GD4XV6NHhQn0CEc2e3fx/5Vg1Rv+83R8+3VWPrSDwjv5i3K6RxxHM+Frsaa0Oc1CDaAe+BcbEsegYoV/fCCRxu80C0OFaM2Y9uMrmIwo+zZQViZthz+tz5CQFuKSVDpk7wB0/2aKGXRCowlm7F31AOsEtvzRsCKBxipWUajVVUluPWcgoQoX5wI8xfb9uwQiaznRmN77OhKR6ZKPXoGk3MzFI+WDsALPpOxv7hypYC+4rW7Rqs3VmD/Rn/cWtxHpddCFAUsR/oX0+Cn8kZkomN0H1H92qPj6L0o1o0vdW2PsbE7EBfwC5aITOToPPMS/DemYs8sJdva6cWlmYDpCIiOwtq1+DA62uJ7e9D0A622oFgYygJqifgI05FjSUzA/ATqtwskxRV0m4Zz86qLEzC/EdwCE2AC9k/gzJkz4lJFmm6i0SRLHuQc0PSDvp0rLakHt8UEbI1ANSMJtqYq68MEmIAjE6DA1YUREWLgqqXf6KXpB1794Mh3GNtWFwLsJNSFGtdhAkzALAQoJmH4iDfEgEJLOwpkEE8/mKVbWagdE6jfdIMdG86qMwEmYLsEIhYtwnPPtYKlVjzokuDpB10i/N1ZCfBIgrP2PNvNBGyYwKKICHHXSGvt5MjTDzZ8c7BqFiXAIwkWxc2NMQEmYCwBSp9sC8sTCwsL1cmXrDWyYSwzLscETE2AnQRTE2V5TIAJmIwAPaCD+vXHkewsi6940DSCph8o6RMdUdHRoDTPfDABZyDA0w3O0MtsIxOwUwKam0FZc1dMmn6g1NE9evTAsCFDQMs19R2fbt7MG0jpA8PX7JbAn5YuXbrUbrVnxZkAE3B4Aq1atcKDB3/g8893429/+xsef/xxq9ncsWNHdP7LX8R8Dk2aNMGLL76o1iUzMxPz58zF5cuXERwSrL7OJ0zAngnwdIM99x7rzgSciACteHjyyScxd948q1tN8RK0g+VTTz0FCrKkUQ7ab4QOcmK+/OZr0CgIH0zA3gmwk2DvPcj6MwEnISDFBdCQP+0gae2D9ElMSMR3hw/jP/+5hZ+vXFWr1Kt3b2yL367+zidMwF4JcEyCvfYc680EnIwAxQXQjo3btm61+B4P+lCTPrTagT41HQQqezwnBxR0yQcTsHcC7CTYew+y/kzAiQjQng60IdOYkaNsIkDwm6+/Ru6pU1V64OHDh4iNia1ynS8wAXsjwE6CvfUY68sEnJyArax4oLiE6dPexoPycr09cjQzg0cT9JLhi/ZEgJ0Ee+ot1pUJMAGRQPfu3cU9HiIjIqy2vfO4sWOr7Y0H5Q94NKFaQvyjPRDgwEV76CXWkQkwAb0EVq1cKV63xooHGkm4ePEijuUcQ2FhAXL+nYWnmjbFb3fvaumafvAAr3TQIsJf7IkAOwn21FusKxNgAloEbG3FAzkOV69exaWLF3H8+HHknjyFee/Nx+vDh2vpzV+YgL0QYCfBXnqK9WQCTEAvAcpRQFkQP1i+HDQNwQcTYAKmI8BOgulYsiQmwASsRIDe4CmZkbX3eLCS+dwsEzAbAQ5cNBtaFswEmIClCNDSyJ27PxN3jbTmHg+WspfbYQKWIsAjCZYize0wASZgdgK7kpKQk5OD1WvWiEmOzN4gN8AEHJwAjyQ4eAezeUzAmQhQumYPDw98vH69M5nNtjIBsxFgJ8FsaFkwE2AC1iDw9jvvoKSkBDSqwAcTYAL1I8DTDfXjx7WZABOwQQK84sEGO4VVsksC7CTYZbex0kyACdREgFc81ESIf2cCNRPg6YaaGXEJJsAE7JAAr3iww05jlW2OAI8k2FyXsEJMgAmYkgCveDAlTZblbAR4JMHZepztZQJORoBXPDhZh7O5JiXAToJJcbIwJsAEbJEAr3iwxV5hneyBAE832EMvsY5MgAnUmwCveKg3QhbghATYSXDCTmeTmYCzEuAVD87a82x3XQnwdENdyXE9JsAE7I4Ar3iwuy5jha1MgEcSrNwB3DwTYAKWJ8ArHizPnFu0TwI8kmCf/cZaMwEmUA8CvOKhHvC4qlMRYCfBqbqbjWUCTEAiwCseJBL8yQQME+DpBsNs+BcmwAQcnACveHDwDmbz6k2AnYR6I2QBTIAJ2DMBXvFgz73HupubAE83mJswy2cCTMCmCWiueCCHgQ8mwAQqCfBIQiULPmMCTMCJCfCKByfufDbdIAEeSTCIhn9gAkzAmQhIKx4+iI52JrPZViZQLQF2EqrFwz8yASbgTARoxcNvv/2GTzZ94kxms61MwCABnm4wiIZ/YAJMwBkJPHjwAAODgvDB8uXo3r27MyJgm5mAmgCPJKhR8AkTYAJMAGjcuDF27tqFRQsW4MyZM4yECTg1AXYSnLr72XgmwAT0EaAVDzSSMGvGDPCKB32E+JqzEODpBmfpabaTCTCBWhM4dOgQtm3Zgu0JCeIIQ60FcAUmYOcEeCTBzjuQ1WcCTMB8BPr27Ytegb0xZ/ZsUKwCH0zA2Qiwk+BsPc72MgEmUCsCk6dMFssnJiTWqh4XZgKOQICdBEfoRbaBCTABsxJYvWYN8vLOghIu8cEEnIkAOwnO1NtsKxNgAnUiQCseFi5ahG1bt+LYsWN1ksGVmIA9EuDARXvsNdaZCTABqxCQNoNKP3gAXl5eVtGBG2UCliTAIwmWpM1tMQEmYNcEpM2gJk2YoLU0koIaIyMiMPz11+3aPlaeCegS4JEEXSL8nQkwASZQAwGacqBkS5R0qWnTphj75pvIPXFSrPVD7inxWg0i+GcmYBcE2Emwi25iJZkAE7A1AhTEuO+LL3DvXimulpSI6jV2aYxPt23jdM621lmsT50J8HRDndFxRSbABJyZwMuvvIKCS/lqB4FYPCh/gKNHjjgzFrbdwQiwk+BgHcrmMAEmYH4CmZmZCOrXHw8fPqzS2OFDh6pc4wtMwF4JsJNgrz3HejMBJmAVAjTNMG2SMsGSPgV+KirG3bt39f3E15iA3RFgJ8HuuowVZgJMwJoEXP78ZzRq3BgNGzY0qEZ+fr7B3/gHJmBPBNhJsKfeYl2ZABOwOoHBgwfj1OkfsTUhHr1699brLBw6yFMOVu8oVsAkBHh1g0kwshAmwASclQAlWErauROff7Yb90tLRQytPTxwODPDWZGw3Q5EgJ0EB+pMNoUJMAHrEaCEShnffYfYmBhQXELexQu8vbT1uoNbNhEBdhJMBJLFMAEmwAQkAoWFhZy2WYLBn3ZNgJ0Eu+4+Vp4JMAEmwASYgPkIcOCi+diyZCbABJgAE2ACdk2AnQS77j5WngkwASbABJiA+Qiwk2A+tiyZCTABJsAEmIBdE2Anwa67j5VnAkyACTABJmA+AuwkmI8tS2YCTIAJMAEmYNcE2Emw6+5j5ZkAE2ACTIAJmI8AOwnmY8uSmQATYAJMgAnYNQF2Euy6+1h5JsAEmAATYALmI8BOgvnYsmQmwASYABNgAnZNgJ0Eu+4+Vp4JMAEmwASYgPkIsJNgPrYsmQkwASbABJiAXRNgJ8Guu4+VZwJMgAkwASZgPgLsJJiPLUtmAkyACTABJmDXBNhJsOvuY+WZABNgAkyACZiPADsJ5mPLkpkAE2ACTIAJ2DWB/w+LTNezwEce6wAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the initial acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the maximum speed of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why scientists sometimes use estimates in making calculations.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ions are likely to spread out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by the gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>change in momentum each second = 6.6 × 10<sup>−6</sup> × 5.2 × 10<sup>4</sup> «= 3.4 × 10<sup>−1 </sup>kg m s<sup>−1</sup>» ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}">
<mfrac>
<mrow>
<mn>3.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>740</mn>
</mrow>
</mfrac>
</math></span> =» 4.6 × 10<sup>−4</sup> «m s<sup>−2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>(considering the acceleration of the spacecraft)</p>
<p>time for acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «4.6 × 10<sup>6</sup>» «s» ✔</p>
<p>max speed = «answer to (a) × 4.6 × 10<sup>6</sup> =» 2.1 × 10<sup>3</sup> «m s<sup>−1</sup>» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>(considering the conservation of momentum)</p>
<p>(momentum of 30 kg of fuel ions = change of momentum of spacecraft)</p>
<p>30 × 5.2 × 10<sup>4 </sup>= 710 × max speed ✔</p>
<p>max speed = 2.2 × 10<sup>3 </sup>«m s<sup>−1</sup>» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>problem may be too complicated for exact treatment ✔</p>
<p>to make equations/calculations simpler ✔</p>
<p>when precision of the calculations is not important ✔</p>
<p>some quantities in the problem may not be known exactly ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ions have same (sign of) charge ✔</p>
<p>ions repel each other ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the forces between the ions do not affect the force on the spacecraft. ✔</p>
<p>there is no effect on the acceleration of the spacecraft. ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force per unit mass ✔</p>
<p>acting on a small/test/point mass «placed at the point in the field» ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>satellite has a much smaller mass/diameter/size than the planet «so approximates to a point mass» ✔ </p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton is moving in a region of uniform magnetic field. The magnetic field is directed into the plane of the paper. The arrow shows the velocity of the proton at one instant and the dotted circle gives the path followed by the proton.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The speed of the proton is 2.0 × 10<sup>6</sup> m s<sup>–1</sup> and the magnetic field strength <em>B</em> is 0.35 T.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the path of the proton is a circle.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the radius of the path is about 6 cm.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the time for <strong>one</strong> complete revolution.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the kinetic energy of the proton is constant.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">magnetic force is to the left «at the instant shown»<br><em><strong>OR</strong></em><br>explains a rule to determine the direction of the magnetic force ✔</span></p>
<p><span style="background-color: #ffffff;">force is perpendicular to velocity/«direction of» motion<br><em><strong>OR</strong></em><br>force is constant in magnitude ✔</span></p>
<p><span style="background-color: #ffffff;">force is centripetal/towards the centre ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept reference to acceleration instead of force</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mi>v</mi><mi>B</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>R</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></mrow></mfrac></math> <em><strong>OR</strong></em> 0.060 « m »</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award MP2 for full replacement or correct answer to at least 2 significant figures</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>v</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> « s » ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br>work done by force is change in kinetic energy ✔<br>work done is zero/force perpendicular to velocity ✔ <br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Award <strong>[2]</strong> for a reference to work done is zero hence E<sub>k</sub> remains constant</em><br></span></p>
<p> </p>
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br>proton moves at constant speed ✔<br>kinetic energy depends on speed ✔<br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Accept mention of speed or velocity indistinctly in MP2</em><br></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A glider is an aircraft with no engine. To be launched, a glider is uniformly accelerated from rest by a cable pulled by a motor that exerts a horizontal force on the glider throughout the launch.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The glider reaches its launch speed of 27.0 m s<sup>–1</sup> after accelerating for 11.0 s. Assume that the glider moves horizontally until it leaves the ground. Calculate the total distance travelled by the glider before it leaves the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The glider and pilot have a total mass of 492 kg. During the acceleration the glider is subject to an average resistive force of 160 N. Determine the average tension in the cable as the glider accelerates.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cable is pulled by an electric motor. The motor has an overall efficiency of 23 %. Determine the average power input to the motor.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The cable is wound onto a cylinder of diameter 1.2 m. Calculate the angular velocity of the cylinder at the instant when the glider has a speed of 27 m s<sup>–1</sup>. Include an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After takeoff the cable is released and the unpowered glider moves horizontally at constant speed. The wings of the glider provide a lift force. The diagram shows the lift force acting on the glider and the direction of motion of the glider.</p>
<p><img 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8JTWlXmid625PbM0KPPb1F1x2bV7AmMYo7xnfIeAQQQQAABBBDIfgEKiezPURbN8KzaGpsUKp2sCdEion9q+ZpQPKn/zei+dx9TY327PFMmqnDQT2FvX6H6N9XWfU6dh36lJk1S8YTor/a9fRfMUW0wqMalJaN43qB/zlN1W7SI6J+eW/kTJqtU76ija+AGp/6Tfd9HahNRd9ubqg/dohm3fWHwXPK9Ki6VjncEYz7xiOuetwjkuMDWrVtzPELCQwABBJwtMOhXOGdTEP2IApEzOnU0OGKzZBqENs3VddFnLcxnJ8w/V6u46tVkuhi+7YhzDuroqTNj/NTgok6f6lRomBmEjp7SaR6HGEaIUwgggAACCCBgVwEKCbtmLhPzdo/XxCleC0f2qHzb29HnCgzzmYTYP1Y9RzDinL2aMnH84E8TRh3hFSqcOFmeYdpf+onLMI05hQACCCCAAAII2EiAQsJGycr8VMdpekW5PMc71TXo4eOwujreSW56BberYrFXxw+/pdCg/2P/odrrvt63ud1Vmnzn3SqPv/2ob1WmgQ3whh25f85HdCIU+5xDROGuTh2Pv21q2L7iT7pVMP0uLfa8rcMn/mXwpxrhoDqOS6XF3t7nLeIv5T0CDhBgQzoHJJkQEUDA0QIUEo5Of7LBu1Uw62G9MO8NLVpZr5PRYsLcsflZbTCXYE3qa7xmfa9G8/b9QDVbDvcVE2Zfm7R6jbR543wVuSX35Ar51n5Omza8qOZoIXBRoZbdqm+a2tcm9vmMCwqH/z1uFm4VlD2gp796UCtqtqo12kdE4ZP1Wrlou4o3r9bCoqvirknibcF0ffvpMu1b8YS2tIZ6iwlzlaiVq7SpeI02Liwa46cdScyBpggkIfAXf/EX6urqSuIKmiKAAAIIIJBYgEIisQtHhxJw36T5W/ZqR2mz5lybJ5erRA//5hat3HzvUFcMedx9w73a0rJFM08/JW+e+XzEdZr1+jitbNuqx6Zd33ud+wbNeXq72pac0wbvlXK5rpR3wzktGWhzlSbPW6a1Fx9Xcd4kLdjTOfiTAbOX/Nu09MW92jnzPfmifeTp2kfe0sydLXpjddllfmJgrjT1nFp2ztRp3zTlmc95XPs36pi5RR1vrNK0QQ+lD0nBCQTSIhAIBBQKhXT33XdTTKRFnEEQQACB3BZwGeaN6VL0Qde+l7kdMdEhgAACDhU4fPiwfvjDH6qkpESNjY1qaGjQhAkTUqZh3trEyk0p46VjBBBAIK0C5qI48bUCn0ikNQUMhgACCGRO4A9/+INmzpyp48eP68EHH9STTz6p8+fPZ25CjIwAAgggYGsBCglbp4/JI4AAAqMXOHHihMrLyxUMBvXAAw/IfF7ie9/7HsXE6AlpiQACCCAQI0AhEYPBSwQQQCCXBVpaWjR+/Hjde++9amtr04oVK6LFxHPPPZeSsLmtKSWsdIoAAghkjQCFRNakgokggAACqRM4e/ZstPNx48ZFb28yCwnzq6qqKnqbU+pGpmcEEEAAgVwV4GHrXM0scSGAAAIxAuaKTb/4xS9UU1Mjs6j43Oc+d8lDczHNeYkAAggggMAggUQPW1NIDCLiDQIIIOAMAXNFpeXLl2vKlCnOCJgoEUAAAQQuSyBRIcGtTZdFysUIIICAPQW+8pWv6NixYymdPDtbp5SXzhFAAIGMC1BIZDwFTMA6gYjCgUbV1exSINLbayTgV4VrunzNZ6wbhp4QyAGBL3/5y9F9JHIgFEJAAAEEEMiQAIVEhuAZNhUCZ9W6bZ3WtF8Y6NxdtFSNRptq54wfOMYLBBCQioqKosvA9j+EjQkCCCCAAALJClBIJCtGewQQQCBHBPqXgc2RcAgDAQQQQCDNAhQSaQZ39nARdTfXyOv6z6praFBdZanMB3dcrgr5drQq1B3Q/rpKeaPHSlX53GGF+m5RirqFA2r2+zQ7et4l12yf/M0BhaMnz6jZd7fmbmqXmqpUnNd7O9OltzaZtz81y++r6Bvbq9k+v5oD3X2p6Z/jQm1tbtGOgXalqqxrVCAcOyFnZ5Po7S9g7nLdvwys/aMhAgQQQACBdAtQSKRbnPEkvaY1z7dp0rrDMoxPFDzwl2pd8iV5S/6nTvzVM+oyevTx26ulzd/V46+9q+iv7uET8i9foEUHb1Rt8JPe62pv1MFFs3RPXavCGq85tb/SgeppUvk2dfQkup0povDJei2ftUoHC59QsMeQ0dOu2sKDWlT8gOraP4zJzqt6aEOTrq16NbpEZk/wWd3wy+V6+CdtfYVLTFNeImBTgVtuuUXr1q1L2ezZkC5ltHSMAAIIZIUAhURWpMFpk5im6vWPaX5RgaQr5Jn+FZV5PCp/eq1WlXnkllv5RV/SzNJ/1b7f/EFhRdTdukuP75+pFzYuU5nnit7ryh7R8zuXqGNNnfYEPn0uYmjNs2r92fPaP+9JbVw1Qx7zp9/tUdmjf6ed1ae1pqZh4CFtKXaOZrM7dFfZ9WrZf0JBPpQYmpgzthIwN6f7zne+o6NHj9pq3kwWAQQQQCA7BCgksiMPzGJYgbNqa2xSqHSqbosWEf2N3cqfMFmlekcdXb03OPWfSfi9+5ga64MqnXFrbxEx0ChfE4onScc71TXkrUujaTPQIS8QsI1AOpaBtQ0GE0UAAQQQSEqAQiIpLhpbIzBJxRPyR99V5IxOHQ0O0z6oo6fO9N4CNUyryOlTOhoapkGoU6dOXxymAacQyD0BloHNvZwSEQIIIJAuAQqJdEkzztgF3OM1cYp3mOu9mjJxvEb6YXYXTtQUzzDdeCZrYqF52xRfCDhHIJXLwLIhnXN+jogUAQScKTDS717OVCHqLBMYp+kV5fIcP6ITodhPDCIKd3XquEb5CUfB7apY7NXxw28NXg1KYXV1vCOVTtaEfP6VyLLkM500CLAMbBqQGQIBBBDIQQF+a8rBpOZeSG4VlD2gp796UCtqtqo1Wkz0rsC0ctF2FW9erYVFV0nqe44hCnBB4fC/x1GMU9m3V+qr+36gmi39S8t266Tfp0WbCrV543wV8W9EnBlvnSDAMrBOyDIxIoAAAtYL8GuT9ab0mAqB/Nu09MW92jnzPfm8V8rlytO1j7ylmTtb9MbqMvU+cXGVJs9bprUXH1dx3iQt2NMZ99yEW/kli/ViyxbNPP2UvHnmHhYleqRjhnZ27NLqadenYub0iUDWC0ydOjWly8BmPQATRAABBBAYk4DLMAzDvNLcGKzv5Zg64iIEEEDAPgIXFPA/qOLdd6tj31IV6aT88+bo8Sk7dbJ2jgpkblz4mjY8vEKbWkK9e5O8eqfe/V+vKviNv1Fl9BOwRNEmuM7s3wb/y8Z8nmH58uWaMmVKosDGdMzsk70kxkTHRQgggEDWCSSqFWzw11vWOTIhBBDINQF3iZY2BhWMFhGSIgHtWblC9ZNeUJe5cWHjEhW2bVflmt+pZ7jYL7nOHkWEGdK8efN07Nix4aJL+hxFRNJkXIAAAgjYSoBCwlbpYrIIIJBWgfHX69qx/FdyrNelNbjBg5WVlamhoWHwQd4hgAACCCAwjMBY/oocpjtOIYAAAjYUiJyUv8Irr69Z/xbwqyLvFlU1hRTaNFfXuf6jvrVkgUrm/q1CelVVxVdH23XHhRm55Lrp8jWfMT/eUDjQLL+vInoLqcvl1WyfX82B/h4i6m6ukddVId/WZ1TpNZ/d6b9WioRatWPg2lJV1jUqELtxYiSk9h0+zXaZ17nkmu2TvzmgUWzROCiCCRMmKBgM6uzZs4OO8wYBBBBAAIGhBCgkhpLhOAIIOFIgr2ipGnve1rZyjzzVB/SR8Xv9fPtenTywVh7dp20d5z+9BSpGyH3JdW2qnTNO4ZP1Wj5rlQ4WPqGgeZtUT7tqCw9qUfEDqmv/MKaHJtUf8mhtoEc9wd16qGycIu83aNm0e7VdD6vj4x4ZH/+DZh5frVmrXtP7EbNGeVcNy8p1T/ONqg1+IsPo0cc/vlUHFy3QqoZ34xYbiBlqiJcPPvig2trahjjLYQQQQAABBAYLUEgM9uBdBgTOnz+vvXv3qqurKwOjMyQCqRQ4q9afPa/9857UxlUz5DH/i+v2qOzRv9PO6tNaU9OggFkQRL+maXHl11SS75bbc7Nuzr+ozsZX5NcSrV93r4rMPU7yb9VfV94j+V9RY+c5dbe8pBX+W/T0uiqVeczNFHtXJnt+5z3at+IltXQPdN4/yLDf77jjDr355pvDtknmJBvSJaNFWwQQQMB+AhQS9stZzszYLCBeeeUV3X777aqsrFRra2vOxEYgCEQFuo+psT6o0hm39hYRAyx9e54c71RX7G1KA+fNTxtO6dDuQ3EbJbpVMGejgsYeLS06p7bGJoUu2ZHdrfwJk1UaalJjW3K3KZnLwG7evFnmv5t8IYAAAgggMJIAhcRIQpy3XCC2gHj00UfV2dmpP/3pT5aPQ4cIZFogcvqUjoaGmUWoU6dOx+7WPkzboU6F/lZzr8vre/6i9zmJvOIqNQ3VfpjjV199tb7zne+oo6NjmFacQgABBBBAoFfgM0AgkC4Bs4B4/fXXtX79eoXDYZ0+fTpdQzMOAhkRcBdO1BSPdHSo0fs/Tbicu/rKt/XuhWHR/xYyl4E9dOiQpftJDBU+xxFAAAEE7C1g0V899kZg9qkX6L+Fqf8TCIqI1JszQhYIFNyuisVeHT/8lkKDHlcIq6vjnbjbluLm656oO++/U4q7/Sm6OpTLqwr//9UdFeXyHD+iE6HYTzUiCrc/p9muhfIHLsR1OvJbcxlYK5+TGHlEWiCAAAII2FWAQsKumbPRvM3lJGtqaqK3MA1XQCxYsGDQ7RnRpSz7l7TM8HcbcTPVlAj0PXcQ7Tuic+Fzo1wRaZzKvr1SX933A9VsOdxXTHTrpN+nRZsKtXnj/GF2vb5Kk+ct09riPdrwzIHeayPvq2X7bjXNWqONC0v0H2Y9rBfmHdSKmq1qjRYTfTtrr35R2rxaC4fcgXtopP5lYK1Y/IAN6YZ25gwCCCCQCwIUErmQxSyPYdy4cfr973+vHTt26MYbbxxytubKTYZhZOWfISfNCccIuCdXyLf2I1UVf1afXfCKOgd9wjAUQ+8qSi+2bNHM00/Jm2c+w1CiRzpmaGfHLq2edv1QF0aPuz1f1dO7dmlJT13vtXlf1IaeRWrbtVzTzFWc3Ddp/pa92jnzPfm8V8rlytO1s17X51fu1q7HypQ/bO9DnzSXgX3rrbeGbsAZBBBAAAEEJLkM8zc384XLFf0FDhUEUilgPifx6quvRp+TeO+99wYNZRYS8+fPH3SMNwggkH6Bw4cPR59n2rRpU/oHZ0QEEEAAgawUSFQr8IlEVqYqdydlrgpj/t/OkydPjvgJRe4qEBkC2S3AMrDZnR9mhwACCGSLAIVEtmTCYfNIVFDk54/1RgyH4REuAikWsGoZWDakS3Gi6B4BBBDIsACFRIYT4PTh+wuKd999V+Xl5U7nIH4EskagfxnYrJkQE0EAAQQQyDoBComsSwkTQgABBDIvwDKwmc8BM0AAAQSyXYBCItszxPwQQACBDAhYuQxsBqbPkAgggAACaRCgkEgDMkMggAACdhRgGVg7Zo05I4AAAukToJBInzUjIYAAArYSuOOOO9jl2lYZY7IIIIBAegXYRyK93oyGAAII2EbA3Pflmmuu0blz52QujMAXAggggIBzBdhHwrm5J3IEEEAgaQGrloFNemAuQAABBBCwhQC3NtkiTUwSAQQQyIwAy8Bmxp1REUAAATsIUEjYIUvMEQEEEMiQwOUsA8uGdBlKGsMigAACaRKgkEgTNMMggAACdhRgGVg7Zo05I4AAAukRoJBIjzOjIIAAArYVYBlY26aOiSOAAAIpFaCQSCkvnSOAAAL2F2AZWPvnkAgQQACBVAhQSKRClT4RQACBHBKYOnWqNm/eLHM5WL4QQAABBBDoF6CQ6JfgOwIIIIBAQgGWgU3IwkEEEEDA8QJsSOf4HwEAEEAAgZEFGhoaFGS2mbUAABfdSURBVAwGtWLFipEb0wIBBBBAIOcE2JAu51JKQAgggEB6BC5nGdj0zJBREEAAAQTSLcCtTekWZzwEEEDAhgIsA2vDpDFlBBBAIMUCFBIpBqZ7BBBAIFcEkl0Glg3pciXzxIEAAggkFqCQSOzCUQQQQACBOAGWgY0D4S0CCCDgcAEKCYf/ABA+AgggMFoBloEdrRTtEEAAAWcIUEg4I89EiQACCFy2gLkM7Jo1a9TR0XHZfdEBAggggID9BSgk7J9DIkAAAQTSJnDXXXfp0KFDaRuPgRBAAAEEsleAQiJ7c8PMEEAAgawTuPXWW/Xmm29m3byYEAIIIIBA+gUoJNJvzogIIICAbQXMZWDNr66urhFj2Lp164htaIAAAgggYF8BCgn75o6ZI4AAAhkRMG9vam1tzcjYDIoAAgggkD0CFBLZkwtmggACCNhC4M4779S+fftsMVcmiQACCCCQOgGXYRiG2b3L5VLfy9SNRs8IIIAAArYXOH/+vK655hqdO3dO5kpOfCGAAAII5L5AolqBTyRyP+9EiAACCFgq0L8M7JEjR4btl52th+XhJAIIIGB7AQoJ26eQABBAAIH0C5jPSfz2t79N/8CMiAACCCCQNQIUElmTCiaCAAII2EfAXAb25Zdfts+EmSkCCCCAgOUCFBKWk9IhAgggkPsC5jKwXq93VMvA5r4GESKAAALOFKCQcGbeiRoBBBC4bAGWgb1sQjpAAAEEbC1AIWHr9DF5BBBAIHMCIy0Dy4Z0mcsNIyOAAALpEGD513QoMwYCCCCQgwIsA5uDSSUkBBBAYAgBln8dAobDCCCAAALJC4x2Gdjke+YKBBBAAAE7CHBrkx2yxBwRQACBLBVgGdgsTQzTQgABBNIgQCGRBmSGQAABBHJVYLhlYNmQLlezTlwIIIBArwCFBD8JCCCAAAJjFmAZ2DHTcSECCCBgewEKCdunkAAQQACBzAqwDGxm/RkdAQQQyJQAhUSm5BkXAQQQyBGBkZaBzZEwCQMBBBBAIE6AQiIOhLcIIIAAAskJFBcX66c//anM5WD5QgABBBBwjgD7SDgn10SKAAIIpEygurpa3/zmNzVjxoyUjUHHCCCAAAKZE2AficzZMzICCCCQ0wIsA5vT6SU4BBBAIKEAtzYlZOEgAggggEAyAsMtA5tMP7RFAAEEELCPAIWEfXLFTBFAAIGsFWAZ2KxNDRNDAAEEUiZAIZEyWjpGAAEEnCUQvwwsG9I5K/9EiwACzhOgkHBezokYAQQQSIkAy8CmhJVOEUAAgawVoJDI2tQwMQQQQMBeAiwDa698MVsEEEDgcgUoJC5XkOsRQAABBKICV199tdasWaMjR44gggACCCDgAAEKCQckmRARQACBdAmwDGy6pBknWYFIwK8K13T5ms8ke+no2kdOyl/hldfXrO7RXWFhq4jCgUbV1exSIJJEt9E5T1aF/6SSuSyJEWia4wIUEjmeYMJDAAEE0ikQuwzs1q1b0zk0YyGQWQF3iZY2BhWsnaOCtM/krFq3rdOa9gtpH5kBnS1AIeHs/BM9AgggYKkAy8BayklnCCCAQFYLUEhkdXqYHAIIIGA/AfP2ptdee02BQEDnz5+3XwDMOIcFPtHpI/+ouspSuVwuuVylqqxrVCAce2OPeZtQs/y+ir42Xs32+dUc6L9hKaLu5hp5XRXybX1GlV6zn+ny7T8Yc2tTfxvzXII/Ff6+W5BGO9ZCbW1u0Y6BOcXO+4yafXdr7qZ2qalKxXmf3r4VCbWroa5S3oE5VMjnb46LN4fTTWgpF6CQSDkxAyCAAALOETCLh5deeklr167Vfffdp2uuuUY//OEPnQNApFkucEIv/7JTk9YdlmEY6gk+qxt+uVwP/6RN4ejMIwqfrNfyWat0sPAJBXsMGT3tqi08qEXFD6iu/cOY+JpUf8ijtYEe9QR366EvfT7mnFsFczYqaBjRccyxDOMTBQ/8D83S17R543wVuZMZ61U9tKFJ11a9mmDe4zWn9lc6UD1NKt+mjp421c4ZL4Vb9ewDD+v1vIfUbsYRjXe18uofiok3Zsq8RGAMAhQSY0DjEgQQQACBSwW6urpkLgF74sQJhcNhHTt2LNpo48aNFBOXcnEkIwLTVL3+Mc0v6n2Kwe35ipYsnqqW/ScUjH4ocVatP3te++c9qY2rZshj/pbk9qjs0b/TzurTWlPTEPMw8zQtrvyaSvLdcntu1s35w/1KZRYN/6DvL/qFbtz2jL477XpJyY01eN536K6y62PmHY8ZUXfra3q2o1yVVf+pN45oKPHxxl/HewSSExjupz65nmiNAAIIIOBoge3btyeM/4MPPtCjjz6qs2fPJjzPQQQyLnC8U13m7U3dx9RYH1TpjFsHfvnunVu+JhRPkvrbJTvhcJt+8sgGvbfkWT2z5Dblm9df1lgjzafvE5Hg0yo7/U9qaGhQQ8Mv5Pd9U8VVryY7e9ojMKTAZ4Y8wwkEEMhZgWXLliWMLXaVnXS2MSeTaLzY+VxOG/Pa2L4SjZWqNpcz79g5D9VPquY9GqP4Oe3fv988lPDLvMXpu9/9rq677rroebvF1h/UaOY9mjZmf7HtRuNtVRtz7ER9xc7nctpkOjZz/LF+RU6f0tHQMFeHOnXq9EVNH6bJJaci76phVZWevXG9mmvmDhQoKRkrdvDwCfmX/1dVvfyvmlX9pFZ+6XO6vmKT2oqv0/THewunomhFE3sRrxFIUsDo+5LM2+f4QgABBBBAYGwC9913n2H+XZLoz0033WR0dHSMrWOuQsACgZ6ObUa5phnVBz6I6e280bHtPkOetcaBj3oM46MDRrXHY5Rve9voiWllGLHt/p/x0YG1hie+r563jW3lHsNTfcD4aODafzPaNn/NkGe5sbfrk4Gj0ReXM9ag+Zgz/cA4UD3NUPk2oyM68f75xo/b164/3uicb04Q7+Cp8g4BUyBRrcCtTUkWXjRHAAEEEEgs8PWvf12FhYUJT37hC19QUVFRwnMcRCBrBApuV8Vir44ffkuh2IWcFFZXxztS6WRNGPZZiNhILur9hsd1zxpp8xtPa/4NV8SelCwda3DXGpjvVN3miRk38id9eOaT+Ma8R2DMAhQSY6bjQgQQQACBWAFzlaYvfvGLCYsJcyUnvhDIfoFxKvv2Sn113w9Us+VwXzHRrZN+nxZtKuxbbWk0UfQ+XF2z4qDm7X1Rj0Ufro6/zqqxzH77npmIDnFB4XCBpleUy9O0W9tb3u/dtToSUuuWJ7TCfyJ+IrxHYMwCFBJjpuNCBBBAAIFYgauvvlq7d+9WbW1tdOnXe++9V+vXr9cf//hHTZkyJbYprxHIUgG38ksW68WWLZp5+il588w9IEr0SMcM7ezYpdUJC4JEofSuyPRy6IT8CyYqb2Afh749Jbw1au6WRWOZ41+lyfOWae3Fx1WcN0kL9ryj/Fkr9cb2Kfr13Am940/4vv7pzyv12t5qeRJNmWMIjEHA1XfPU3TDlN7bn8bQC5cggAACCCCAAAIIIIBAzgqYmyvG1wp8IpGz6SYwBBBAAAEEEEAAAQRSJ0AhkTpbekYAAQQcLZBoiVFHgxA8AgggkGMCFBI5llDCQQABBBBAAAEEEEAgHQIUEulQZgwEEEAAAQQQQAABBHJMgEIixxJKOAgggAACCCCAAAIIpEOAQiIdyoyBAAIIIIAAAggggECOCVBI5FhCCQcBBBBAAAEEEEAAgXQIsI9EOpQZAwEEEEAAAQQQQAABGwuwj4SNk8fUEUAAAQQQQAABBBDIJgFubcqmbDAXBBBAAAEEEEAAAQRsIkAhYZNEMU0EEEDAbgJsSGe3jDFfBBBAIDkBConkvGiNAAIIIIAAAggggAACkigk+DFAAAEEEEAAAQQQQACBpAUoJJIm4wIEEEAAAQQQQAABBBCgkOBnAAEEEEAAAQQQQAABBJIWoJBImowLEEAAAQQQQAABBBBAgA3p+BlAAAEEEEAAAQQQQACBYQXYkG5YHk4igAACCCCAAAIIIIDAaAW4tWm0UrRDAAEEEEAAAQQQQACBAQEKiQEKXiCAAAIIIIAAAggggMBoBSgkRitFOwQQQACBpATY2TopLhojgAACthOgkLBdypgwAggggAACCCCAAAKZF6CQyHwOmAECCCCAAAIIIIAAArYToJCwXcqYMAIIIIAAAggggAACmRegkMh8DpgBAggggAACCCCAAAK2E2BDOtuljAkjgAACCCCAAAIIIJBeATakS683oyGAAAIIIIAAAgggkLMC3NqUs6klMAQQQAABBBBAAAEEUidAIZE6W3pGAAEEEEAAAQQQQCBnBSgkcja1BIYAAghkVoAN6TLrz+gIIIBAqgUoJFItTP8IIIAAAggggAACCOSgAIVEDiaVkBBAAAEEEEAAAQQQSLUAhUSqhekfAQQQQAABBBBAAIEcFKCQyMGkEhICCCCAAAIIIIAAAqkWYEO6VAvTPwIIIIAAAggggAACNhdgQzqbJ5DpI4AAAggggAACCCCQLQLc2pQtmWAeCCCAAAIIIIAAAgjYSIBCwkbJYqoIIIAAAggggAACCGSLAIVEtmSCeSCAAAI5JsCGdDmWUMJBAAEE4gQoJOJAeIsAAggggAACCCCAAAIjC1BIjGxECwQQQAABBBBAAAEEEIgToJCIA+EtAggggAACCCCAAAIIjCxAITGyES0QQAABBBBAAAEEEEAgToAN6eJAeIsAAggggAACCCCAAAKDBdiQbrAH7xBAAAEEEEAAAQQQQGCMAtzaNEY4LkMAAQQQQAABBBBAwMkCFBJOzj6xI4AAAggggAACCCAwRgEKiTHCcRkCCCCAwPACbEg3vA9nEUAAAbsLUEjYPYPMHwEEEEAAAQQQQACBDAhQSGQAnSERQAABBBBAAAEEELC7AIWE3TPI/BFAAAEEEEAAAQQQyIAAhUQG0BkSAQQQQAABBBBAAAG7C1BI2D2DzB8BBBBAAAEEEEAAgQwIsLN1BtAZEgEEEEAAAQQQQAABOwmws7WdssVcEUAAAQQQQAABBBDIYgFubcri5DA1BBBAAAEEEEAAAQSyVYBCIlszw7wQQAABmwuwIZ3NE8j0EUAAgREEKCRGAOI0AggggAACCCCAAAIIXCpAIXGpCUcQQAABBBBAAAEEEEBgBAEKiRGAOI0AAggggAACCCCAAAKXClBIXGrCEQQQQAABBBBAAAEEEBhBgEJiBCBOI4AAAggggAACCCCAwKUCbEh3qQlHEEAAAQQQQAABBBBAIEaADeliMHiJAAIIIIAAAggggAACYxfg1qax23ElAggggAACCCCAAAKOFaCQcGzqCRwBBBBIrQAb0qXWl94RQACBTAtQSGQ6A4yPAAIIIIAAAggggIANBSgkbJg0powAAggggAACCCCAQKYFKCQynQHGRwABBBBAAAEEEEDAhgIUEjZMGlNGAAEEEEAAAQQQQCDTAhQSmc4A4yOAAAIIIIAAAgggYEMBNqSzYdKYMgIIIIAAAggggAAC6RRgQ7p0ajMWAggggAACCCCAAAI5LMCtTTmcXEJDAAEEEEAAAQQQQCBVAhQSqZKlXwQQQAABBBBAAAEEcliAQiKHk0toCCCAQCYF2Nk6k/qMjQACCKRegEIi9caMgAACCCCAAAIIIIBAzglQSORcSgkIAQQQQAABBBBAAIHUC1BIpN6YERBAAAEEEEAAAQQQyDkBComcSykBIYAAAggggAACCCCQegE2pEu9MSMggAACCCCAAAIIIGBrATaks3X6mDwCCCCAAAIIIIAAAtkjwK1N2ZMLZoIAAggggAACCCCAgG0EKCRskyomigACCCCAAAIIIIBA9ghQSGRPLpgJAgggkFMCbEiXU+kkGAQQQOASAQqJS0g4gAACCCCAAAIIIIAAAiMJUEiMJMR5BBBAAAEEEEAAAQQQuESAQuISEg4ggAACCCCAAAIIIIDASAIUEiMJcR4BBBBAAAEEEEAAAQQuEWBDuktIOIAAAggggAACCCCAAAKxAmxIF6vBawQQQAABBBBAAAEEEBizALc2jZmOCxFAAAEEEEAAAQQQcK4AhYRzc0/kCCCAAAIIIIAAAgiMWYBCYsx0XIgAAgggMJwAG9INp8M5BBBAwP4CFBL2zyERIIAAAggggAACCCCQdgEKibSTMyACCCCAAAIIIIAAAvYXoJCwfw6JAAEEEEAAAQQQQACBtAtQSKSdnAERQAABBBBAAAEEELC/ABvS2T+HRIAAAggggAACCCCAQEoF2JAupbx0jgACCCCAAAIIIICAcwS4tck5uSZSBBBAAAEEEEAAAQQsE6CQsIySjhBAAAEEEEAAAQQQcI4AhYRzck2kCCCAQFoF2JAurdwMhgACCKRdgEIi7eQMiAACCCCAAAIIIICA/QUoJOyfQyJAAAEEEEAAAQQQQCDtAhQSaSdnQAQQQAABBBBAAAEE7C9AIWH/HBIBAggggAACCCCAAAJpF6CQSDs5AyKAAAIIIIAAAgggYH8Bdra2fw6JAAEEEEAAAQQQQACBlAqws3VKeekcAQQQQAABBBBAAAHnCHBrk3NyTaQIIIAAAggggAACCFgmQCFhGSUdIYAAAggggAACCCDgHAEKCefkmkgRQAABBBBAAAEEELBMgELCMko6QgABBBBAAAEEEEDAOQIUEs7JNZEigAACCCCAAAIIIGCZAIWEZZR0hAACCCCAAAIIIICAcwQoJJyTayJFAAEEEEAAAQQQQMAyAQoJyyjpCAEEEEAAAQQQQAAB5whQSDgn10SKAAIIIIAAAggggIBlAhQSllHSEQIIIIAAAggggAACzhGgkHBOrokUAQQQQAABBBBAAAHLBCgkLKOkIwQQQAABBBBAAAEEnCNAIeGcXBMpAggggAACCCCAAAKWCVBIWEZJRwgggAACCCCAAAIIOEeAQsI5uSZSBBBAAAEEEEAAAQQsE6CQsIySjhBAAAEEEEAAAQQQcI4AhYRzck2kCCCAAAIIIIAAAghYJkAhYRklHSGAAAIIIIAAAggg4BwBCgnn5JpIEUAAAQQQQAABBBCwTIBCwjJKOkIAAQQQQAABBBBAwDkCFBLOyTWRIoAAAggggAACCCBgmQCFhGWUdIQAAggggAACCCCAgHMEKCSck2siRQABBBBAAAEEEEDAMgEKCcso6QgBBBBAAAEEEEAAAecIUEg4J9dEigACCCCAAAIIIICAZQIUEpZR0hECCCCAAAIIIIAAAs4RoJBwTq6JFAEEEEAAAQQQQAABywQoJCyjpCMEEEAAAQQQQAABBJwjQCHhnFwTKQIIIIAAAggggAAClglQSFhGSUcIIIAAAggggAACCDhHgELCObkmUgQQQAABBBBAAAEELBOgkLCMko4QQAABBBBAAAEEEHCOAIWEc3JNpAgggAACCCCAAAIIWCZAIWEZJR0hgAACCCCAAAIIIOAcAQoJ5+SaSBFAAAEEEEAAAQQQsEyAQsIySjpCAAEEEEAAAQQQQMA5AhQSzsk1kSKAAAIIIIAAAgggYJkAhYRllHSEAAIIIIAAAggggIBzBCgknJNrIkUAAQQQQAABBBBAwDIBCgnLKOkIAQQQQAABBBBAAAHnCFBIOCfXRIoAAggggAACCCCAgGUCFBKWUdIRAggggAACCCCAAALOEaCQcE6uiRQBBBBAAAEEEEAAAcsEKCQso6QjBBBAAAEEEEAAAQScI0Ah4ZxcEykCCCCAAAIIIIAAApYJUEhYRklHCCCAAAIIIIAAAgg4R4BCwjm5JlIEEEAAAQQQQAABBCwToJCwjJKOEEAAAQQQQAABBBBwjgCFhHNyTaQIIIAAAggggAACCFgmQCFhGSUdIYAAAggggAACCCDgHAEKCefkmkgRQAABBBBAAAEEELBMgELCMko6QgABBBBAAAEEEEDAOQIUEs7JNZEigAACCCCAAAIIIGCZgMswDMPlclnWIR0hgAACCCCAAAIIIIBAbgoYhjEQ2GfMV7EHBs7wAgEEEEAAAQQQQAABBBAYQoBbm4aA4TACCCCAAAIIIIAAAggMLUAhMbQNZxBAAAEEEEAAAQQQQGAIAQqJIWA4jAACCCCAAAIIIIAAAkMLUEgMbcMZBBBAAAEEEEAAAQQQGEKAQmIIGA4jgAACCCCAAAIIIIDA0AL/H1JxX8VuQBasAAAAAElFTkSuQmCC"></p>
<p>Draw the forces acting on the glider to complete the free-body diagram. The dotted lines show the horizontal and vertical directions.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, using appropriate laws of motion, how the forces acting on the glider maintain it in level flight.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At a particular instant in the flight the glider is losing 1.00 m of vertical height for every 6.00 m that it goes forward horizontally. At this instant, the horizontal speed of the glider is 12.5 m s<sup>–1</sup>. Calculate the <strong>velocity</strong> of the glider. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>correct use of kinematic equation/equations</p>
<p>148.5 <em><strong>or</strong> </em>149 <em><strong>or</strong> </em>150 «m»</p>
<p> </p>
<p><em>Substitution(s) must be correct.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27}}{{11}}">
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mn>11</mn>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong></em> 2.45 «m s<sup>–2</sup>»</p>
<p><em>F</em> – 160 = 492 × 2.45</p>
<p>1370 «N»</p>
<p> </p>
<p><em>Could be seen in part (a).</em><br><em>Award <strong>[0]</strong> for solution that uses a = 9.81 m s<sup>–2</sup></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>«work done to launch glider» = 1370 x 149 «= 204 kJ»</p>
<p>«work done by motor» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{204 \times 100}}{{23}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>204</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</mfrac>
</math></span></p>
<p>«power input to motor» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{204 \times 100}}{{23}} \times \frac{1}{{11}} = 80">
<mo>=</mo>
<mfrac>
<mrow>
<mn>204</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>11</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>80</mn>
</math></span> <em><strong>or</strong> </em>80.4 <em><strong>or</strong> </em>81 k«W»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>use of average speed 13.5 m s<sup>–1</sup></p>
<p>«useful power output» = force x average speed «= 1370 x 13.5»</p>
<p>power input = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1370 \times 13.5 \times \frac{{100}}{{23}} = ">
<mn>1370</mn>
<mo>×</mo>
<mn>13.5</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 80 <em><strong>or</strong> </em>80.4 <em><strong>or</strong> </em>81 k«W»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p>work required from motor = KE + work done against friction «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.5 \times 492 \times {27^2} + \left( {160 \times 148.5} \right)">
<mo>=</mo>
<mn>0.5</mn>
<mo>×</mo>
<mn>492</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>27</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>160</mn>
<mo>×</mo>
<mn>148.5</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span>» = 204 «kJ»</p>
<p>«energy input» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{{\text{work required from motor}} \times 100}}{{23}}">
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>work required from motor</mtext>
</mrow>
<mo>×</mo>
<mn>100</mn>
</mrow>
<mrow>
<mn>23</mn>
</mrow>
</mfrac>
</math></span></p>
<p>power input <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{883000}}{{11}} = 80.3">
<mo>=</mo>
<mfrac>
<mrow>
<mn>883000</mn>
</mrow>
<mrow>
<mn>11</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>80.3</mn>
</math></span> k«W»</p>
<p> </p>
<p><em>Award <strong>[2 max]</strong> for an answer of 160 k«W».</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega = ">
<mi>ω</mi>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{r} = ">
<mfrac>
<mi>v</mi>
<mi>r</mi>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{27}}{{0.6}} = 45">
<mfrac>
<mrow>
<mn>27</mn>
</mrow>
<mrow>
<mn>0.6</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>45</mn>
</math></span></p>
<p>rad s<sup>–1</sup></p>
<p> </p>
<p><em>Do not accept Hz.</em><br><em>Award <strong>[1 max]</strong> if unit is missing.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>drag correctly labelled and in correct direction</p>
<p>weight correctly labelled and in correct direction <em><strong>AND</strong></em> no other incorrect force shown</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if forces do not touch the dot, but are otherwise OK.</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>name Newton's first law</p>
<p>vertical/all forces are in equilibrium/balanced/add to zero<br><em><strong>OR</strong></em><br>vertical component of lift mentioned</p>
<p>as equal to weight</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>any speed and any direction quoted together as the answer</p>
<p>quotes their answer(s) to 3 significant figures</p>
<p>speed = 12.7 m s<sup>–1</sup> <em><strong>or</strong></em> direction = 9.46<sup>º</sup> <em><strong>or</strong></em> 0.165 rad «below the horizontal» <em><strong>or </strong></em>gradient of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{1}{6}">
<mo>−</mo>
<mfrac>
<mn>1</mn>
<mn>6</mn>
</mfrac>
</math></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A company delivers packages to customers using a small unmanned aircraft. Rotating horizontal blades exert a force on the surrounding air. The air above the aircraft is initially stationary.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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" width="319" height="179"></p>
<p>The air is propelled vertically downwards with speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. The aircraft hovers motionless above the ground. A package is suspended from the aircraft on a string. The mass of the aircraft is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>95</mn><mtext> kg</mtext></math> and the combined mass of the package and string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>45</mn><mo> </mo><mi>kg</mi></math>. The mass of air pushed downwards by the blades in one second is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kg</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the value of the resultant force on the aircraft when hovering.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, by reference to Newton’s third law, how the upward lift force on the aircraft is achieved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">zero </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">Blades exert a downward force on the air </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0"><br>air exerts an equal and opposite force on the blades </span><span class="fontstyle3">«</span><span class="fontstyle0">by Newton’s third law</span><span class="fontstyle3">»<br></span><span class="fontstyle4"><em><strong>OR</strong></em><br></span><span class="fontstyle0">air exerts a reaction force on the blades </span><span class="fontstyle3">«</span><span class="fontstyle0">by Newton’s third law</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<p><em><span class="fontstyle5"><br>Downward direction required for </span><strong><span class="fontstyle4">MP1</span></strong></em><span class="fontstyle4">.</span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">lift force/change of momentum in one second</span><span class="fontstyle0">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi><mo>=</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>95</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>45</mn></mrow></mfenced><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> ✓</span></p>
<p><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>1</mn><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <em><strong>AND </strong></em></span><span class="fontstyle1">answer expressed to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> sf only </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle5">Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">8</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">2</mn></math> from </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn><mo mathvariant="italic"> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">2</mn></mrow></msup></math>.</p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">vertical force = lift force – weight </span><span class="fontstyle2"><em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo>»</mo><mo> </mo></math></span><span class="fontstyle4">✓</span></p>
<p><span class="fontstyle0">acceleration<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfrac><mo>=</mo><mn>4</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo><mo> </mo></math></span><span class="fontstyle4">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A ball of mass 0.250 kg is released from rest at time <em>t</em> = 0, from a height <em>H</em> above a horizontal floor.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The graph shows the variation with time <em>t</em> of the velocity <em>v</em> of the ball. Air resistance is negligible. Take <em>g</em> = −9.80 m s<sup>−2</sup>. The ball reaches the floor after 1.0 s.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine <em>H</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label the time and velocity graph, using the letter M, the point where the ball reaches the maximum rebound height.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the acceleration of the ball at the maximum rebound height.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the average force exerted on the floor by the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest why the momentum of the ball was not conserved during the collision with the floor.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>H</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math><em>gt</em><sup>2</sup> =» 4.9 «m» <strong>✓</strong></p>
<p><em><br>Accept other methods as area from graph, alternative kinematics equations or conservation of mechanical energy.<br></em><em>Award <strong>[1]</strong> for a bald correct answer in the range 4.9 - 5.1.<br></em><em>Award<strong> [0]</strong> if time used is different than 1.0 s.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>M at 1.6 s <strong>✓</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>g</em> =» 9.80 «ms<sup>−2</sup>» ✓</p>
<p><br><em>Accept 9.81, 10 or a plain “g”.</em><br><em>Ignore sign if provided.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><img src="data:image/png;base64,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"></em></p>
<p>concave down parabola as shown «with non-zero initial slope and zero final slope» ✓</p>
<p> </p>
<p><em>Award <strong>[1]</strong> mark if curve starts from a positive time value.</em><br><em>Award <strong>[0]</strong> if the final slope is negative.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>« loss of KE is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><mfenced><mrow><mn>9</mn><mo>.</mo><msup><mn>8</mn><mn>2</mn></msup><mo>-</mo><msup><mn>5</mn><mn>2</mn></msup></mrow></mfenced><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>9</mn><mo> </mo></math>«J» ✓</p>
<p><br><em>Award <strong>[1]</strong> mark for an answer in the range 8.7 - 9.5.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>250</mn><mo>×</mo><mfenced><mrow><mn>9</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>5</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math> ✓</p>
<p><em>F</em><sub>net</sub> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>∆</mo><mi>p</mi></mrow><mrow><mo>∆</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>7</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37</mn></math> «N» ✓</p>
<p><em>N</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>37</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>250</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>=</mo><mn>39</mn><mo>.</mo><mn>5</mn></math> «N» ✓</p>
<p><br><em>Allow<strong> ECF</strong> for <strong>MP2</strong> and <strong>MP3</strong>.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is an external force acting on the ball</p>
<p><em><strong>OR</strong></em></p>
<p>some momentum is transferred to the floor ✓</p>
<p><br><em>Allow references to impulse instead of force. </em><br><em>Do not award references to energy.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A small ball of mass <em>m </em>is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_12.45.38.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a"></p>
<p>The normal reaction force <em>N </em>makes an angle <em>θ</em> to the horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant force on the ball.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, construct an arrow of the correct length to represent the weight of the ball.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the net force <em>F </em>on the ball is given by the following equation.</p>
<p> <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="F = \frac{{mg}}{{\tan \theta }}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the bowl is 8.0 m and <em>θ</em> = 22°. Determine the speed of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.</p>
<p> <img src="images/Schermafbeelding_2018-08-12_om_13.41.19.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.d"></p>
<p>The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>towards the centre <strong>«</strong>of the circle<strong>» </strong>/ horizontally to the right</p>
<p> </p>
<p><em>Do not accept towards the centre of the bowl</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>downward vertical arrow of any length</p>
<p>arrow of correct length</p>
<p> </p>
<p><em>Judge the length of the vertical arrow by eye. The construction lines are not required. A label is not required</em></p>
<p><em>eg</em>: <img src="images/Schermafbeelding_2018-08-12_om_13.22.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>F</em> = <em>N</em> cos <em>θ</em></p>
<p><em>mg</em> = <em>N</em> sin <em>θ</em></p>
<p>dividing/substituting to get result</p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>right angle triangle drawn with <em>F</em>, <em>N </em>and <em>W/mg </em>labelled</p>
<p>angle correctly labelled and arrows on forces in correct directions</p>
<p>correct use of trigonometry leading to the required relationship</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-12_om_13.28.39.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em>tan θ</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{O}}}{A} = \frac{{mg}}{F}">
<mfrac>
<mrow>
<mtext>O</mtext>
</mrow>
<mi>A</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mi>F</mi>
</mfrac>
</math></span></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg}}{{\tan \theta }}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span> = <em>m</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><em>r</em> = <em>R</em> cos <em>θ</em></p>
<p><em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{gR{{\cos }^2}\theta }}{{\sin \theta }}} /\sqrt {\frac{{gR\cos \theta }}{{\tan \theta }}} /\sqrt {\frac{{9.81 \times 8.0\cos 22}}{{\tan 22}}} ">
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mrow>
<msup>
<mrow>
<mi>cos</mi>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>θ</mi>
</mrow>
<mrow>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mi>cos</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>9.81</mn>
<mo>×</mo>
<mn>8.0</mn>
<mi>cos</mi>
<mo></mo>
<mn>22</mn>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mn>22</mn>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p><em>v</em> = 13.4/13 <strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[4] </em></strong><em>for a bald correct answer </em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for an answer of 13.9/14 </em><strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong><em>. MP2 omitted</em></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is no force to balance the weight/N is horizontal</p>
<p>so no / it is not possible</p>
<p> </p>
<p><em>Must see correct justification to award MP2</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>speed before collision <em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gR} ">
<msqrt>
<mn>2</mn>
<mi>g</mi>
<mi>R</mi>
</msqrt>
</math></span> =<strong>»</strong> 12.5 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p><strong>«</strong>from conservation of momentum<strong>» </strong>common speed after collision is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> initial speed <strong>«</strong><em>v<sub>c</sub></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12.5}}{2}">
<mfrac>
<mrow>
<mn>12.5</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> = 6.25 ms<sup>–1</sup><strong>»</strong></p>
<p><em>h = </em><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v_c}^2}}{{2g}} = \frac{{{{6.25}^2}}}{{2 \times 9.81}}">
<mfrac>
<mrow>
<msup>
<mrow>
<msub>
<mi>v</mi>
<mi>c</mi>
</msub>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mn>2</mn>
<mi>g</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>6.25</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> 2.0 <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Allow 12.5 from incorrect use of kinematics equations</em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for mg(8) = 2mgh leading to h = 4 m if done in one step.</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><em>Allow ECF from MP2</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The Rotor is an amusement park ride that can be modelled as a vertical cylinder of inner radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> rotating about its axis. When the cylinder rotates sufficiently fast, the floor drops out and the passengers stay motionless against the inner surface of the cylinder. The diagram shows a person taking the Rotor ride. The floor of the Rotor has been lowered away from the person.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="291" height="330"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw and label the free-body diagram for the person.</p>
<p> </p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The person must not slide down the wall. Show that the minimum angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math> of the cylinder for this situation is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><msqrt><mfrac><mi>g</mi><mrow><mi>μ</mi><mi>R</mi></mrow></mfrac></msqrt></math></p>
<p style="text-align: left;">where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> is the coefficient of static friction between the person and the cylinder.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coefficient of static friction between the person and the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>40</mn></math>. The radius of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. The cylinder makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math> revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">arrow downwards labelled weight/W/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>g</mi></math> </span><span class="fontstyle0">and arrow upwards labelled friction/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">arrow horizontally to the left labelled </span><span class="fontstyle4">«</span><span class="fontstyle0">normal</span><span class="fontstyle4">» </span><span class="fontstyle0">reaction/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><img src="data:image/png;base64,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"></p>
<p><em><span class="fontstyle0"><br>Ignore point of application of the forces but do not allow arrows that do not touch the object.</span></em></p>
<p><em><span class="fontstyle0">Do not allow horizontal force to be labelled ‘centripetal’ or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">See <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>μ</mi><mi>N</mi></math> </span><span class="fontstyle2"><em><strong>AND</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>m</mi><mi>R</mi><msup><mi>ω</mi><mn>2</mn></msup></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle4">«</span><span class="fontstyle0">substituting for N</span><span class="fontstyle4">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><mi>R</mi><mo>=</mo><mi>m</mi><mi>g</mi></math> </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span class="fontstyle0">ALTERNATIVE 1</span></strong></em></p>
<p><span class="fontstyle0">minimum required angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><msqrt><mfrac><mrow><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>40</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></msqrt><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>6</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">actual angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mfenced><mstyle displaystyle="true"><mfrac><mn>60</mn><mn>28</mn></mfrac></mstyle></mfenced></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math></span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">actual angular velocity is greater than the minimum, so the person does not slide </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><span class="fontstyle3"><em><strong>ALTERNATIVE 2</strong></em></span></p>
<p><span class="fontstyle0">Minimum friction force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>m</mi><mi>g</mi><mo>=</mo><mo>«</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">Actual friction force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>μ</mi><mi>m</mi><mi>R</mi><msup><mi>ω</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn><msup><mfenced><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mfrac><mn>28</mn><mn>60</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>»</mo><mo>=</mo><mn>12</mn><mo>.</mo><mn>0</mn><mo> </mo><mi mathvariant="normal">m</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">Actual friction force is greater than the minimum frictional force so the person does not slide </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle4">Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">2</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">7</mn></math> from </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn><mo mathvariant="italic"> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">2</mn></mrow></msup></math>.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).</p>
<p>The following data are available for binding energies per nucleon:</p>
<p style="padding-left: 30px;">plutonium 7.568 MeV</p>
<p style="padding-left: 30px;">uranium 7.600 MeV</p>
<p style="padding-left: 30px;">alpha particle 7.074 MeV</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the binding energy of a nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, a graph to show the variation with nucleon number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of the binding energy per nucleon, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>BE</mtext><mi>A</mi></mfrac></math>. Numbers are not required on the vertical axis.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy released in this decay is about 6 MeV.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The plutonium nucleus is at rest when it decays.</p>
<p>Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>kinetic energy of alpha particle</mtext><mtext>kinetic energy of uranium</mtext></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the energy needed to «completely» separate the nucleons of a nucleus</p>
<p><em><strong>OR</strong></em></p>
<p>the energy released when a nucleus is assembled from its constituent nucleons ✓</p>
<p> </p>
<p><em>Accept reference to protons <strong>AND</strong> neutrons.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve rising to a maximum between 50 and 100 ✓</p>
<p>curve continued and decreasing ✓</p>
<p> </p>
<p><em>Ignore starting point.<br></em></p>
<p><em>Ignore maximum at alpha particle</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At a point on the peak of their graph ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct mass numbers for uranium (234) and alpha (4) ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>234</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>600</mn><mo>+</mo><mn>4</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>074</mn><mo>-</mo><mn>238</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>568</mn></math> «MeV» ✓</p>
<p>energy released 5.51 «MeV» ✓</p>
<p> </p>
<p><em>Ignore any negative sign.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>K</mi><msub><mi>E</mi><mi>α</mi></msub></mrow><mrow><mi>K</mi><msub><mi>E</mi><mi>U</mi></msub></mrow></mfrac><mo>=</mo></math>»<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>U</mi></msub></mrow></mfrac></mfrac></mstyle></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mi>U</mi></msub><msub><mi>m</mi><mi>α</mi></msub></mfrac></math> ✓</p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>234</mn><mn>4</mn></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>.</mo><mn>5</mn></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>117</mn><mn>2</mn></mfrac></math> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the magnetic force <em>F</em> on the proton. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the velocity vector <em>v</em> of the proton.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The speed of the proton is 2.16 × 10<sup>6</sup> m s<sup>-1</sup> and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>F</em> towards centre ✔</span></p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>v</em> tangent to circle and in the direction shown in the diagram ✔</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="qvB = \frac{{m{v^2}}}{R} \Rightarrow » R = \frac{{mv}}{{qB}}/\frac{{1.673 \times {{10}^{ - 27}} \times 2.16 \times {{10}^6}}}{{1.60 \times {{10}^{ - 19}} \times 0.042}}">
<mi>q</mi>
<mi>v</mi>
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
<mo stretchy="false">⇒</mo>
<mrow>
<mo>»</mo>
</mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi>q</mi>
<mi>B</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>1.673</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>2.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.042</mn>
</mrow>
</mfrac>
</math></span> </span> <span style="background-color:#ffffff;">✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.538 «m»✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.54 «m» ✔<br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered although usually to 3 sf. Common mistakes were to substitute 0.042 for F and 1 for q. Also some candidates tried to answer in terms of electric fields.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground. Point B is 20 m above level ground.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.</p>
</div>
<div class="specification">
<p>At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the safety net with speed 9.6 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The dot on the following diagram represents the skier as she passes point B.<br>Draw and label the vertical forces acting on the skier.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxMAAAENCAYAAAB0GTiSAAAZl0lEQVR4Ae3dTYiV9RcH8N/8cVO4UZMgNCJIoVpYlAUaRQszCBIjqBYRZC2iFi2KyEWbiqhFYdLGIpRoEw290YtIFBmEvWgRRC56mxiKynYFbebPeeoOo46jM56Zufeez2xG75059zmfcxfzvb/f8zwjExMTE80XAQIECBAgQIAAAQIEZinwv1n+vB8nQIAAAQIECBAgQIBAJ7Ck5zAyMtL7p+8ECBAgQIAAAQIECBCYVmDqxqbJMBEPRqCY+uS0v+1BAgQIECBAgAABAgTKCUyXFWxzKvc20DABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcAWEix1EVAgQIECBAgAABAuUEhIlyI9cwAQIECBAgQIAAgRwBYSLHURUCBAgQIECAAAEC5QSEiXIj1zABAgQIECBAgACBHAFhIsdRFQIECBAgQIAAAQLlBISJciPXMAECBAgQIECAAIEcgSU5ZVQhQIAAgWESOHz4cNfOWWed1ZYvXz5MremFAAECBBIFrEwkYipFgACBQRf4+eef2wUXXNA2btzY1q5d21asWNGeeeaZQW/L8RMgQIDAPAmMTExMTPRqj4yMtCn/7T3sOwECBAgUEDhy5Ei77LLL2vfff39UtytXrmw7duxot9xyy1GP+w8BAgQI1BKYLitYmaj1HtAtAQIETijwxhtvHBck4od/++239txzz7UIG74IECBAgMBUASsTUzX8mwABAkMmEOc+/PXXX+27777rOvvkk0+673/++Wd7/vnnT7vbBx54YLLGlVde2f37/PPPb2eeeWZbs2bN5HP+QYAAAQKDLzDdyoQwMfhz1QEBAgRahIYffvih/fLLL+3rr79uH3zwQfv0008nZbZt29aWLVvWLr744rZ06dLu8d4f/b0f+vzzz9ttt93W++9R3zdv3tx27drVBZPeE1NDyvj4ePvpp5/asSHl8ssvb9dcc00799xzu3Bx3nnntdWrV7czzjijV8Z3AgQIEBgQAWFiQAblMAkQIDCTQJwk/eOPP7aDBw+2L7/8cnKF4cYbb+z+YI8VgrPPPrvFuQ6z+cP977//bhdddNFxW52izptvvtmuuOKKmQ7rqOei1tjYWLdF6tdff22xIhKB5/XXX+9+Lo51/fr13TkaETCsYhzF5z8ECBDoSwFhoi/H4qAIECAws0Ccq/DNN9+0Dz/8sL322mvdikPvE/8IDrHaMJvQMNOrRVC55557uteIFYx//vmnvfjii+3aa6+d6ddm9VxvFeWzzz5rBw4cmAwYsWWq149wMStSP0yAAIEFERAmFoTZixAgQOD0BeIP7vg0f3R0tPtjO8LDli1buk/yL7zwwrZq1arTf5EZKkSA+f333xdkxSBeK7ZIffXVV+2jjz6aXGl57LHHun7jClPudTHDsDxFgACBBRIQJhYI2ssQIEBgLgKHDh1q+/fvb3v27OlWBuI8h6uuuqpbFZjv8DCX452v34ktUl988UW3jatnEduitm7dWs5ivozVJUCAwFwEhIm5qPkdAgQIzKNArEDs3bv3qABx8803d5/I+zT+X/jYevX+++9PrtIIFvP4hlSaAAECMwgIEzPgeIoAAQILJRDbeuJqS/Gpe5yQHCsQAsSp6YddnGvxyiuvdNuhesHihhtusBXq1Aj9FAECBOYsIEzMmc4vEiBA4PQFYhvT22+/3bZv3978EXz6nseuWEQou+OOO9qll17q0rOnz6sCAQIEjhMQJo4j8QABAgTmVyD2/8dJxXEH6ViFiCsWxb0c1q1bN78vXKx6b7vYfffd1+Jk9dtvv707Yb3SuSbFRq5dAgQWQUCYWAR0L0mAQE2B2I7z1ltvtZ07d3YA9957b7MVZ/7fC9OFt1gF2rBhw/y/uFcgQIDAkAsIE0M+YO0RILD4AhEiXn755RafkMcfsXHPhrgikzs+L/xspq5WxCxiteL66683i4UfhVckQGBIBISJIRmkNggQ6D+BY0NEbGfyaXh/zMkqUX/MwVEQIDD4AtOFif8Nfls6IECAwOIJxB+qsZVpxYoVbd++fd19IuIu1YLE4s3k2FeOS+zGqkTcQfzRRx/tLjEb84q5xfx8ESBAgMDcBYSJudv5TQIECgvE3nwhYrDeALHVbNOmTS3CXtwcMMKfUDFYM3S0BAj0n4Aw0X8zcUQECPSxQISI0dHRdvXVV1uJ6OM5nezQYuVIqDiZkucJECBwcoGRiYmJid6PTbcPqvec7wQIEKgu8PHHH7ennnqqjY+Pt4ceesjJvEP0hujNNi7fu3v37u4mgk6aH6IBa4UAgRSB6bKCMJFCqwgBAsMsEDdH27FjRxcknn322XbnnXe6ItCQDjxCxf333991JzAO6ZC1RYDAnAWmCxO2Oc2Z0y8SIDDsArGlac+ePW316tVdq2NjYy3uF+ET6+GdfGx/ihO1I0g88cQT7dZbb20RMHwRIECAwPQCViamd/EoAQLFBQ4dOtTuvvvuTiGuABQn7vqqJRBh8oUXXujuGbJt27bu7uVr1qyphaBbAgQITBGwMjEFwz8JECAwnUD8Afn444+3Sy65ZPJyooLEdFLD/1isQMVKVKxILVu2rK1du7a7gle8R3wRIECAwL8Ctjl5JxAgQOA/gViNiKs0HThwoH377be2NHlndAKrVq1qTz75ZDt48GB3Ba94j+zdu5cOAQIECLTWbHPyNiBAoLxAfNL89NNPt+3bt7uST/l3w8wA8V5555132k033dRi69MjjzzSImz4IkCAQAUB25wqTFmPBAjMSuDY1Yi4U7ITrGdFWOqH472xdevW9scff3Rbn+Lk/DhJ39anUm8DzRIgMEXAysQUDP8kQKCOQPzx1zu51uVe68w9u9PepWTPOeecbiuUE7SzhdUjQKCfBKxM9NM0HAsBAosmEPeNiEt+xifKsQ/e5V4XbRQD/8K9S8muX7/eCdoDP00NECAwFwEnYM9Fze8QIDCwAnHibGxNiU+Q33333bZu3bqB7cWB94dAbH16+OGHu2AaATVO0D58+HB/HJyjIECAwDwLCBPzDKw8AQL9IRDbmuKSr9ddd1179dVXuy0py5cv74+DcxRDIRDBNG54t2XLlm6VwrkUQzFWTRAgcBIB50ycBMjTBAgMvkBsa4qtTOPj4+2ll17qViUGvysd9LNA76aHcS7Fzp07XfGpn4fl2AgQOGUB50ycMpUfJEBgWATiBNm4+s7KlSu7T42dIDssk+3vPnqrFPF+i211o6Oj/X3Ajo4AAQJzFLDNaY5wfo0Agf4XiE+EN27c2K1K7Nq1yyVf+39kQ3WEcS5F3Ozuvffe6+5Lcdddd7UjR44MVY+aIUCAgDDhPUCAwNAJxPkRDz74YHe1pv3797e4d4QvAoslsGnTpjY2Nta9/ObNm1tsgfJFgACBYRFwzsSwTFIfBAh0AlPPj4itJe5O7I3RLwJT722ye/duIbdfBuM4CBA4ZQHnTJwylR8kQGAQBeIT36nnRwgSgzjF4T3m2PYUFwKI1bKlS5cOb6M6I0CglICViVLj1iyB4RWIE63j/Ah3sx7eGeuMAAECBBZXwMrE4vp7dQIE5kmgd6J13D/C3aznCVlZAgQIECAwjcCSaR7zEAECBAZGIPah79u3r9s6smHDhoE5bgdKgAABAgSGQcA2p2GYoh4IECBAgAABAgQIzLOAbU7zDKw8AQIECBAgQIAAgUoC7jNRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJKAMFFp2nolQIAAAQIECBAgkCggTCRiKkWAAAECBAgQIECgkoAwUWnaeiVAgAABAgQIECCQKCBMJGIqRYAAAQIECBAgQKCSgDBRadp6JUCAAAECBAgQIJAoIEwkYipFgAABAgQIECBAoJLAyMTExEQ0PDIyUqlvvRIgQIAAAQIECBAgMAeB/+JD95tLer8/9cHeY74TIECAAAECBAgQIEDgRAK2OZ1IxuMECBAgQIAAAQIECMwoIEzMyONJAgQIECBAgAABAgROJCBMnEjG4wQIECBAgAABAgQIzCggTMzI40kCBAgQIECAAAECBE4kIEycSMbjBAgQIECAAAECBAjMKPB/FlAGW067S60AAAAASUVORK5CYII="></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The skier reaches point C with a speed of 8.2 m s<sup>–1</sup>. She stops after a distance of 24 m at point D.</p>
<p>Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the impulse required from the net to stop the skier and state an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{v^2} = 0.24\,{\text{gh}}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>0.24</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>gh</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 11.9">
<mi>v</mi>
<mo>=</mo>
<mn>11.9</mn>
</math></span> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Award GPE lost = 65 × 9.81 × 30 = «19130 J»</em></p>
<p><em>Must see the 11.9 value for MP2, not simply 12.</em></p>
<p><em>Allow g = 9.8 ms<sup>–2</sup>.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>internal energy is the total KE «and PE» of the molecules/particles/atoms in an object</p>
<p>temperature is a measure of the average KE of the molecules/particles/atoms</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if there is no mention of molecules/particles/atoms.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arrow vertically downwards from dot labelled weight/W/mg/gravitational force/F<sub>g</sub>/F<sub>gravitational</sub> <strong><em>AND</em></strong> arrow vertically upwards from dot labelled reaction force/R/normal contact force/N/F<sub>N</sub></p>
<p>W > R</p>
<p> </p>
<p><em>Do not allow gravity.</em><br><em>Do not award MP1 if additional ‘centripetal’ force arrow is added.</em><br><em>Arrows must connect to dot.</em><br><em>Ignore any horizontal arrow labelled friction.</em><br><em>Judge by eye for MP2. Arrows do not have to be correctly labelled or connect to dot for MP2.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>= 468 «N»</p>
<p>W/640 N (weight) is larger than the centripetal force required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>recognition that centripetal acceleration is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>a = 7.2 «ms<sup>–2</sup>»</p>
<p><em>g</em> is larger than the centripetal acceleration required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p>recognition that to lose contact with the ground centripetal force ≥ weight</p>
<p>calculation that v ≥ 14 «ms<sup>–1</sup>»</p>
<p>comment that 12 «ms<sup>–1</sup>» is less than 14 «ms<sup>–1</sup>» so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 4</strong></em></p>
<p>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>calculation that reaction force = 172 «N»</p>
<p>reaction force > 0 so the skier does not lose contact with the ground</p>
<p> </p>
<p> </p>
<p><em>Do not award a mark for the bald statement that the skier does not lose contact with the ground.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>0 = 8.2<sup>2 </sup>+ 2 × <em>a</em> × 24 therefore <em>a</em> = «−»1.40 «m s<sup>−2</sup>»</p>
<p>friction force = <em>ma </em>= 65 × 1.4 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br><em>KE</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> = 0.5 x 65 x 8.2<sup>2</sup> = 2185 «J»</p>
<p>friction force = KE/distance = 2185/24 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«76 × 9.6»= 730<br>Ns <em><strong>OR</strong></em> kg ms<sup>–1</sup></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>safety net extends stopping time</p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta p}}{{\Delta t}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> therefore <em>F</em> is smaller «with safety net»</p>
<p><em><strong>OR</strong></em></p>
<p>force is proportional to rate of change of momentum therefore <em>F</em> is smaller «with safety net»</p>
<p> </p>
<p><em>Accept reverse argument.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A chicken’s egg of mass 58 g is dropped onto grass from a height of 1.1 m. The egg comes to rest in a time of 55 ms. Assume that air resistance is negligible and that the egg does not bounce or break.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude of the average decelerating force that the ground exerts on the egg.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the egg is likely to break when dropped onto concrete from the same height.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>initial momentum = <em>mv</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 0.058 \times 0.63} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mn>0.63</mn>
</msqrt>
</math></span> «= 0.27 kg m s<sup>−1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>mv</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.058 \times \sqrt {2 \times 9.81 \times 1.1} ">
<mn>0.058</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>1.1</mn>
</msqrt>
</math></span> «= 0.27 kg m s<sup>−1</sup>» ✔</p>
<p>force = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{change in momentum}}}}{{{\text{time}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>change in momentum</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>time</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.27}}{{0.055}}">
<mfrac>
<mrow>
<mn>0.27</mn>
</mrow>
<mrow>
<mn>0.055</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>4.9 «N» ✔</p>
<p><em>F − mg</em> = 4.9 so <em>F</em>= 5.5 «N» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>«<em>E</em><sub>k</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>mv<sup>2</sup> = 0.63 J» v = 4.7 m s<sup>−1</sup> ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta v}}{{\Delta t}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.7}}{{55 \times {{10}^{ - 3}}}}">
<mfrac>
<mrow>
<mn>4.7</mn>
</mrow>
<mrow>
<mn>55</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «85 m s<sup>−2</sup>» ✔</p>
<p>4.9 «N» ✔</p>
<p><em>F − mg</em> = 4.9 so <em>F</em>= 5.5 «N» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>concrete reduces the stopping time/distance ✔</p>
<p>impulse/change in momentum same so force greater</p>
<p><em><strong>OR</strong></em></p>
<p>work done same so force greater ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>concrete reduces the stopping time ✔</p>
<p>deceleration is greater so force is greater ✔</p>
<p> </p>
<p><em>Allow reverse argument for grass.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234.</span></p>
<p><span style="background-color: #ffffff;">The following data are available.</span></p>
<p style="text-align: left; padding-left: 30px;"><span style="background-color: #ffffff;">Energy released in decay 4.27 MeV<br>Binding energy per nucleon for helium 7.07 MeV<br>Binding energy per nucleon for thorium 7.60 MeV</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Radioactive decay is said to be “random” and “spontaneous”. Outline what is meant by each of these terms.</span></p>
<p><span style="background-color: #ffffff;">Random: </span></p>
<p><span style="background-color: #ffffff;">Spontaneous:</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the binding energy per nucleon for uranium-238.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>kinetic</mi><mo> </mo><mi>energy</mi><mo> </mo><mi>of</mi><mo> </mo><mi>alpha</mi><mo> </mo><mi>particle</mi></mrow><mrow><mi>kinetic</mi><mo> </mo><mi>energy</mi><mo> </mo><mi>of</mi><mo> </mo><mi>thorium</mi><mo> </mo><mi>nucleus</mi></mrow></mfrac></math>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em>random:</em><br>it cannot be predicted which nucleus will decay<br><em><strong>OR</strong></em><br>it cannot be predicted when a nucleus will decay ✔<br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: OWTTE</em><br></span></p>
<p> </p>
<p><span style="background-color: #ffffff;"><em>spontaneous:</em><br>the decay cannot be influenced/modified in any way ✔<br></span></p>
<p><span style="background-color: #ffffff;"><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">NOTE: </span><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">OWTTE</span><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">234 × 7.6 <em><strong>OR </strong></em> 4 × 7.07 ✔</span></p>
<p><em>BE</em><sub>U </sub>=<span style="background-color: #ffffff;"><span style="background-color: #ffffff;">« 234<span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"> ×</span> 7.6<span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"> + 4 × 7.07 – 4.27 =</span>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1802</mn></math> « MeV » ✔</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><msub><mi>E</mi><mi mathvariant="normal">U</mi></msub></mrow><mi>A</mi></mfrac><mo>=</mo><mo>«</mo><mfrac><mn>1802</mn><mn>238</mn></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>57</mn></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">« MeV » ✔</span></span></span></p>
<p><span style="font-size: 14px;"><em><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><span style="text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-variant: normal;font-weight: 400;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;"> NOTE: Allow ECF from MP2<br>Award <strong>[3]</strong> for bald correct answer<br>Allow conversion to J, final answer is 1.2 <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">×</span> 10<sup>–12</sup></span></span></span></em></span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">states or applies conservation of momentum ✔</span></p>
<p><span style="background-color: #ffffff;">ratio is «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>E</mi><mrow><mi mathvariant="normal">k</mi><mi>α</mi></mrow></msub><msub><mi>E</mi><mi>kTh</mi></msub></mfrac><mo>=</mo><mfrac><mstyle displaystyle="true"><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac></mstyle><mstyle displaystyle="true"><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>Th</mi></msub></mrow></mfrac></mstyle></mfrac><mo>=</mo><mfrac><mn>234</mn><mn>4</mn></mfrac></math>» 58.5 <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span><br></span></p>
<p><em> NOTE: Award<strong> [2]</strong> for bald correct answer</em></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A charged particle, P, of charge +68 μC is fixed in space. A second particle, Q, of charge +0.25 μC is held at a distance of 48 cm from P and is then released.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The diagram shows two parallel wires X and Y that carry equal currents into the page.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Point Q is equidistant from the two wires. The magnetic field at Q due to wire X <strong>alone </strong>is 15 mT.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the force on Q at the instant it is released.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the motion of Q after release.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram draw an arrow to show the direction of the magnetic field at Q due to wire X <strong>alone</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude and direction of the resultant magnetic field at Q.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» 18 «V» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>68</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>48</mn><mn>2</mn></msup></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>66</mn></math> «N» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer. </em></p>
<p><em>Allow symbolic k in substitutions for <strong>MP1</strong>. </em></p>
<p><em>Do <strong>not</strong> allow <strong>ECF</strong> from incorrect or not squared distance.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Q moves to the right/away from P «along a straight line»</p>
<p><em><strong>OR</strong></em></p>
<p>Q is repelled from P ✓</p>
<p><br>with increasing speed/Q accelerates ✓</p>
<p>acceleration decreases ✓</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<p>arrow of any length as shown ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«using components or Pythagoras to get» <em>B</em> = 21 «mT» ✓</p>
<p>directed «horizontally» to the right ✓</p>
<p> </p>
<p><em>If no unit seen, assume</em> mT.</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The Moon has no atmosphere and orbits the Earth. The diagram shows the Moon with rays of light from the Sun that are incident at 90° to the axis of rotation of the Moon.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another black body is on the Moon’s surface at point B.</p>
<p>Outline, without calculation, why the aximum temperature of the black body at point B is less than at point A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why a force acts on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why this force does no work on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> = <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {\frac{{1360}}{\sigma }} \right)^{0.25}}">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1360</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>0.25</mn>
</mrow>
</msup>
</mrow>
</math></span> </span>✔</p>
<p>390 «K» ✔</p>
<p><em>Must see 1360 (from data booklet) used for MP1.</em></p>
<p><em>Must see at least 2 s.f</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy/Power/Intensity lower at B ✔</p>
<p>connection made between energy/power/intensity and temperature of blackbody ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(28 %) of sun’s energy is scattered/reflected by earth’s atmosphere <em><strong>OR</strong></em> only 72 % of incident energy gets absorbed by blackbody ✔</p>
<p><em>Must be clear that the energy is being scattered by the atmosphere.</em></p>
<p><em>Award <strong>[0]</strong> for simple definition of “albedo”</em>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gravitational attraction/force/field «of the planet/Moon» ✔</p>
<p><em>Do not accept “gravity”</em>.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the force/field and the velocity/displacement are at 90° to each other<em><strong> OR</strong></em> there is no change in GPE of the moon ✔</p>
<p><em>Award <strong>[0]</strong> for any mention of no net force on the satellite.</em></p>
<p><em>Do not accept acceleration is perpendicular to velocity.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. A significant portion attempted to apply Wein’s Law and simply stated that a particular wavelength was the peak and then used that to determine the temperature. Some did use the solar constant from the data booklet and were able to calculate the correct temperature. As part of their preparation for the exam candidates should thoroughly review the data booklet and be aware of what constants are given there. As with all “show that” questions candidates should be reminded to include an unrounded answer.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This is question is another example of candidates not thinking beyond the obvious in the question. Many simply said that point B is farther away, or that it is at an angle. Some used vague terms like “the sunlight is more spread out” rather than using proper physics terms. Few candidates connected the lower intensity at B with the lower temperature of the blackbody.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was assessing the understanding of the concept of albedo. Many candidates were able to connect that an albedo of 0.28 meant that 28 % of the incident energy from the sun was being reflected or scattered by the atmosphere before reaching the black body.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10<sup>–7</sup> m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the speed of the train.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In another experiment the student replaces the light sensor with a sound sensor. The train travels away from a loudspeaker that is emitting sound waves of constant amplitude and frequency towards a reflecting barrier.</p>
<p><img 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"></p>
<p>The sound sensor gives a graph of the variation of output voltage with time along the track that is similar in shape to the graph shown in the resource. Explain how this effect arises.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«light» superposes/interferes</p>
<p>pattern consists of «intensity» maxima and minima<br><em><strong>OR</strong></em><br>consisting of constructive and destructive «interference»</p>
<p>voltage peaks correspond to interference maxima</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} = \frac{{6.3 \times {{10}^{ - 7}} \times 5.0}}{{1.5 \times {{10}^{ - 3}}}} = ">
<mi>s</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>λ</mi>
<mi>D</mi>
</mrow>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>5.0</mn>
</mrow>
<mrow>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2.1 x 10<sup>–3 </sup>«m» </p>
<p> </p>
<p><em>If no unit assume m.</em><br><em>Correct answer only.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct read-off from graph of 25 m s</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{t} = \frac{{2.1 \times {{10}^{ - 3}}}}{{25 \times {{10}^{ - 3}}}} = ">
<mfrac>
<mi>x</mi>
<mi>t</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 8.4 x 10<sup>–2</sup> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow ECF from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>«reflection at barrier» leads to two waves travelling in opposite directions</p>
<p>mention of formation of standing wave</p>
<p>maximum corresponds to antinode/maximum displacement «of air molecules»<br><em><strong>OR</strong></em><br>complete cancellation at node position</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge per unit area on the surface of the wall is<em> σ</em>. It can be shown that the electric field strength <em>E</em> due to the charge on the wall is given by the equation</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mi>σ</mi><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac></math>.</p>
<p>Demonstrate that the units of the quantities in this equation are consistent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.</p>
<p>Determine the horizontal force that acts on the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge on the ball is 1.2 × 10<sup>−6 </sup>C. Determine <em>σ</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The centre of the ball, still carrying a charge of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mtext>C</mtext></math>, is now placed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math> from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.</p>
<p>P is the point on the line joining the charges where the electric field strength is zero.<br>The distance PQ is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>22</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Calculate the charge on Q. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies units of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>C</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>×</mo><mfrac><mrow><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><msup><mi>C</mi><mn>2</mn></msup></mfrac></math> seen and reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>N C</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <strong>✓</strong></p>
<p> </p>
<p><em>Accept any analysis (eg dimensional) that yields answer correctly</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on the ball<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>T</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>30</mn></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>cos</mi><mo> </mo><mn>30</mn></mrow></mfrac></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>«</mo><mo>=</mo><mi>m</mi><mi>g</mi><mo> </mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>×</mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow g = 10 N kg<sup>−1</sup></em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer.</em></p>
<p><em>Award <strong>[1max]</strong> for an answer of zero, interpreting that the horizontal force refers to the horizontal component of the net force.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>»</mo></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>85</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em> <br>Allow <strong>ECF</strong> from the calculated F in (b)(i)</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>Q</mi><mrow><mn>0</mn><mo>.</mo><msup><mn>22</mn><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>18</mn><mn>2</mn></msup></mrow></mfrac></math> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>+</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><mtext>C</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p>2sf <strong>✓</strong></p>
<p><em><br>Do not award <strong>MP2</strong> if charge is negative </em></p>
<p><em>Any answer given to 2 sig figs scores <strong>MP3</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br>