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<h2>SL Paper 2</h2><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><div class="specification">
<p>A sample of vegetable oil, initially in the liquid state, is placed in a freezer that transfers thermal energy from the sample at a constant rate. The graph shows how temperature <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> of the sample varies with time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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" width="515" height="299"></p>
<p>The following data are available.</p>
<p style="padding-left: 30px;">Mass of the sample <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo> </mo><mi>kg</mi></math><br>Specific latent heat of fusion of the oil <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>130</mn><mo> </mo><mi>kJ</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br>Rate of thermal energy transfer <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>15</mn><mo> </mo><mi mathvariant="normal">W</mi></math></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the thermal energy transferred from the sample during the first <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes.</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>Estimate the specific heat capacity of the oil in its liquid phase. State an appropriate unit for your answer.</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 sample begins to freeze during the thermal energy transfer. Explain, in terms of the molecular model of matter, why the temperature of the sample remains constant during freezing.</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>Calculate the mass of the oil that remains unfrozen after <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes.</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 class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>15</mn><mo>×</mo><mn>30</mn><mo>×</mo><mn>60</mn><mo>»</mo><mo>=</mo><mn>27000</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>×</mo><mi>c</mi><mo>×</mo><mfenced><mrow><mn>290</mn><mo>-</mo><mn>250</mn></mrow></mfenced></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2100</mn></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">K</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi><mo> </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo> </mo><msup><mo> </mo><mn>0</mn></msup><msup><mi mathvariant="normal">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> ✓</p>
<p><span class="fontstyle0"><em><br>Allow any appropriate unit that is</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>e</mi><mi>n</mi><mi>e</mi><mi>r</mi><mi>g</mi><mi>y</mi></mrow><mrow><mi>m</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>×</mo><mi>t</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi></mrow></mfrac></math></span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«intermolecular» bonds are formed during freezing </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0"><br>bond-forming process releases energy<br></span><span class="fontstyle3"><em><strong>OR</strong></em><br></span><span class="fontstyle4">«</span><span class="fontstyle0">intermolecular</span><span class="fontstyle4">» </span><span class="fontstyle0">PE decreases </span><span class="fontstyle4">«</span><span class="fontstyle0">and the difference is transferred as heat</span><span class="fontstyle4">» </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle4">«</span><span class="fontstyle0">average random</span><span class="fontstyle4">» </span><span class="fontstyle0">KE of the molecules does not decrease/change </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle2"><br></span><span class="fontstyle0">temperature is related to «average» KE of the molecules «hence unchanged» </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle5">To award MP3 or MP4 molecules/particles/atoms must be mentioned.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">mass of frozen oil <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>27</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>130</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">unfrozen mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>32</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mo>«</mo><mi>kg</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></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(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.</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>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;" src="data:image/png;base64,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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>A pipe is open at both ends. A first-harmonic standing wave is set up in the pipe. The diagram shows the variation of displacement of air molecules in the pipe with distance along the pipe at time <em>t</em> = 0. The frequency of the first harmonic is <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A transmitter of electromagnetic waves is next to a long straight vertical wall that acts as a plane mirror to the waves. An observer on a boat detects the waves both directly and as an image from the other side of the wall. The diagram shows one ray from the transmitter reflected at the wall and the position of the image.</p>
<p><img 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a4B5wUWYG+c2l8dfT6171uoJXvbOms06l1Doe4a8L2JGtvOskZdozHd2svnGrW7XJOvOCPK9WFEOzzwtL5LUw80vZ4mnpmv6f2f06KT28vn662hay7T7SV3qKBb5HQnOz5bOcPn6el5WfpoXD/nw+k7bp6Kjv2F/vj7PGUfaKG7RLa5SGMmdpfajdHkEcc3MN3pKHW9fKnKHu2kTnNODtSn2490Z8fb9cgfZgR/KQTrPWCM8tspbOTFskpdbhF+vxPUpy0fjXo+IbyMAAIIIIBAhgh00ZkFf9O6x67XzaPckQibEnSX7lrzqB4Z4A4DtNWJo2bplrp9vmwrGqIaZPWaqlsKbEqSbe3UtvagKhXreSKLzFabgb/Xn9bcpbumOLmjgjsMUd7tT+lPv75EJzmXK7bfb/Xoyjkh7ZCyL/mp5qx8QM9c0FVZWafrktt+q1/XlTNEefP+qNV/+b7OtdZETb5jp8tWm363696V4XXIvuQWzVv5S93VzxdZaU8+P8Lv9x921Ws3dLN5Yd7a7MZ2wzR2wy+0fHkwa4C3AGgtAggggAACCCCAAAKNCkTGCnwN3SgZOyCAAAIIIIAAAggggEB9AgQU9cnwOgIIIIAAAggggAACCDQqwJSnRonYAQEEEEAAAQQQQAABBFwBpjy5EvxEAAEEEEAAAQQQQACBuAWY8hQ3IQUggAACCCCAAAIIIOBdAQIK7/Y9LUcAAQQQQAABBBBAIG4BAoq4CSkAAQQQQAABBBBAAAHvChBQeLfvaTkCCCCAAAIIIIAAAnELEFDETUgBCCCAAAIIIIAAAgh4V4CAwrt9T8sRQAABBBBAAAEEEIhbgIAibkIKQAABBBBAAAEEEEDAuwIEFN7te1qOAAIIIIAAAggggEDcAgQUcRNSAAIIIIAAAggggAAC3hUgoPBu39NyBBBAAAEEEEAAAQTiFiCgiJuQAhBAAAEEEEAAAQQQ8K4AAYV3+56WI4AAAggggAACCCAQtwABRdyEFIAAAggggAACCCCAgHcFCCi82/e0HAEEEEAAAQQQQACBuAUIKOImpAAEEEAAAQQQQAABBLwrQEDh3b6n5QgggAACCCCAAAIIxC1AQBE3IQUggAACCCCAAAIIIOBdAQIK7/Y9LUcAAQQQQAABBBBAIG4BAoq4CSkAAQQQQAABBBBAAAHvChBQeLfvaTkCCCCAAAIIIIAAAnELEFDETUgBCCCAAAIIIIAAAgh4V4CAwrt9T8sRQAABBBBAAAEEEIhbgIAibkIKQAABBBBAAAEEEEDAuwIEFN7te1qOAAIIIIAAAggggEDcAgQUcRNSAAIIIIAAAggggAAC3hUgoPBu39NyBBBAAAEEEEAAAQTiFiCgiJuQAhBAAAEEEEAAAQQQ8K4AAYV3+56WI4AAAggggAACCCAQtwABRdyEFIAAAggggAACCCCAgHcFCCi82/e0HAEEEEAAAQQQQACBuAUIKOImpAAEEEAAAQQQQAABBLwrQEDh3b6n5QgggAACCCCAAAIIxC1AQBE3IQUggAACCCCAAAIIIOBdAQIK7/Y9LUcAAQQQQAABBBBAIG4BAoq4CSkAAQTSWaC2fKZG+r6tmeWfOs2IfJ7ObaPuCCCAAAIIJEKAgCIRypwDAQQQQAABBBBAAIEMFSCgyNCOpVkIIIAAAggggAACCCRCgIAiEcqcAwEE4hSo1tb7vyZf7s1aVFUbLKtG+18co1zfAI16seJQ+VWLNLvjacHXPtZ7qwt154Rj5fP5Av8Nn6OZK8oVcsShY3mEAAIIIIAAAk0WIKBoMhkHIIBA4gXa6sSzh2tI5Yt69pV/B0+/U6+98IYq9YHe2V6hGufVGu1/5Tkt0kiNHeDTgXXXKP8b5dpyzRvaW1Wlqqr3tXn2u3oz/0bNfKUy8c3gjAgggAACCGSgAAFFBnYqTUIgEwWyeo3RZWf981DwULtD29ZKA4bmqOKJNVrrDFwEggxNPV/f8u3SK089rw1Tr9Dtg49VtoNylLqc/0NNPGut1q7fEwxCMlGLNiGAAAIIIJA4gcDf2MSdjzMhgAACzRPIOl15l3fR9U+v1topfTRk63P646ZJuvbPH+u333hb5dW1ytMqPf/g0Rr0eH+1VyedN3+X9mqPNj87Xw+V16hz5w9U/vCjWvBmG3Ue37xqcBQCCCCAAAIIhAswQhHuwTMEEEhZgeC0p9XP69mtH+nAzrf15tTzdfagsfp2ryXOVKja9zfrf53pTh0k1ejAptmanNtbgya/pNK2udqzp6d63rtEvx54QBVvv8c6ipTtayqGAAIIIJBOAoxQpFNvUVcEPC5g057G9btCz+z8p177y3q179tFbbO+qOOGSO9s36kt21bp9am/0h98WVJtiZ68bpH+fP5DWr3wUp3kfn1StUhzttRIp3kck+YjgAACCCDQQgIEFC0ESTEIIJAAgaweOi6vRmsfvlMP/OUsjS77qrKUrTNH9FfFbb/Uz/dWatDd/dXZqlL9tspflzpd3k+93WBCUm31h9qbgKpyCgQQQAABBLwiEPJn1itNpp0IIJC+At115oWnq03xMhW36aW+x35BUrbadO+pAW8Wa2X1RI0dYNOdJPmG66IpR2rP0if08Hv/dV6q3b1Yv7nxHj1BgqeAEf9HAAEEEECgBQQIKFoAMTWL2KMty6/WmPs2p38mm9qX9dCFHdVx9kva42Db3Pjfac6Yh1Tq3pJAKdLe6pf19PW9g/c8+LZmln+amh+PtK1VtnIGjFF+Oyl7/HCNtqlNkmwq1OUDs6V+J6hPW/fX2nH6+nW/1q/7L9bMvkc7fXL0Te/ro/EP66Gr26atABVHAAEEEEAg1QSO8Pv9/shK2Q2gqqqqIl/meToJ2M29jp+tZfPKtHFqn2DKzHRqQEN13aaXZg3T2A2/0PLlU5Rn148p0V67+downXX7MM0pu0sF3ezbczYEEEAAAQQQQCCzBCJjBfervMxqJa1BIKkCOTq6LcuTktoFnBwBBBBAAAEEEiZAQJEw6gSeyLLY9J+pBTU12jNzoDrm3qxFVXv00qxu8g2fo6LbBirX55PPeb1Wqt2sVxZfocm5vuBUnVydMHORFm1yR6lsRKCbfCOLtLz0Js0+p2Ngv9zJumLFlpDUm3tUvmLmofd9EeXYKELHjuo99wmtdOvg7POIlu3+l7Ysv7KuDh2v+J2e2h2Y966QKU/7FByduL9aWn29RrUfoFFLorU3MBeqdvdTeqhuClJEfVSj/S+OUa5vpEb9Zlbw3AM06sWK6J1VXaoX7x2l4WZn/w2fo5krygPtd+r4VZ01a5tUea9m9mgfMkUrenG8igACCCCAAAIIZISATXmK3HJyciJf4nm6CVQu9N/YoYO/18LN/s+cuv+ff9UNXf05Oaf6ByxY7//Q/6l/R8lmf6V/t//VO/r4O0y61//krv8EWnlwg/+vN/Ty55x3t//Z6oN+v989tof/+B8/5S/Zb6995N/9/Dj/eTnf8E9at8/v93/mr147xX92hyn+H2+sDC9nxAP+EjukcqF/do8cf07OCP/FSzf7P/T7/Qd33+cvOLtDoF6FJf5Ntl/18/6F+Z39HaY87d9gzw/+3f/gBR38HW5c5X8/tC1uufbaYe31+w/uvMM/pUNf/wC3XP/7/s33DfZ36DDDf8dOa+tn/qoXvuHvkZPj7zDpEf/f9x/0H9y+2r/aaV+gCXX/d+tU5/SRf3fZdP+kDh38x89d57TF79/v3/L7U/05PW7yL6y0irMhgAACCCCAAAKZJxAZKzBCkRFhYRMa0W6Urhp/kjrpi+qe10e+qhV68pdf0qDvfFvjugbn/GedpHOvHK0hr61Rya7gKIGdot13VPCzscpzFr0epS4DL9KZ2WVau36PavWJ3vvH63pzwFCN7eMLVCjrJA2fv0VVK4PrHILVzJ42Sw+M76NOtpi2y0U6f8CR0pBrddeNeeprn8g2g3X2149RzV9f15rqulXXTWik7bpNf//N7/TUgBsOlavO6jNtsZ6c8if98rel2iP3499bg75zsc5pm6WsHoM1uG5Rr3vKGu1fc69mP3+pbrj9qqDTUeoy5B799vGhqrnjLhWy+NrF4icCCCCAAAIIeEzAvaLyWLNpbp2Ab6rm7f1fLR9Urj8VFqqwsFCP3ztKFwxcpNV1O9XzoG1P9TlDzh2H/6Uvq8upZ+jM1QtU+MTL+lNhsUqbHQzUc76mvFy1Si88Ua3s/l/ViWGf8k7q1rOTah5fpeKqgzGWuFOvvfCGagacoWFdQhdaB9KV9tM2le88EGNZ7IYAAggggAACCGSWQNilVmY1jdbEJrBH5QuGKLfbKE36a5UqjjlG26qn67cvfE9DmnShnKU2A3+vP62Zru9W3Kl75k7UqG7tw9cZSPIfyFannl2c0YnY6hffXjULxqq3u+bB+dktsM6hKcXW7tD2f3zSwBEf6J3tFWruWEoDBfMWAggggAACCCCQ8gKkokn5LmrdCtaWz9f1sz9W10Xr9e5lucH0srZY+X5tknRyk06frTb9vqfx9t8Ppdrdy/TMQ4Wamf+Syp9aoeUDmlRY3Dtb8NL5robS5tZofyxnyeqh3FOPlDbUt/MxOjG3U90Eqvr24nUEEEAAAQQQQCATBRihyMRejblNNTqw821tUm8NPuWYkHtV/FfV+6pjLqW+HbO6XqJx11yl8dnvJv4b/OBdkivWbNKWsKGD9/RaYV/5Rj6o0tpYP/6BuzNnv/K6SoJ3XA602fU7Tn26t6mPgdcRQAABBBBAAIGMFoj1iiqjETKycW17qvdpn3OalrW/QvvDLqrdFgfuOjw++69a9kCJNjv7fKz3Vt+gm2e9oUp3t5h+fqKt939NvuE3q3Czm252j7aufE5rNV6TRxzfgt/gB9ZBBKr1qSoqaqSI9lbUHqev/+gHumTZTzTlztJg2/Zo6+PTNHtuT13y80uVlxUVJUprs5Uz+Iead9Ez+uXNC4PpbO1u3TfrmvFlyr5ppgr6fCnKcbyEAAIIIIAAAghkvgABRab2cdZZGnHjOeo2c6Dad/+Bfr61ntltvgn60fLva9wr4zWovd1fYYjGvjRUlz42S9OyP2uCzpHqNXWpXpyyS1tG9Ajez6K3Bq88WyP+fLNmtehdo9vqxNHT9IOPZ2lU+94auuwd1Ua0t3Drp8rqNku/KfmxrvrgymDbAvU5f+UCPTCgXRPaZpmnLtTU3z+px89aofv6HS2fr6O6XnOEOj1apnWzByRsTUjTKs3eCCCAAAIIIIBA6wscYZlxI08TeTvtyPd5jgACCKS6gP0es62qyh0xS/UaUz8EEEAAAQTSQyAyVmCEIj36jVoigAACCCCAAAIIIJCSAgQUKdktVAoBBBBAAAEEEEAAgfQQIKBIj36ilggggAACCCCAAAIIpKQAAUVKdguVQgABBBBAAAEEEEAgPQQIKNKjn6glAggggAACCCCAAAIpKUBAkZLdQqUQQAABBBBAAAEEEEgPAQKK9OgnaokAAggggAACCCCAQEoKEFCkRLdUB+4yPfJBlcZ68+aY6r1HW5ZfrTH3bVZNTPt7aadIm2Af5N6sRVUt2gleQqWtCCCAAAIIIOBBAQKKTO70qmI9OOlpbfn8EZncyua17TCbtup19Zuq2n67pvr4Z9E8VI5CAAEEEEAAAS8KcOXkxV6nzQgggEAKCdSWz9RI3wCNerEiUKvqUq28Nl+zyz8NPK99WQ9d2FEdZ7+kPSlT7z3a+vgYDff55PPlqvei8sNGgg9rV8rUnYoggAACLStAQNGynvWU9rHeW3uTZp/TUXarcp9vpEbd+6JKqxuaWhPbMbW7n9JD1/cOlvs1DbxtZaDcqkWa03+mFtTUaM/MgeroTOXZo5dmdZNv+BwV3TZQuVaXuik+e1S+YmYDddwWOHbkPD325ys1Odfa4XPKmr12t6o2/U53Tjg28FruZF255v2QP64f673VhYfeDx43c0W5gpcPAbfqUr3g1stnbXlIi6xtbh2rFtU6G/8AACAASURBVGl2x47qveBFrV0wKviH3KeOV9ytBZuqwuzDXXJ1wsxFWuTuE9Xm48C0M/dcTmkRfZA7WVes2BJeZ/esUS94gmZhZdZo/4tj1LHjTcGpVY3Y1L6sB8//SpSLlUDZhy6wIuoa02fMrTw/EUiuQFafu7Sy6hUtv6CTpBrtX3unpj1Se+h3SNY5+t4Le7V33nnqnNyq1p29tny+fvT9Hfpk0XrtrdquLVP7KLvu3cCD8HZFvMlTBBBAIIMECChavTM/1u4nRumUUbtVMXeD9lZVqWr39Rq7epK+ed0ybYwaU8R2TO2uQl3V//u6LesOLd+1T1W779RVm6YEym07VXPX36Vp2dnqfNc67XWm8nwSaO1rf9EjRy/S61X/0obF39U4379UvuBSDf1uRV0d9236js5fPUmjLrlHyw6EVHJ1kf7n7xdr6oZ9qtq3Ws+c/qwWXNRPx8+Tjp+/XVVVW7SuYKuWjb5N83f917k4OLDuGuV/o1xbrnkj0P6q97V59rt6M/9GzXylMlCn2jf0zLWXKf/tH+gP1paqv+iRTgt164Ph30ce0aZGe2b/Sre2u0t/NMt9q/XEVxZo9jUP1dUz4PIzLTjmAa3dV6WqqnVa3vNBzR52kwqtTr5oNgcjPgmBPhh80f9qw/QyvVu1T7tXHiN9d6zGPLn90IWOe1TW6Ro6rrtqHl+lYncNRtUqvfBEtVT5jja/bxa27dRrL7whTT1fo31SozZZpyvv8i7a8/RqrQ3pBlWt0vMPHq1B5/dXZ8X2eQlWgB8IINBiAl9Q+3ZfPiyQaLHiKQgBBBBIFwF/lC0nJyfKq7zULIHKhf4bO3Tw91q42f9ZaAHO61/zX/zCh36/f79/y+9P9eeMeMBfctDv9zflmB43+RdW2kG2feaveuEb/h45l/t/vPmTKOX8n3/VDV39OWHHuOfr6x/8xD+j1DFQ94P+aMdGnC9Yi4Obf+wfkXNWsG2B4zrcuMr/fvB958fBv/sfGH500CVQTocOM/x37PxPyF4R56xc6J/dI8cfXlZkHYLHuJZ1pUXU4zDjYB+4Ngf/7n/wgg4R56qv7MBJAu0O2vv9fnt+QYdL/Pnjuh7q/7B+j6iTW9cwm0A5I3K+4Z+0bl9wD9erIND3h7UluFvYudzCvfPTfo/xu6y5/e1+1n/nX1ky3X9Fj4Blznmz/Teu2R3+e2J/if+F317sPy/obfv8ePlmv/1mC2yf+as3LvQvvK6X0x9Ov0Tsc+h3xgfB32HB8+UE/r1XRvv32Nh53X8X973gX3Pfofp1mPQr/30bK93K1fPzff/m5T/233h2h2CdR/gv/u0L/pL99rs2+LvCba/9dH9vRJR2qF2m4ZrO9T/63JQI013+yo33+ufldw6cr8cV/imr3wtx/si/u+yOQ+/bOSMMnVPvL/E/f+sAfw+nbqf6B9z6YMA9rH4f+XevKainbREN4CkCCCBQj0Dk31dGKFo18qvR/lee0+M1J+jE3E7h32K17ak+Z+zQ2r+u156wd2pjOqaq9g2VPbVT6neC+rR1uzFbORc8p+1Vf9Rdfb4UY8vcOp6iwaccE1YTOXWUKt5+T+ETimIs2tntOJ03f5f2zuunfc/OV2FhoR566DrNPvdSXf/qkc4eWcFv7WsGnKFhXb4QUngndetpUyAa2rLVpntP9dM2le88IPvm3kYFsvt/VSe6LM7hgbLCRhAaKLZ263N6Yl0bderZRYdqEGhL1copygsrO1BQVq8xuuysv6m49J+qVbXe+X+r9PrUK3XdBZ0cwwoF+naRRmrsgA6SGrexkrN6TdRVl76q4qffCMwfr12vvz72htrdeIku8Smmz0v4OE8DDectBEIFVhdo4sKTNHr1h87o46tXbdJrF03Tle7I4oEXtOj7l2n8qxdr+ibb531tvnW/Kr47VAPnvRKYHnhgmYq+e4sW9nlK79qoYt0I5f+o0F0jUXfOLOVc8IzeeuoctdMITV33gTPNyVf3fvBBLOeVFMuIZmTR0p5GRmy/7CRw2Lduqoaot/KeerdpyRySOsrLaObh/c0rCCDQEgJRLotaoljKCBfYotJxJwTXOQTXHrQfo+vWNZTMtTnHhJ81tmefaM+2HQpOPIp6SM36f2pj7VGB98ICmKi7R7xYowObZmtybm8NmvySStvmas+enup57xL9euCBOIOViFOFPK1ZMFa9nfUqQW9fN501a1vIHq3wMGR60uraj7Vz03806PxBOvPs4Tpj0V9VXPWpYx2Y7mT/9Bq3cdaYZPXX+RPOkpwyalW7dbEWLhuqS77ZX53kzoNK1OelFdwoMnUF2k3SDbdfpXFdLdDvrF7jf6Obr34jGNzWav+aezX7+UtD9jlKXYbco98+PlQ1d9zlBAy1u9bob+8MVd45PYPB+VHqcuGTWtWkLz5CiWI7r3tE9rRZemB8n8C5s3rrrAt7q91ra1TiTMl09wr5WVWsh26uVO8Fv9DvBx/rfMmS1XWirr/vVk1781bNfnzr4VMeQw5v9GG776jgZ2OVZ18EufXRCE0uuPKQ89cHa0DNqyrdvN+ZJvnKU89rw9QrdHuwPtJR6nL+DzXxrLVau36PamzdyapbdNVz1hfjdY7zJVNn9Zm2WA9d3fZQlaqW6J7p69VpXkFd29TmQk2971ZNXXarblwVtqrt0HE8QgABBBoRiFxD1sjuvN08Afum7ZEGRg2qZX82wrdGjql9OXz3Zj87Up2P66F2DRxv3/aflPWx/reBfep9q7ZMT163SH8+/yGtXnipTnJDWFsYvaVGOq3eI5v9hv+ArRsp08YoiyTrCm3+kEtdEYc/aKsTzx6ugQXvaPvOZ7X+0ZPVZ1obZR3bV6fpeW3evVFHPFSpQb+wdQ+SYrbJVs6AMZqq3+nZV6br7G2rtHrItbq5l41CuUFpI5+XwyvLKwg0LtDvtKijhjW3r1LxTf10/AtvqGbAJRH7uKOGJc6oYdbgwRr+te+r8KFijRmwU2/3naKp/Q4bc2i8LsE9vqjtzjqkxs6rY6MVGV43HTaSe2jEdlwDI7YV6qOvRCu+VV4LjmRqjzY/O18Pldeoc+cPVP7wo1rwZht1Hi8dGuWN7IvQUd6DdaOZJ9czYr7IRswvSJ2F763CSaEIINAqAu7lXasUTqGBC8Hx2W9pzVsf1F36OS4HntL8vED2Hvc75oBXlnPx2OgxwUXA2vSuykOyRQXSFAZSGIaXW19vNFDH6rdV/rqcaT/N/vPvljG4n3qHfNpqqz/U3mCV/qNcnXnh6cp+5Z2wtkgV2vV2E78x8w3XRVOOVMWaTdoSBvCeXivsK1+MNw+06UuXB0dQDtUgePM737c187CpGsHec4KHZXp4+u+06IyLNdYu+q1Ok1/Vsv+5Q3/YOiE43UlSDDZ1vea060Ot/ctiPf3Ee+r8rSEa5Hg20H8hnzE37KgrjwcIxCNgiQZ27dT2fwQTPUQt6wO9s71CNW3G6YbiP+mxPqVacc9tmjm4R4yZ7qIWqqzaHTGdN+yff/Siorwa24jtO80rPHC+pI/yMpoZpeN5CQEE4hQIucSLsyQOjy7gm6Br7ztGW6b9TN93U6lWv6ynf3qzbvviTZo3vpcO64SYjmmrE0dP0w+6L1Thbau02f7A1W7U3x4o1uozrw+U27anep/2OadeWfsrtL++P4K+0fre7e3C62hzlKf/VAu+9tPodYze2sNfDV7g71n6hB5+L5DpqHb3Yv3mxnv0RN08qyzlDL9FC0f/QYW/eDaYTtdyvP9It99ffXiZDb5ynL7+ox/okmU/0ZQ7SwMusrKmafbcnrrk55cG1j9E2FTUBpzqis46SxfdcJ6+tmC+rn5xtxMM1r63WA//4T11ummmCg77ZjN4pNPe/XqlbId0Wm5wHUcndevdThUvvKQNTnanYI/HZOPWqLsGjLtIX1tUqLmvnqvReV89tN4lhs8LQ5GuIz9bRKDdierbrbtyTw2sg4pe5jGH1o61zdPI7/1a817eq6p9a/Vi0Vd09Pxx+uZtf2/yfSVqs3rEdN7Dfq9Gr2TEq7GN2Iavz4oooqWfho5k7lup5T+coIKCH2hqj53aYqO8Td4Ca1OqnPUstqbl0H+plJa3yc3iAAQQSKpA837nJrXK6Xbyo9T18qUqe7STOs05WR1tXn+3H+nOjrfrkT/M0CVtonVBbMdkdZmm2/5YpJ/U/FCD2vvka3+xrq696VC5WWdpxI3nqNvMgWrf/Qf6+db6Littru0z4XXsereeHfIHLV92bT11jLUfjtPXr/u1ft1/sWb2PdpZR3L0Te/ro/EPh8/tzTpdl977uO5rf6cmdmsvn2+EvvvOJM2Y3SPWE9Xtl9Vtln5T8mNd9cGVARdfbw1eebbOX7lADwwITu6KsCnc6qZ1dYuxed6P6NHnT1Pf2/o7/da+75/0j+88p+JZA0IWarv7uz+7O6Mt7dQ7mNLVXg9MhRqidoct8o7Jxik6W23OmqTvDMxW9rhva4oz3ck9Z2yfF3dvfiIQs0DECKg7apg9frhG+74SHFl8XSXBLwsC5dbowM63tUnHqU/3NoefKquvBky8RZMubytbn9XUb/sPjWg28byH1yTKKw2M+LkjimGJGqIU0dIvueeNe5T3czGNfjcnRGnpJlMeAgikoUC0bFCRqaCi7cNrCLS+QCA9Y3ia2NY/K2fIDAEnPSkpsJvZmcEUpzk9/Mf/+KlgutT3/ZvvG+wPS+9c/bx/YX5nf4dJ9/qf3GUpny1F7I3+SR06+I+fu85JHRtInTrCf/FSN5XsZ/7qTXf4bzi9a12q6vD0qm6qZEvBfMBf9WGV/2Bk2tgYzmvptw9PM+2W7aa1jsbjtnPSodStwfPlnHe3/9nqQJruyDpHKyl8HzdtbDA9uHNAZNrrQClRjzvv5/6FuwNptQ/uesz/q2CK2brfjwdf9z89qWtYf21Z+o1AOt+6tLEf+Xf98ev+Dh1C2rb/7/6nLKVvSNuitYXXEEAAgVCByFgh2tfjaRgWUeX0FnDvHn2lZrp3s5bdQXq2bi/oqtHfOj1l7o6b3s7UHoEmCpyZr+n9n9Oik23UsLeGrrlMt5fcoYJuwfTOliHo90/q8bNW6L5+NgLZUV2vOUKdHi3TutmBkbysPrfqgZVn65znztUJTua1juo6Yov+9eNn9MC3cg9N3QupWlavKbrh6je1aGAXdf/uU3o1crpmDOcNKa6JD1tzxLaJVXF2b8lRXkYzm9MDHIMAAo0LHGHRRuRuPp/PmVcZ+TrPEWg1gdrNemXpXBXdtEzPBtdWZF/yU93w/QmaNaRL1IuOVqsLBWeEgP0es83miLM1VWCbXpo1TGM3/ELLl0e/70pTS2T/ZAhYIolhGvzur7RxHtmbktEDnBOBTBWIjBXqm1Sfqe2nXakq4MyrfkQDJkoPp2odqRcCCCCQkgI2ynupjht/tCaX/Ep3OWl5Q0Z5VzLKm5LdRqUQyCABpjxlUGfSFAQQQAABLwpkK2f4PK28p0Z7R1paXruh57E65ffHq8+fFx5KRuFFGtqMAAIJEWDKU0KYOQkCCCRagClPiRbnfAgggAACXhGInPLECIVXep52IoAAAggggAACCCDQCgIEFK2ASpEIIIAAAggggAACCHhFgIDCKz1NOxFAAAEEEEAAAQQQaAUBsjy1AipFtpxAaWmpSkpKNGzYMOXl5bVcwZSEAAIIhAhYemH7XfPWW29p9OjROuWUU0Le5SECCCCAQEMCLMpuSIf3kiZgf9zPO+88VVRUqGPHjtq/f7+OOOIIPfPMM/yhT1qvpNeJWZSdXv2VzNpaEHHRRRfpqKOOUk5Ojvbu3avjjz9ey5YtczImJbNunBsBBBBIRYHIRdkEFKnYS9RJ5557rv7973+rR48edRoffPCBc5OyLVu21L3GAwTqEyCgqE+G10MF7MuLvn37OgFE+/btnbcOHjyo7du367TTTtNjjz0WujuPEUAAAQQk58uW0BvHsoaCj0XKCezYsUPl5eXq2rVrWN2OOeYYffrpp7JpUGwIIIBASwjYNCcbmXCDCSvzc5/7nLp3764///nPLXEKykAAAQQyXoCAIuO7OP0aaAGF/XG3P+qR25e+9KXIl3iOAAIINFvApjvZNKfI7fOf/3zkSzxHAAEEEKhHgICiHhheTp6ALYbcvXu3Pvvss7BK2DQEW0sROg0qbAeeIIAAAk0UsIQPtmYicvvoo4/05S9/OfJlniOAAAIIRBEgoIiCwkvJFbC571OmTNE777xTF1RYcLF582b179+fgCK53cPZEcgoAcseZ1Oe/u///k/2pYVtFkxs3LhRc+bMyai20hgEEECgtQRIG9taspQbl8Ddd9/tTENYuHCh88fdCjvzzDO1c+dOZ2G2u+A2rpNwMAIIICCpurpaJ598ssrKyhwPG5m4+eabde211+KDAAIIIBCDAFmeYkBil9QRmD59utavX1/3hz91akZNUk3ADTpDs1CkWh2pDwIIIIAAAukoYH9jQ/++MuUpHXvRw3W+7777nNZbYMGGAAIIIIAAAgggkHwBAork9wE1aKLAihUrnDvaFhYWNvFIdkcAAQQCArY+YvHixXAggAACCLSAAAFFCyBSRGIFbJht6dKlKioq4oIgsfScDYGMELAvI+z+E6NHj86I9tAIBBBAINkCLMpOdg9w/mYJWGpZCyry8/OdzE/2nA0BBBBoTMBGJezLCBvpdNfZNHYM7yOAAAIINCzACEXDPrybwgKW7nHu3Lm6+OKLZTfDY0MAAQQaE1i+fLnzZQRfQjQmxfsIIIBA7AJkeYrdij1TVMDN/MQ3jinaQUmqlvvtc2gWiiRVhdMigAACCCCQUQJkecqo7qQxJmCZn3Jzc0XmJz4PCCCAAAIIIIBA4gWY8pR4c87YCgIWVGzfvp2gohVsKRKBdBewLxvICpfuvUj9EUAglQUIKFK5d6hbzAJu5qfi4mIyP8Wsxo4IZL6ABRJ2M8wZM2ZkfmNpIQIIIJAkAbI8JQme07a8QI8ePZzMLbZI26ZA2aJtNgQQ8K4AGZ282/e0HAEEEivACEVivTlbKwtY5hbL/GTpZN96661WPhvFI4BAKgvY7wBLL01Gp1TuJeqGAAKZIECWp0zoRdpwmIBNc7BvJ8vKysg1f5iON14gy5M3+plWIoAAAggkXoAsT4k354xJECgoKNCwYcOce1Qk4fScEgEEEEAAAQQQ8IwAU54809Xea6hNfbKNdLLe63ta7F0BMjp5t+9pOQIIJE+AgCJ59py5lQVsOM5udldSUqKioqJWPhvFI4BAsgXI6JTsHuD8CCDgVQGyPHm15z3SbjedrGV+sscTJ070SMtpJgLeEiCjk7f6m9YigEBqCTBCkVr9QW1aQcAyvNiN7+bMmUPmp1bwpUgEUkGgqqrKGZEko1Mq9AZ1QAABrwkwQuG1Hvdoe0ePHi274LCRig0bNpD5yaOfA5qduQLcuC5z+5aWIYBA6gswQpH6fUQNW0jApjtZYGFBhQUXbAggkN4C9u+Y+82kdx9SewQQyAwB7kORGf1IK5ogMGrUKGeEYsmSJU04il3TTcDWzNhG8JhuPRd7fSdMmODszL/l2M3YEwEEEGgJAfsbG/r3lRGKllCljLQSsIuP7du3O2sq0qriVBYBBOoEbE2U/Tu29VFsCCCAAALJFWANRXL9OXsSBNzMT0OHDpUt4CTzUxI6gVMiEIdAcXGxLKuTpYV2R6LiKI5DEUAAAQTiFCCgiBOQw9NToEePHs7FSF5ennJzc2U/2RBAID0E2rVrR0an9OgqaokAAh4RYMqTRzqaZh4uYKMTdsO7/Px8FnYezsMrCKSsgH0BQHrYlO0eKoYAAh4UIKDwYKfT5EMCNt3J0k1OmzYtbHHRoT14hAACqSBgi/9KS0tToSrUAQEEEEAgQoApTxEgPPWeQEFBgXbs2OGkky0rK/MeAC1GIA0Epk+f7tSS6Ylp0FlUEQEEPCfACIXnupwGRxOYO3eu87J70RJtH15DAIHkCJDRKTnunBUBBBCIVYCAIlYp9stoAcsUYxljSkpKnHUVGd1YGodAGgm4GZ0WLFhARqc06jeqigAC3hJgypO3+pvWNiDgppO1O2nbY9LJNoDFWwgkSKB///6yqYiWmY0NAQQQQCA1BRihSM1+oVZJErDMMXajLJti8dZbbyWpFpwWAQRcAQskCCZcDX4igAACqSlAQJGa/UKtkigwevRo2ZoKG6kIva18EqvEqRHwlID9uyssLPRUm2ksAgggkM4CBBTp3HvUvdUEbLqTBRYEFa1GTMEI1CtgyRFIEVsvD28ggAACKSdAQJFyXUKFUkXApj7ZHXnJ/JQqPUI9vCDgZnRasmSJF5pLGxFAAIGMECCgyIhupBGtJWAXNdu3b3fWVLTWOSgXAQQCArZuafHixVq6dCkZnfhQIIAAAmkkQECRRp1FVRMv4GZ+sosc+48NAQRaT8AWX5PRqfV8KRkBBBBoLQHSxraWLOVmjIBd5Ng9KuwOvbm5uc7PjGkcDUEghQQsgLf/2BBAAAEE0kuAEYr06i9qmyQBSydbVFSk/Px80skmqQ84bWYKWEanCRMmZGbjaBUCCCDgEQFGKDzS0TQzfgHL/LRjxw5NmzbNGbHgm9T4TSkBAZIe8BlAAAEE0l+AEYr070NakECBgoIC2Z17LZ0sGwIIxCfgZnSyjGpsCCCAAALpK0BAkb59R82TJGA3vbONb1aT1AGcNiMEyOiUEd1IIxBAAAFHgICCDwICTRSwqU62SLukpMRZV9HEw9kdAQQk2bqknTt3ypIesCGAAAIIpLcAayjSu/+ofZIELKiwXPk29cke2/oKNgQQQAABBBBAwIsCjFB4sddpc4sI2DesNvfb5oHb9A02BBBoWMDN6GTJDdgQQAABBDJHgBGKzOlLWpIEgdGjR8sukmykYsOGDeTQT0IfcMr0EXDXHTHNKX36jJoigAACsQgwQhGLEvsg0ICATXeywMKCCgsu2BBA4HABMjodbsIrCCCAQKYIHOH3+/2RjbE54VwYRarwHIGGBUaNGuWMUCxZsqThHXk3IQL2e8w2fpclhLvBk1gfnHzyySorK2MRdoNSvIkAAgikh0BkrMAIRXr0G7VMAwELJLZv3+6sqUiD6lJFBBImYH94yOiUMG5OhAACCCRcgIAi4eScMFMF7KLJMj8tXrzY+S9T20m7EEAAAQQQQACBUAECilANHiMQp4AtNrV7VMyYMUOlpaVxlsbhCKSvgE1zGjp0KP8O0rcLqTkCCCAQswABRcxU7IhAbAKWTraoqEj5+fmkk42NjL0yUGDChAnKzc1VXl5eBraOJiGAAAIIhAoQUIRq8BiBFhKwzE/237Rp01gU3EKmFJM+ApYetrKy0rlPS/rUmpoigAACCDRXgICiuXIch0AjAnPnzlX//v1l39SyIeAlAbtxna0ncjNteanttBUBBBDwogBpY73Y67Q5YQI2j9zuT2GBhd1Vmy1xAu7FLGljE2fOmRBAAAEEvCFgf2ND/74yQuGNfqeVSRKwf3C2SLu4uNhZV5GkanBaBBBAAAEEEECg1QQIKFqNloIRCAi4QUVhYaETWOCCQKYJkNEp03qU9iCAAAJNEyCgaJoXeyPQLAHL/GRTnmyx6ltvvdWsMjgIgVQVIKNTqvYM9UIAAQQSI5CdmNNwFgQQGD16tGyxqq2p2LBhAwtW+UhkhICb0cnuFM+GAAIIIOBNAUYovNnvtDpJAnbDOwssLKgIXcyUpOpwWgTiFiCjU9yEFIAAAgikvQBZntK+C2lAOgqMGjVKdldtMj+1Xu+R5an1bCkZAQQQQMDbAmR58nb/0/oUEbDpIevXr9ecOXNSpEZUA4HYBWxUwv5jQwABBBBAwASY8sTnAIEkCFhkv2DBAi1evNj5LwlV4JQINEvApurl5+eTsaxZehyEAAIIZKYAU54ys19pVZoIWManvLw8lZaWyjJBsbWcAFOeWs4ytCSm64Vq8BgBBBDwpgBTnrzZ77Q6RQUsiCgqKnIWaZNONkU7iWrVCdgUvcrKSs2dO7fuNR4ggAACCCDAlCc+AwgkWWDixImy/6ZNm0bmpyT3BadvWMACYLvzuzv60/DevIsAAggg4BUBpjx5padpZ8oLWD5/W+i6fPnylK9rOlTQveglPW869BZ1RAABBBBIJwGmPKVTb1FXTwnYNBKbTmKBBRsCqSJARqdU6QnqgQACCKSuAFOeUrdvqJnHBCzat+kkxcXFzroKjzWf5qagABmdUrBTqBICCCCQggLZKVgnqoSAZwXcoMLupG03vrO7arMhkCyBCRMmqH///rI7vLMhgAACCCBQnwAjFPXJ8DoCSRKwha92B22b+hQt85Pdu4INgdYWIKNTawtTPgIIIJA5AgQUmdOXtCSDBGxkoqCgwEknG7mouLCwMGqgkUHNpykpIEBGpxToBKqAAAIIpIkAAUWadBTV9J6ATTOxwMKmP4UGFTYFpaSkxHsgtDihApbK2M2UldATczIEEEAAgbQTIKBIuy6jwl4SsKlP7dq1k00/cTf3ztruc34i0FICNsWOKXUtpUk5CCCAgHcECCi809e0NE0FlixZovXr19cFFcOGDWOEIk37MpWrbaNgdnNFSxPLhgACCCCAQFMECCiaosW+CCRBwKadLFiwwPnm2L49trnttnHhl4TOyOBTuhmdbO0OGwIIIIAAAk0RIKBoihb7IpAgAQsc7AKvtLTUOaO7QNbWVdi0FEYpEtQRHjlNUVGRc1NFu7kiGwIIIIAAAk0VIKBoqhj7I5AAAVuMbUGETUE5+eSTndEJuy+FXfjZIu0TTjihLthIQHU4RYYL2OfNbqrIIuwM72iahwACCLSSwBF+v98fWbb9UQnNKhP5Ps8RQCBxAjZa4a6jsMw71dXVWrt2rT755BNt2rQpcRVJszO5k98TOgAAIABJREFUF8f8LkuzjqO6CCCAAAIpLxAZKzBCkfJdRgW9LmBBxPLly51vkO3i+LHHHnOCid27d7OOwusfjjjaT0anOPA4FAEEEEAgTICAIoyDJwikroBNgbI0srYY+7LLLtMXvvAFXXfddalbYWqWsgIWmObn5xOQpmwPUTEEEEAgvQSY8pRe/UVtEagTsItCW19hWXlssTZbuABTnsI9Qp8NHTpUdoNEC1DZEEAAAQQQaKpA5JSn7KYWwP4IIJAaAvaP2RbS2iJtW7BtC2vZEGhMwBb220ZGp8akeB8BBBBAIFYBpjzFKsV+CKSggDsNavr06U462RSsIlVKMQELPMvKysjolGL9QnUQQACBdBZghCKde4+6IyA5IxO2rsJGKjZs2MCFIp+KBgVsNIsNAQQQQACBlhRghKIlNSkLgSQJ2BoK++bZggrSpCapE1L4tJbRyUax2BBAAAEEEGgNAQKK1lClTASSIOAusJ0zZ04Szs4pU1XAzejEyESq9hD1QgABBNJfgIAi/fuQFiBQJ2CLtNevX6/CwsK613jgbQEbtRo2bJiTDczbErQeAQQQQKC1BFhD0VqylItAEgQs89OCBQvqMj/ZTfHYvCtgd1m3jYxO3v0M0HIEEEAgEQLchyIRypwDgQQLlJaWatSoUbKflgnKixv3ofBir9NmBBBAAIFECETeh4IpT4lQ5xwIJFggLy9Pdr8Bm+5iGaDYEEAAAQQQQACB1hIgoGgtWcpFIMkCNt3J/svPzyfzU5L7IpGnt4xOdidsNgQQQAABBBIlQECRKGnOg0ASBGzufG5uriZMmJCEs3PKRAu4GZ24a3qi5TkfAggg4G0BAgpv9z+t94CApZOtrKzkPgQe6GsyOnmgk2kiAgggkIICBBQp2ClUCYGWFLCFU5ZOtri4WG7Wn5Ysn7JSQ8AW4NtolHs/ktSoFbVAAAEEEPCCAGljvdDLtNHzAm5QYd9g22OmxGTeR8IW4tt/bAgggAACCCRagBGKRItzPgSSJGDpY21NxfTp02ULd9kQQAABBBBAAIGWECCgaAlFykAgTQQs61NBQQGZn9KkvxqrpgWG3bt3b2w33kcAAQQQQKBVBQgoWpWXwhFIPYEZM2Zo2LBhzj0qLCsQW3oKuBmdLEBkQwABBBBAIJkCBBTJ1OfcCCRJwF24O2fOnCTVgNPGK+BmdLIAkQ0BBBBAAIFkChBQJFOfcyOQRAHL/LR+/XoVFhYmsRacujkCNtWJjE7NkeMYBBBAAIHWEDjC7/f7Iwu2LDBMhYhU4TkCmSdgF6b2Tbct1rb1FZm02e8x2/hdlkm9SlsQQAABBFJBIDJWYIQiFXqFOiCQJAHL/LR06VLZtBkyPyWpE5pw2h07dhAgNcGLXRFAAAEEEiNAQJEYZ86CQMoK2L0LioqKnJEKu2BlS00BC/iGDh0q+ig1+4daIYAAAl4WIKDwcu/TdgSCAjbdyf7Lz8/nG/AU/FSEZnSyUSU2BBBAAAEEUkmANRSp1BvUBYEkC0yYMMEJKJYvX57kmsR/+kxaQ2EjE/3795ebnSt+HUpAAAEEEECg+QKsoWi+HUcikPECdsFaWVnp3E074xubRg0cPXo0wUQa9RdVRQABBLwmwAiF13qc9iLQiIBNrzn55JPTPvNTJo1QNNJlvI0AAggggEBCBSJHKLITenZOhgACKS9gvyTsHhWWTtYe27fjbIkXsMXX5m//sSGAAAIIIJDKAizKTuXeoW4IJEnAFv7avSmmT59OOtkk9AEZnZKAzikRQAABBJotwAhFs+k4EIHMFrCsT252obKyMr4pT1B3m7mNDhUUFIiMTglC5zQIIIAAAnEJMEIRFx8HI5DZAnbDu2HDhjkXuHahy9b6AhZM2DQzs2dDAAEEEEAgHQQIKNKhl6gjAkkUcFOVzpkzJ4m18M6pyejknb6mpQgggECmCBBQZEpP0g4EWlHAFmmvX79ehYWFrXgWijYBm+rEhgACCCCAQDoJEFCkU29RVwSSJGCZhhYsWKCioiItXrw4SbXI3NMWFxez+D1zu5eWIYAAAhkvQECR8V1MAxFoGQFbILx06VJnbr9lIWJrGQGztGxa27dvb5kCKQUBBBBAAIEECxBQJBic0yGQzgJ5eXnOKIUtHLb7JLDFJxCa0Yn7fcRnydEIIIAAAskT4E7ZybPnzAikrYAt0C4pKXFugJeqN15z65XK2akmTJjgpON1F76n7QeCiiOAAAIIeErA/saG/n0loPBU99NYBFpOwC6G7ZfJ8uXLW67QFiwpHQIKm+7EvSZasNMpCgEEEEAgIQKRAQVTnhLCzkkQyDwB+1a9srLSmf+fea1LTIsIJhLjzFkQQAABBFpXgICidX0pHYGMFbBvJ2yRtmUoIvNT7N1sXqWlpbEfwJ4IIIAAAgikuAABRYp3ENVDIJUFevTo4ayjsDUVdqHM1rCAm9HJRnbYEEAAAQQQyBQBAopM6UnagUCSBGzazty5c52pT6STrb8T3IxOZkVGp/qdeAcBBBBAIP0EstOvytQYAQRSTWDixIlOGtn8/HyVlZU5mYtSrY7Jro/da8ICCbNiQwABBBBAIJMEyPKUSb1JWxBIsoBdNK9fv94JKpJclbqgJjStXTLrREanZOpzbgQQQACBlhQgy1NLalIWAgiECbj3U7DAgi1cgIxO4R48QwABBBDIHAHWUGROX9ISBFJCYMWKFc5N7woLC1OiPsmshGW/IgNWMnuAcyOAAAIIJEKAgCIRypwDAQ8JuOlki4qKPH0xbVOcLPtVbm6uh3qfpiKAAAIIeFGAgMKLvU6bEWhlAZveY/eosAtqL2Z+Cs3olJeX18raFI8AAggggEByBQgokuvP2RHIWAG7kLYUqRdffLGTASpjGxqlYWR0ioLCSwgggAACGStAlqeM7VoahkBqCLiZn2xthU2HStTmnitVsjwlqt2cBwEEEEAAgdYWIMtTawtTPgIIhAlY5idbR0DmpzAWniCAAAIIIJAxAkx5ypiupCEIpK6ABRXbt2/P6KDCsjnZmhE2BBBAAAEEvCZAQOG1Hqe9CCRBwM38VFxcnJGZn9yMTnYnbDYEEEAAAQS8JpDttQbTXgQQSI5Ajx49ZOsobJG2TYHKlOxHZHRKzueJsyKAAAIIpI4AIxSp0xfUBIGMF7B0spb5KT8/P2PSydr9NmxkYuLEiRnffzQQAQQQQACBaAJkeYqmwmsIINCqAnYXbVtzUFZW1mqZn8jy1KpdSOEIIIAAAh4WIMuThzufpiOQKgIFBQUaNmyYM/0pVepEPRBAAAEEEECgeQJMeWqeG0chgECcApb5ybZ0TCdroyujRo2KU4DDEUAAAQQQyAwBAorM6EdagUBaCtgi7ZKSEtkUqHTZLKPTjBkzZKMsbAgggAACCCAgkeWJTwECCCRNwE0na5mfLAtUqi9s3rFjhzNNyxZiZ0qWqqR1PidGAAEEEMgYAUYoMqYraQgC6SlgmZ+WLl3q3BTOvv1P5c1GUyzoSfXAJ5UNqRsCCCCAQOYJkOUp8/qUFiGQlgLunaYt85ONVsS7keUpXkGORwABBBBAILoAWZ6iu/AqAggkWcC+9bf7Odg9KuxmcWwIIIAAAgggkB4CTHlKj36ilgh4QsAyP9ldtFMp85ONnHTv3t0T/jQSAQQQQACB5ggQUDRHjWMQQKDVBCyo2L59e0oEFW5GJ1vjwYYAAggggAAC0QUIKKK78CoCCCRJwM38VFxc7NxNO0nVEBmdkiXPeRFAAAEE0k2AtLHp1mPUFwEPCNiibLtHhaWTtSlQyUjRaus47H4TZHTywAeOJiKAAAIIxCVAlqe4+DgYAQRaU8DN/GTBhaWXbcpGlqemaLEvAggggAACsQuQ5Sl2K/ZEAIEkC9jogI0SJDLzU6rfCyPJXcLpEUAAAQQQOEyANRSHkfACAgikkkBBQYGGDRvmTH9q7XrZiIhNs2JDAAEEEEAAgdgFCChit2JPBBBIkoBlfrKtNdPJktEpSZ3LaRFAAAEE0l6AgCLtu5AGIOANAVtHUVJSosLCwhZvMBmdWpyUAhFAAAEEPCRAlicPdTZNRSCdBdx0sjYlybJAtXT2pblz57Z4mensTd0RQAABBBCIVYAsT7FKsR8CCKSEQGlpqbNIu7HMT2R5SonuohIIIIAAAhkoQJanDOxUmoSAlwTsnhQ2mmAjFTZVKZ6NjE7x6HEsAggggAACAQHWUPBJQACBtBOw6U6jR4+OK52sm9Ep3qAk7fCoMAIIIIAAAi0sQEDRwqAUhwACiRGwzE/t2rVrVuYnN6OTTZuy9RhsCCCAAAIIINB8AQKK5ttxJAIIJFlgyZIl2r59u+bMmRNzTUIzOjX17tsxn4QdEUAAAQQQ8JAAWZ481Nk0FYFME3AzPw0dOlQWHMSS+clGJJYuXSpbi8GGAAIIIIAAAvELEFDEb0gJCCCQRAELEGzqkgUIubm5MQUKBBNJ7DBOjQACCCCQcQJMecq4LqVBCHhPwEYnioqKnEXa9WVuskXYLMD23meDFiOAAAIItL4AAUXrG3MGBBBIgIBNd5oxY4amTZumqqqqsDNaMNGUdRZhB/MEAQQQQAABBBoUYMpTgzy8iQAC6SRQUFDgjELYPSrczc3oZDfEI6OTq8JPBBBAAAEEWk6AEYqWs6QkBBBIAQG76V3oZsGFTYcio1OoCo8RQAABBBBoOYEj/H6/P7K4yNtpR77PcwQQQCCVBWzKkzsaYSMTBBOp3FvUDQEEEEAg3QQiYwVGKNKtB6kvAgg0KmC/6NyNYMKV4CcCCCCAAAKtI0BA0TqulIoAAkkUYAF2EvE5NQIIIICA5wQIKDzX5TQYgcwWsIxO9h8bAggggAACCCRGgIAiMc6cBQEEEiDgZnSyG92xIYAAAggggEBiBAgoEuPMWRBAoJUF7KZ1ZHRqZWSKRwABBBBAIIoAAUUUFF5CAIH0ErCsTvn5+bKb29l/bAgggAACCCCQOAECisRZcyYEEGglgenTpys3N1eR96BopdNRLAIIIIAAAgiECHCn7BAMHiKAQPoJWEan7du3i3UT6dd31BgBBBBAIDMECCgyox9pBQKeFHAzOpWVlSn03hOexKDRCCCAAAIIJEmAgCJJ8JwWAQTiE7A7YM+YMUP2070rdnwlcjQCCCCAAAIINEeANRTNUeMYBBBIqoClh7VF2EVFReJO2EntCk6OAAIIIICACCj4ECCAQFoJWEanadOmkdEprXqNyiKAAAIIZLIAAUUm9y5tQyADBSZMmEBGpwzsV5qEAAIIIJC+AqyhSN++o+YIeE7A0sNWVlZqyZIlnms7DUYAAQQQQCBVBQgoUrVnqBcCCIQJWEan4uJikdEpjIUnCCCAAAIIJF2AgCLpXUAFEECgMQEyOjUmxPsIIIAAAggkT4A1FMmz58wIIBCDABmdYkBiFwQQQAABBJIoQECRRHxOjQACDQuQ0alhH95FAAEEEEAgFQQIKFKhF6gDAghEFSCjU1QWXkQAAQQQQCClBFhDkVLdQWUQQMAVIKOTK8FPBBBAAAEEUluAgCK1+4faIeBJATI6ebLbaTQCCCCAQJoKEFCkacdRbQQyVYCMTpnas7QLAQQQQCBTBVhDkak9S7sQSEMBMjqlYadRZQQQQAABzwsQUHj+IwAAAqkh4GZ0mjFjhiZOnJgalaIWCCCAAAIIINCoAAFFo0TsgAACiRCwjE79+/dXQUFBIk7HORBAAAEEEECghQRYQ9FCkBSDAALNFyCjU/PtOBIBBBBAAIFkCxBQJLsHOD8CHhdwMzpt2LBBPp/P4xo0HwEEEEAAgfQTYMpT+vUZNUYgYwQso9OcOXO0YsUKgomM6VUaggACCCDgNQECCq/1OO1FIEUE3IxOc+fO1SmnnJIitaIaCCCAAAIIINBUAQKKpoqxPwIIxC1ARqe4CSkAAQQQQACBlBEgoEiZrqAiCHhHgIxO3ulrWooAAgggkPkCLMrO/D6mhQiklAAZnVKqO6gMAggggAACcQsQUMRNSAEIIBCrABmdYpViPwQQQAABBNJHgClP6dNX1BSBtBYgo1Nadx+VRwABBBBAoF4BRijqpeENBBBoKYFkZHSyhd9sCCCAAAIIIND6AoxQtL4xZ0DA0wJkdPJ099N4BBBAAAEPCBBQeKCTaSICyRQgo1My9Tk3AggggAACrS/AlKfWN+YMCHhWgIxOnu16Go4AAggg4CEBAgoPdTZNRSCRAmR0SqQ250IAAQQQQCB5Akx5Sp49Z0YgYwWKi4s1Z84crVixQj6fL2PbScMQQAABBBBAQCKg4FOAAAItKmAZnWyq09y5c3XKKae0aNkUhgACCCCAAAKpJ0BAkXp9Qo0QSFsBy+iUn5+vGTNmaOLEiWnbDiqOAAIIIIAAArELEFDEbsWeCCDQiMDFF1+sYcOGqaCgoJE9eRsBBBBAAAEEMkWAgCJTepJ2IJBkAZvmZJtNdWJDAAEEEEAAAe8IEFB4p69pKQJxC+zYsUNFRUWHlWOv2UJsFmEfRsMLnheo1tb7vybfyAdVWpsIjG16aVa3BJ4vEW3iHAggkOoCBBSp3kPUD4EUErCgwRZdh272WmFhIcFEKAqPEUAAAQQQ8JAAAYWHOpumIhCvQGlpqfLy8uqKIaNTHQUPEEAAAQQQ8KwAAYVnu56GI9B0gZKSEvXv3985kIxOTffjCAQcgdrNemXxFZqc63Pu0+Lz5eqEmYu0aFNVEMidtlSk5aU3afY5HQP75U7WFSu2qCKEsXb3Mj1120Dl+qysr2ngbS/otd0HQ/bgIQIIIND6AgQUrW/MGRDICAFbP2Gbe28JMjplRLfSiIQLvKfX5l2qkS8M0OjVH8oC86p9K3R/1nzNvOYhLTsQstBi9Txd++wZ+kax7fe+Ni/8SLvyZ2nmK5WBWh94Snd9+2rN3nejFu/ap6qqv+jRE5fr+eUfJ7xVnBABBLwtQEDh7f6n9QjELBA6OhEto5MbcMRcIDsi4EWBqhV68pdf0qDvfFvjun4hIJB1ks69crSGvLZGJbv+e0il3XdU8LOxymtrf6qPUpeBF+nM7DKtXb9HNarR/jV/0NzNU0P26axe43+jm69ue6gMHiGAAAIJEMhOwDk4BQIIZICArZew9RNuRqcNGzY40zAskLBF2UuWLNHy5cvD1lhkQLNpAgItK+Cbqnl7p0rVpfpTYYk2STqubakW3lyq1zRC/Ro6W9ue6nOGVPH2e6rWF/W/L7yhmgGXqI8TcLgHdlK3np2kDe5zfiKAAAKtL8AIResbcwYEMkLARiiys7PrMjpZgDFq1CgNHTrUCSzcgCMjGksjEGg1gT0qXzBEud1GadJfq1RxzDHaVj1dv33hexqibSrfeSCmM2fV7tD2f3wS077shAACCLS2ACMUrS1M+QhkgIDN87YRCRuNyM/Pd/6zZs2YMcMZmfD5fBnQSpqAQOsL1JbP1/WzP1bXRev17mW5CvwRrtH+F+93RitOjrEKtVk9lHvqkYxExOjFbggg0LoCBBSt60vpCGSEwJo1a5x2/Pe//9XGjRtVUFCgiRMnZkTbaAQCiROo1YGdb2uTemvcKccEgwk7+39Vva+6SdX4j3J15oWnK/vBd1ReXas8nzvhoEK73g7NA9WkYtkZAQQQaJaA+xuoWQdzEAIIeENg1qxZOu644/T000876yQIJrzR77SypQWylDNgjMZn/1XLHijRZieh08d6b/UNunnWGwrmborxpFnKGX6LFo55SLOvfUwvV1the7T18R/p9vubFpzEeEJ2QwABBOoVIKCol4Y3EEDABCyjU05Ojt58800WXPORQCBeAd8E/Wj59zXulfEa1N7uHTFEY18aqksfm6Vp2Z81rfSs03XpPU9qac/faVK39vL5Bmrkq9/SjNk9mlYOeyOAAAJxChzh9/v9kWXYfGibM82GAALeFrCMTvZfWVmZs/Da2xq0HgEEEEAAAQRMIDJWYA0FnwsEEIgqUFxcXJfRiUXXUYl4EQEEEEAAAQQkMeWJjwECCBwmYClgbarTfffdV3dn7MN24gUEEEAAAQQQQICAgs8AAghECth0R0sNa5mcRo8eHfk2zxFAAAEEEEAAgTABRijCOHiCAAIXX3yxhg0b5txjAg0EEEAAAQQQQKAxAQKKxoR4HwEPCdg0J9tsqhMbAggggAACCCAQiwCLsmNRYh8EPCBg2ZxKSkqcjE4eaC5NRAABBBBAAIEWEiCgaCFIikEgnQXI6JTOvUfdEUAAAQQQSK4AAUXQn7SYyf0gcvbUEMjLy0uNilALBBBAIE4B7qcVJyCHI9AEAQKKIFboL57PPvtM//jHP/Tvf/9bZ5xxhjp27Fgv6a5du5x9Tz31VHXr1i1sPytn3bp1zmsDBw7U5z//+br37b1NmzbJju/Zs6eOO+64sPfrdgx58Mknn+jII48MeaX+h3v37tX69eudHfr3799gG/bv36+1a9fqmGOOkbUj2rZ161a9/fbbTl179ep12C5uez744IMGzWy/119/XXbO+mytnS+99JJzjlGjRoWdy+rxz3/+Ux06dHDqGmoauqOdhz4MFZGi9aF97ocOHeoswL7qqqucz2RL9aH1s5Xfr18/5/MdWhv6MVTj0ONU/LdIPwb6h9+p6f879dC/NB4hgEBLC3Cn7AhR+4Nuf0DtQjUyCIjYVdu2bXMuwKIFE1aOe0EfWY4FERZM5OTkOBdb9rOlNrsY37hxoxMMffWrX1W0i//QczV2ARN6YW6BSefOnUMPdx7bOc3MNtunvvbYH2Tbz963YCJaMODuY2Wde+65dfs09Y85feh0h/O/hvrQggnrs1/96lct3ocW9FmQHfqZoR8P9Uvko1T9t0g/8js13f8uRv5b4zkCCMQvEHmnbAKKEFP3Qr+hb+rd3e3bb/sm1759jRyZcC8MIr9Ft9ctkLCf0Y5zy3Z/2n71XZy7+4T+dOtv5z3ppJPqRjOsHBvZiLyAt9cbGpmw992gyAKAaKMje/bscfaJbGtoveyxG3xZkGN1i7a5+9iIjRsI2cVwU0ZyXAP6MCDcUB9aRifr36effrpV+9BqQj8GRhbT+d8i/cjv1PpGsN3f56n4d9GtGz8RQKBlBQgo6vG0C2v79jTaaEPkIe4vzUGDBh12wR/tIt0uptwpHhZ8WDAReXEfeo7Qb3HtW/rIzS6abfqRzXcPLcfO/fHHH9d9Ixz6zXTk9KJo9Qw9jxso2IV5ffW1kRCbfhQaAISWYY9D61DfCId7sWkBWug+Vv7u3bsdY+uXaAGNez4zMxP60BWRGurDwsJCLV68WA888IAqKiparQ9t9MrqYX1jwTH9ePg0ynT4t0g/BkZmQ3+f8Tv10O8ae5SqfxfDa8kzBBBoKQECinok7YI/lnUMTf2l6X5jftRRR6lv374NrmWwqjV2kW7lWR0aC3zci8loF3FuGRbcWDmRW7SRgtB93ClO9sfVAoD61pjYhZI79ai+EQ63LCvfynJHZJYvX+6c0o4LnTITWg977AYj1qZY16J4vQ8tkJg9e7Zuv/129ejRo9X60F2zYUFvaKAY2Yf04z+cUc5U/bdIPwY+sfxOjfYvN/BauvxOrb8FvIMAAk0VIKBoqlhwf7twtQXWNgIQbWTCvhm3i2d3qk3oN1nuhW5Dp3YvrO04u4h2L6xDj3EDgcaCCTcosZEFC5JCt8bKcP8w1HcBaMfbFKTGpji556kvaLE6ud/MhpblBiHm3Fgw0dAf+NA2u4/pQ+mtt97SiBEjZNOd7Kd9lkJHuVwr+xlvH1oZVnbkGqLQc9hj+vHwhA7mkir/FunHQ1/08Ds1/F9vOv1ODa85zxBAIF4BAopmCLoX+3ZotIsj98LLnfpjF8WNrT0IrYZ7QRV6YR36vj12vyVsKJhwf7nXF5S4Iw/RymjsWHvfLnAs85X9UY1cNxJaX/dCqKH9XLPQNRXRXgst130cWpdYgjU7jj6UM7XJAsXLLrtMs2bNSmofWp/Qj5uijjSm079F+rH+xBzp1I+Z/G/R/bvBTwQQaFkBAoomerojD/Vd7LsXwe5FerRv3Rs6pRsoRPvmyz3OvUC3b+wbml5k60BsZMP2i/zW2S0j2kV+aAAULWCyetg+Vld3sbf9AbIt9DzuRbu9V98oix0TrS4NBTvOiYL/c4OvaFO5QvcLfUwfyknfaiMS3bt31yOPPOKsR0lWH1rf0I/1J3Rwv4xI9X+L9GPDiTnSpR8z+d9i6N8BHiOAQMsKEFDE6GkXW3YB3dCi48gLYzeYcKc9NXQqK9+Ob+xeF+45ok2zcst3g5rQb/vd9+w8NhXL6hatjNA6W7ARGiC4ZUT+tIt/W2TbtWvXuoxNjV20WxlWl2jTxtw21jfNyj22sf6IrCd9eEjEzehUVlbmvJiMPqQfM+PfIv2YGf0Yy+/HQ79BAo9iOcb9ff7/2zsTMKmKq+8fhkFZBSKgbCIqyihoVMAFcEEFBRLEF/2MJkoQo0FjTJAXcd+FCFGicRdRX3GNS14BJRESIRr8EBcUcEMEJCAYICCiMMz7/G/3mTldU3W7B7qd6en/fR64d/rWreV3quqeU3Wqrg5e2XcMBt7iDsSfzfdi3Ex6XD54jwRIID0BGhTpGUU7BWF0Cco1lFx3PQM6SNxH56cj8TrKk4kxoSP5yIovfs2idsw+Q8ANo523/o6zKvmhWYs4Q8TGo9coN9ZPIP9YYK6LpTUedfnS8PaMZ3WBth15zaSMPt42bt81yk4ZJsjojk4wJurUqVMtMkROKMfwN1i0DfkGBXz1u7raIuUY/y2dfJFjobTFvn37+poPfyMBEsgCARoUMRAzGX1RFyU1HGB06EskTqHWZNGRwzUp5EKFcMhH3KxCJmE0n6E86X111dL8hc7qkgSFB9+I0JkMNQh8Bo3GFTK29Nk4gwlsM1kErmlRhkoiccaOTpdffrlMmzbmm2EiAAAgAElEQVRNGjduHLH8vmWInFCO4a/M50tbpBw/imZm2afun9rJmDV+Nf29WCnj/IEESGCHCdCgCKCDoq8j6L5ZAx3Rwe5D1jVHjYlMFHMNGzcKCYUYbkE47Ei+zbbmxRfGGiOhNReqyIfu27QwG4HwSNOGt+nEGQRqiMDgsDtOaR5CzyqHDRs2RIvA7bM2f/aaMrQ0Ejs69e/fXyZOnCht2rT53mWI3GCmCPUe/9w6kJrbir8oxwoW9qq62iLyQDkm3EZtH2hlo/1Z6L4Nu2Ny3CabFt4nN13eUA6/f4A0fOv/V2pPmgf2qeF3p5UDr0mABHaOAA2KAD9898AdudWg6m/uziqogZCJMZHJKKQq0Ug3ZEyoGxNGgqCg6UwBnoEiFrcwG/HjpYN1G6GXjpYZZ51ZcMutxsS2bdsiIyP0wTl9wVkDLNM86HcoevfuXcnlzOZRr5UvZZggAkOsS5cucvHFF8uhhx5aaUbs+5Chtg98gwWKlus6qLKzZ8rR0qi4rs62SDmGN7vItD9TSe64HD+TmaN6y+B5l8r1t50gZ7ZrXe5ymmkeCrVPVfY8kwAJZJeAa1AUZzf6/I0NCra7g5IdSbJKMUqpL9lMjAlVrH1pKDEYA+l2BdE0fVPuOhMQmv3AS0dnPqCkh4wA5Adh4WaEL1cjLTs7YPMJJdEXj6aFszVc9PfQtzxs2riGwZROCYWMMLOkcVKGiR2dTjnlFDn66KMjY6K6ZIj6g8P9onv0o/Mf5egASf5ZE9oi5bh3+eYTVkran+G3XPeppaXbZMW6bSKl30pJSWfZs1GDKCuaB+3/fP2l1iE8UGh9qpUXr0mABHJLoE5ZWVmZm4Rrdbj3C+Hv0EgSyq6KfTpjAh15urUQiE9nFtyZAMtZR27dNPVlgZc+Xha+XS1UWUN8oZkPTcsaDK7rlzVa7DoKfRZnPK+uYzYtffEhjBuvPh+Xtoax5zgZIVzc/dosw/POOy+SwV133VWJdU2TYTo5pbtfm+UY1x4oR/+uddo/gF26tWq56FO3Lx4pA46YLUXPTpOpJ7WIsvPN6jvl0sOvkmcG3Clz7zhdOjWAMZCYcRjy3V1y5xkt5Zji+fLGy4/JqN9/KOujp46WXjf/Vsace4IcXvyBPHXRSfLrP32TLN4B0uvZafLCcU3lw0VPy6Jn75G7Jy6Q+bjb7ZcyfORQGdO/syD1KO2Sa2X6oAvlwi2TZNy0b6T4wuflg3F9ZM9kbPYU12ciXNz9mtgW8b7kQQIkkBsCrq3AGQqHs1XQ3ZFdBK1Kp6kzAscff3yKa5JNUl98upjN3tNrneFw3X+soWBnAvQ5nDX+OGNFw6NsmJlw3amsYYRZCd3dSZ/Ts3XHsh25NSaskaHP4RxK24ax13FfAy9kGY4ZM0b+/ve/y+TJk1OMx5ooQ8iTcrS1uuI61B4ox8T6sprapxbt/2M544jJctlf35NVJ/WROquXypLnnpKpG0VKl22V1bs2kE4iUvrvGfL0Q82l8y0/kIF7L5b7fjxO/nT6k/Lyul5SUiSyfeW9ctUZZ8vP/v2M3Navvhxz1SR5fvdfyOD3b5CpU4fJEaVb5ePFj8nfrhsj1za+Wu5bOFOGtC2STQuvlIt6nyY/vne6TDmmvmz4aKkUNyyVDTO/lK+mfygbHv9S5rzTymtM1Ma2WNGieEUCJJBrAjQoDGE7IuhT0DM1JlSJD23XqknqaE/ImFBFHGc3P6q8xxkKmo9Q/JoPxK8uTu4sh6aDssRN6ysb1+VKy4C0QsaEvsjc2RfNnz0jPp31cQ0shCtkGU6YMCEyJB577LHIzUi51TQZIl+Uo0on9ZxPbZFy9Ix+Fx0mPYe0l23PfyavLFkqnVa9K/W+XS/fDDxVBr78sjz/0dnStfUGWfjUY/K09Jabhhwudd4eL+OWniPjfnl0ZEyAa1Gbs2XwkLvkj8/+Tb4Zep7ss1crWZqsKttKS2X+/Nel+P3Jcturx8rQucNlSNtdoruND7xZ7nxykez9/34vdzz3U7lm7z2lSV2R4jPPklEHNhWRptLrsGREyVNtboupJeVfJEACuSRAgyJJNzQiqPBVYU6n9GaqxGt8vvUQSBOdvM5wuD7o+qyrvGtecc40H3EKuLoEhPKo6Wl+XDa2DD5jIt2LTOPXs82rb4QS+fDNsOjzoXzqfT1nyk7jC/Gx5c+1DJ9//vloNyfMTJx44olalOjjjPgIYSiPGlDLkmsZIj3KUamnni0XdwChprVFytFjTETibCJtjzhGfjjqOXllUXc547h6MmXkJjny2nOkz5Lz5PF3P5WF696Ule8tkTrn3yCntWgku530Z/nqK+zi9IjcevcqqV+/VIo+nCzXPLFGpPvu0rFdu8hFKlFbymThhx/KMY2+lFWLlsj6Zr2lpHXCmMD9rVvLZFXpbtKldJYs3jRKftC8eeKxwP+2zhVCnxrAwJ9JgASyQIAGRRIi3IqwGw0UKveALy5GebHg17dGQcNrOPzti8cNh/iwFsE9VLnD73369Elxl9KdOvDsQQcd5D4a/Z1pPlBmpKXp6AJrlBVx4EiniNr8WDZQpmfMmBHFAeXI7kaFH90yatrRA57/3PBufJqPQpQhlM3Ro0fL2LFjpV+/fhG9mihDn9wpx0Rlz6e2SDlWfkckpCjRLnrfbWknxx8wRaYsL5Jdt62Ujz49S046uKu0OGEXeefl16XZTQ1l4Tu7yJE3HJxwPdo0Qx78xbkycuou0mL4FXLsurki+10pj1z2Ozn3wX/J4o3bpVdTke1Y7bhxhWze9LXs3WU/+bKOiKy/S0budZeM1AyUnztJr13rl//luyi0PtXHgL+RAAlkjwANiiRLKL3uDkG4hU4Xypk7cuuKINNwcO+Jiw8jRhhlh3JujRId7U63BWdV8oGwcHGyuzipGxZYYL2Eq/BpubF+A2XB4XM9QhnwrDvSivBIF/fjZlgQDizwDyxQfrhudevWLUrT/gdlDGkhv4UmQxgTt912mwwePFiGDh0aYalJMqQc0/cdaEc1vS1SjpnL8bDD+stZw6fInZ/+S75488/yYJd+cvXKZdJhv9ZS580iKdswX5766Cw5o8cPYCHIR1P+W0b+Y4iMfOdW6f/VYlm9up306bOXvHHNRtvNyVcbS0WKiqRr1y7SuNGqxL2jb4/WVOy9MtGntm3bNnWgaUNKFAXbp6ZS4F8kQAK5IECDIkk1pIhCWc3EmMgkHMJgNyafAo5sqKLtrnmAUq07J7muM7ZSQJFMlw8o5roGwTWidC1D3KwEDAkoscgrFH1fWbScPmNC00jHFGWePXt2lAbSgdFjDR8tN+IDU19ayjQdk6qE07L5yq3xqNuVNQhzJcPp06dLy5Yt5Z577omQKN+aIENkaM6cOdGWvqjTlGMkovL/8qUtUo7x74DKcmwqjTruJTLmbrnkg3nSuOcw6bf77lIy+GcyfOSjcu21K+St4Q/Io02LRGStLP1wjcg+HaTh6kVSr8EuibVqu34i69eWlteVJUsWyaYtZSINW0mjaJeo9tKt72FSPOkteW7e8XLCmoXJ99SesmnueTKo7yb54dxHZELr8ihkI7bYLsA+tYIAr0iABHJJgAZFgC4U5mwponjhIK64D8qF0tPRZtfIcLMNhRXfscCoPxQ332GVWijE6maku0UhnyFFGfHBkFi6dGn0kTS4YunzNi1VuF0F3zKIS0PjgjGBwyrles+e27dvL/jn2389xNQ+j+tMwtn8u2XT+ELx5EqGcEv78MMPZdq0aVITZYi6gA/soT5SjlpLEud8aouUY9X71PqHnixDGoyRJ2d3kKMu7CYlHduJbO8knQ9/X+6dsa/0ejbh7vTZZ1ukyX4dpcmDU2XWv4fIpf33luLti2Tu734pv3lus0gzkRXLl8mq/2yVHj1aibxUT0S2yNq1xdL8uKvk5uN/LFfc1Fx++PtR0q5dI9m06Da5ceT/ytIrXpKnOtcXMTMUb86fj+gKqi2mtjr+RQIkkEsCNCg8dEOKoRsUL1qEjRtthyKqi6utEm/jCqWnv7tuSfZZvcaoOHZ8Cq2rQFy+kXO4X2HGAgq5b+E04ldjBWUJuRUhXJwxoQxCyriWQ+PBGbxCB/KNPPsMCTyj7OJkg3D5KsP3339fHnjggciYwBfLwbemyRAzR9inOs6YKHQ5WjY1tS1Sjv61anF96pLPGssxpzSUJ2cMlCG92yS6seQOUDK3o+zbqjiavUOf2v2s2+SFOjfJ6J8cIrsjZLPBcuoNN8hT9/1B+o/YKBvXrZMuhxwvjfceIRc9PUoGNL9e9rxtutx/SJkcc9k18ugbf5bbD99LfqXP3vKSvPSTHtF3KBIJi5RtXCMiiRll/c0918a26JaRf5MACeSOAD9s57DNVBHFaD12z4lTWKGIYxQZ6x5Cyrq6qLjxqHLubuPqZDf6U2cOQsq6puEaJlqGkHsMXnYaN2Y+Qh+zQyY0v24erEEVYmDLFIpHw2AkHmHA1v16uYap7TLctGmT9O/fX5544glp1apVVA/zSYaQE+WYunYpH9si5bi00hq0fJRjbW6Lvk1P9D3BMwmQwM4RcD9sR4PC4Qn3FIz4WrchKMV2cXImCmto9Momp8qzNRqQFn6Pc4+ycWhefB+cs3HZmQX8ruso7O82XjsrAcXdt8YE4TGqtWjRomjRNOJyZwzgQ48jG8aEug4hDRhgPpcrpFWbZVhcXCxdunSRm2++OTLwIKd8kqHKB+55hSxHbU/52hYpx3+ntLt8lWNt71MHDBiAqsqDBEggBwRoUFQRqquwYzRn5syZwZkJ3MeMAAwCjBr7FhIjC2pM2BF9vJTUNQhKYkhh1iJo3nR24+6774581nF/+/btkdsPrrH+Ytddd40eQ/5Wrlwp9evXl9atW0tRERYGph4wEpD/Zs2aRYaELwzihyvE5s2bo3DNmzevFNfXX38dpbXvvvtWumdTtHHBkNO82jBr1qyR9evXRwuQka+qHFC6kdc2bdpIo0aNIuMHa0HAxTWAEC/ksHbt2qhsUPxC6eFljDLaPFvu4GsNUV+eNW++vNi4cL+srEymTJkiLVq0iFzbQjLca6+9pHv37tHMRdzMEsqpxivCoa66+UUZYXz27du30j1bHhuXrdM2DK5Ds2VuON/fWt/RNvC19prcFm3+bbuGca51zro4oUwue8ShI96UY/X0qbVZjoXYFq08eU0CJLBzBGhQZMjPKkh2BuGzzz6LFibjI0D2gHKAe1BcoWBiqjVkECAc1jPYxclW6chkNF+VKzUmkBcI94ADDrDZ4nUBEkBdRJ3FR+50JNzFkOnIJAwOKO4wEkKHrbtWYbbhNQzOUJ5VqbZhQtd4Rg2ffGmLWhYYjHB7RHmt0aB9AAwF37onMIchh7LHzRBSjgnSyjPbfWptlGOhtkWVJc8kQALZIeAaFFyU7eEKhQwuGRgxdEdbv/jii8hvXR/Dix/KDhQH7AEe2v1IwyNuGBMwBFSpCikd+ox71penNSY0DEayeRQ2AcxgwA1t5MiR0dez0ej1sMp53AwawqNuw0CGEh86VDnB/ZAhbOt3KEwo/nxui1putEm0VRyWv860uGXHYIFushDiZeOhHHPbp9YmOWpZ8O4J1S23Purf+dwWtQw8kwAJ5I4ADQrDFi9pXYTsW+SK0UBsgwlFAId2zthdCTMWPpcFE32kTEDRw6ixXaOBNNHBx40CazwwXqDk+YwJDcNzYROoW7duNEOG9SsnnHCCvPrqq9HsFeorRr1RT0M7jik5KA+oq9hQwNZVvY9zOmMC9/Vr6aGReBufvc73tqh9gzUm8BsGKnD4+KPMvpkYywXXlGMFETDLZZ9am+SoA1GF1hYraguvSIAEckmABkWSrh19sdPmCl9djGBoqCsTXBmswqBhfWe8+Oz6CBsGX3/G/XSHGhPurAmew2gyDxJQAmpUYEYNs2aPPfZY5JLnUyZQ92DUurt4YcZtR40JVXqRn6oav7WhLbp9g7omob/AjI87+KC8fLOiKlOctR+iHFMNWh3kUVbZ6lNrkxwx64XD52Kn3NxzvrdFtzz8mwRIIHcEuMtTku3UqVOjj8K5SpWih8IOxUvdlPA7/nYVAw1vz1ZZqOo0s6ajuzL5jAmEgbFxzDHHRP9s2rwmgWXLlkU7l02aNClyc7BEUIfV0M20bqarz1Z5xkJv22Zs2u61GjZYMA+FOZ/bIjY10HVWurAahoRvk4ZMR451QMGuI1GGlCM++Jb5AV6Z9Km1SY6YbezVq1dGkGpLW8yosAxEAiSwQwTcNRQ0KJIYMRITWsC6Q6RNvHhxhUYm08VtFQWMwunsiH1O3bROP/10GhQWDK/LCcCowE5Zr7zyinTt2jX63datqhgTOmrrG2lX5TikPJdnyLmwI6ElJSV53xZh+KOtqgsT2q7bv4C/3sfCa+xc5TtUTjgjHtdA0/t4lnL0EUz9zfJK16cWohxrU1vEoAQPEiCB3BBwDQq6PCU5uy97Fz9eQnj5Y4QxXVh9VpUr33oMDRN3TjcSjGfhAoEP7OHFx4MEQgSwlSxGKPv16xcZFZ07d67yzAQUDTWOdZGxTU9H0KGkhZRjGx7XaFdqEGfaTvKhLWLmUmd+fOslbNv23VdOCAcDDkaEz1iwyrHvvsZjz5RjYh1RiJftUwtJjrWxLdKgsC2f1ySQWwI0KDLgi5e6LqZ0Rwd9j6Njhr8qFk9XRbmycVm3EZ/yhrC6jzjuZ+J6ZePndeERwO5PWFuBb0pcffXV0XakIaXKpaO++z6lH/U9nfuIGx/+VsUNdde3bsn3TL60xdmzZws2a/C1TZQb/UO6WUsbztcH7IgxQTm+F7vuze1TC0WOtbUt+voQ/kYCJJAbAjQo0nC1L3W4cWA0FdM8ocWqVuEJrXdIk2S0eBYKR5zbiI4GIw0oZBjF5EEC6QjgA4T40OCYMWPk9ttvT+tTDaVV3XKg1Lr1HmuLYEzgyGSnM4TTNoKPIqKOu3GGypBPbTG0WYNVWOPKresufMzBp6rGBOWY+PZPVfvU2i7H2t4WQ30JfycBEsg+ARoUAaZ4AS9feLvcfd5YebjTTfLc/SfKwoULolmH9u3bi8g22bTwSrmo9//Kx/dOl9dO7yBrV62KZjLSjTxi9gELT103JfvSj5vZsMYEZkzgWoUdeXiQQCYEYFSgfl1xxRXRF8yHDh3qfUxnyVDHfG45UEZgyIZG4n2RqqKMRdfpZ0e2yaa5F8igvn+Vjy+cKL8/rbUcmTRAtA3ss892mTnqSBn89GC5/B8TZEy7XaJkNe/V1RbdnXTQtnUWJ91sjJYN/YPPvRJxqTtVeoYiyqL65JioCbZ/U0NSy5roUyvXGM075Zh9OVatLeanDDPxKKhc6/gLCZDAjhDgomwPNX2JtWjRSDpufkCGDJgln4y4Uyacuof0LSlJLIrc9KyMH3CB3LrfAzLz3kFS/NFiwRad+qKEsoXD16Fhb37dxUaTtwvhoOz5Fl+rIoGRXd/sB2ZOsNMTDxLIhMCWLVtkwYIFkWFxySWXlD+iip9+1M63M5G2kdAIbnlkItG3W66//nrp2bNnZHzEffnZPofr9evflZevHiwXPLqP/GjaFHm4R/Nyd8KePbtJ2fujZFDft+SbB1+MjPqy5JqM6m6Lthx2FifOAND2jTP6AF/foWFCfYBNN9tyRNw6oo24qyJHrS8oE2ZdiouLy+Xo68sQPxReyjExG6WGV2iGRflm0h4LWYa2ffCaBEhg5whwUXYMP/sCVl/x0tL2MmL48TLs7onywsAnZMhuu4lsny/P/epXcmPx1XLP2H6yce4bUaz6YtSRW1/nDrcNHK6ShtFL18iwWdWXAH7L1LXEPs9rEnAJ1K9fP9rx6ZZbbpH58+fL5MmTxRq2oZF01GEoOCHlxqaDNgUDGnE/9NBD0TcxJk6c6B15d59TJeq4S34jV793ndx4zf/I+LH9pPe3GxMzJqVTZfx/vyDvDHlAXvuvDrLZrHWqKW1R+4J0szjW6MDWnr41UWCJmYlMjIlcyBFyxwYQ6WYLQnLUPlXLgXChmS9ds0Y5fhXNesetM6pKe4SRhtnxQpShrZe8JgESyD4BzlAkmeoID3bCwcgbRtJUGejQ/l/y/tjLZdiK0fLIixdK92mnyNHnN5FuU26TYfJJuSGATh+duy649C2knDVrlrRq1arKHxeCwZFOKeEMRfYbSCHECAXvk08+iUaOhw0bJqr4+cqubhIh3377DJRauERBCR0/frxs3Lix/Da+4H3HHXcIdp9yj8ptsaGsfW2YDPzRTFn5iz/I3LGDpHXd1TLv1hPkhL9eII+8eIkcuPKTKB01yqu7LaJM2n/4BhZsmTVcXPtWJTydMYFwqjRmW45gGre9rS0TrivLsaJPRf+KWRjEaQ+tX5Rj9uUIwx71A9wz3YWttsjQ1jFekwAJZIcAZygCHDEihhewzhzoqA9ebAeU9JVON6+UaYfcKCN//nfZa8ZX0uy6a2R441Vy6AEVnbNuExtStqBgQSHYZ599Armo/LPNh+uXXTk0fyGBqhOAUoftFd955x158skn5a677vJGojMGGDX2+fbbh3TxMX7Ddy+KiorsbXn11Vej361hAWUHaeBjYm5bXFZ8klw74g058+7Jcvnpx8ofy66W0WM7ycCXzpQW77wuSzdvTlGUqrstqpGQzphQhS0unBoTABg3O4k0dWQ/NLuEOHZUjr7ZhBShJv+IkyPSRp/q9mWad/SPVuGlHHt7Xd92RI6QCzYCyMSYqE0y9NVR/kYCJJB9ApyhSDKFywHWLaAj1S1fdT1EIshmWf5kfznqgrdlc59r5cHxg+VHe7UrH2HTl3TqM6kCQxikA4Us3RHOh/9JvJCxsJFrKPx8+Gt6AqWlpdHodrNmzSKFH6MPOGxdVBeUUGzquoNndB3AnDlz5KyzzorWUoSeO/roo+Xss8+W/fbbL5op8bbFNl/Kc+cNkJ8vO0F+9O0MmXPcozL25MZS0qRJ5H6lo901oS1iZibOSAAHHSyIm0kAx0wWYKvibUf2XdY7K0c3Pt/fyAdmpHSthFeO7dqVP4o86TNQdtF/Uo4LU2a9y2ElL3ItR5VHbZChy45/kwAJZI8AZygCLPHis8pQJcVp+2L56wuLJXLamP+RfLhrWzmtXr1I2YICg1FVfUYVsUBS/JkEaiQBfKOiZcuWkUHtc0XKZaZff/11GTRoULmx7W+L7eTUGy+R6T3HytMdLpOrTusoJ3VoUT5bAkXLbYu+PCNuKPM+l0Q3vOYDv2v7dsPYv9VI8I3C23BqAIRmMxEW5UlnTNgy25F9m5aNC+HTlUNnTeCCFbeI3KaBAQ0MxOBsB1WUXyhdcNC+U2e9bJni8ko5HhmcvYBsqirH2ijDuK2Zbf3lNQmQwM4T4LaxSYbxne8qWXz/xXLd9B5y6tM/l663DJcbz+0s+//pItnj/blRDNYdYMOGDZUkA99g7FgCl4W4w+YDyoaO1vmewYvXzqa4bgS+Z/gbCYQIrFu3Tj7//HN5/PHHZeDAgRkptBqX+r5DmVS3Qb2Xbobi2GOPjdZTqCugbQOuQlvUpKXsLiLFR/WUnx12QHSNdNAWVPm2bVHzYM/Lly+PvhqeTtmw+ahKW4wzEpAPnUHJxABAeJeBlgUKINZWoY+IK7NlE1rwrXHGyVHDuGd9BjxRJu2zLL9QGdwvGdu8xpUJeaAcU9efWLmoTHzt0YbTaw1f22SYro1r+XkmARLYeQI0KJIM8WL2ux5gL/wr5aLRm2XP390sE/odJPWbvSRT+94ul163hzx4/sHSZ//9y1+iPpHgJYmdNRB/6EAYNQ6s/3govN3FJW4UL/Q8fycBSwDGxJIlS+SVV16J1jZYxS6kDOJ5hEPbgXILBRBuEpkecHMaN25ctNBXn9G1F/62qKFSz0gbLkahhb42dHW3RTUm4tqslgcbRITYYyYE/UU6t6pcylH7IPBFeXSGAX9TjhWL8muyHGu7DG3b5zUJkEBuCdCgSPJ1X4iKffvKB+UW3Zry/K7SAnvjH3CJXHDOLLng4YdlyllPSz9npxJ9Vs+Y1seoXWi0RDt1hIlTNBAfFASMJqmB4o7waZo8k0CmBJYtWyZr1qypsjGhii8U+bjFwsjHtm3byrPTo0cPueqqqwQzE3qoa4zuYmSVUw3jO+soeDrFWp+trraoir2WL2R4KdO48qhbVbqZEE0TZQ8ZJrinaWYiR4RHvGoYuYYf5Zioacq0psqxkGWYkBD/JwESyDYBGhRJol4FZvt8eeHK6+WPxb+WCTcOlIOKJFpAuHDhCjnhN9fJhK9Gy8gxf5AHH7tchrdJfKHXFRBeLFikaF0BNAw6dYwyQkFwX8waxp5VecKIV1VHg208vCYBJQBjAh8Zq+rMhCq16dYKIB2sKfr6668jY3nEiBHSt2/flA83ar3OVKEtz/vq1bLmrbcy+h4GnqmutmgV+zjDK5NZB+WeLWNC48tEjmAIg0wXXffp0ycrckSc6Aczdc+hHLUFVJyrIsdClmEFMV6RAAlkmwANiiDRlTJv3Nny8+e6y6l/uSQyGHRUDi/zlu3aybDffSFze46V0VcfJN3vPVUOqVc3JTYoEtjGEaNU7lZ9VolyX8wpkYhEi8WRNl6kmbhDuc/zbxLwEVBjYubMmZHSbxXfuBFt2w5Cs26aHlyRMDvxwgsvSElJSaV2sCOuMYi7bOMa+ezzz6XnIYekzPyhDDjUj1/zUV1tEW1Wt3KNY6pKdchQQP51ZjIUxpZV15PEpbkjckQ+fN+i2FE5hvJAOaauC8qGHDETjvao31py30m1XYbaPngmARLIDQFuG5sBV7zc1E/cdUnS0R5X0UfnjWcw6hqanYCy4Z0ZSebJKhFQ3DCC5ypKNvsYCea2sZYIr30EsD3s4sWLpXnz5qLGBMJBucPH50LKC+ojFICPDc0AAB66SURBVFWcUadDbjuIS9344OLj28pUFe1M4rJlQPh8aIvIM8oIBS7ug3XKffXq1V5FXeOBUZIpK8oRy/b9BxiqYZZJn4pYaoscURdxYIbQvkcKoS36awN/JQES2BkC3Da2ivTUJxiP2V1H8GLCixtbHrojdrpjhs+NCYoWOnMoY3HGhLo/IFxofUcVi8LgJCD6rYlDDz1UJk2aFM1MAAsMY9Q51DWrbCgyVapQH0MGh4ZFu0BcqP8YBXUNDzXCMXOXzkjWOHHOp7aovOJ86LU86EvcgQott/YDmbKiHMPGhLKsSp9am+SIOtStWzetWtG5ENpiSoH5BwmQQM4I0OUpBq2+TNwRRvyOUVIoXtYn2hoZrhGAZ+AnjDMMEFfJ0mzA4Fi0aFE0Gglly3UpQRo+hQ8vSx4kEEdAjQlsHTp58uQoqK2zmHXwGbmoWzASUBfhbhM6EJfOHvjW+ECBRjzaBlyXi1C8+B3P+Eb78XtNbIvpdmBSl8fQtx6sXHz9gMvKhqccU+nsTJ9aW+VYKG0xtSbwLxIggVwSoMtTgK6OZrkjjKoIuL/raCOiwwsdH8rTQ2csfK4fGsZ28AiHvfyt4QCFAS83zIi4e8mrwoevEdPlSYnybAls2bJFFixYICeffHK5MaF1GT7Vbp3VZ9Wvemf89lF3MRKKnclc4xzpwChA3caMRsig8Sl2mv+a2BZhBLjf40BZwUJdbkJhrJEUN/igMlIOlKMSSZyz0aeGZJSvciy0tugOyKXWEP5FAiSwMwTo8pQBPTUAXCUKShEUG/f30OgpOm8dsXVnLDQb9sWkI8DWGEE49UeHgQHFzxoaNk8aJ88kYAmoMXHxxRdH27VC0YKhAONUjVwbHteol6jr8O0P1V19xirAPncoLMpGWr6Rc2u4+2bt8rUt+hQZLWvcLm3aniGXdB+qpBxTv32h9TGbfWptk2OhtUWf/LSe8EwCJJBdApyhcHjCJcO3QDL0u84OuAoAjAAYE1CSXCNAk4TyoFsw+kZn8WLUdH3rMfSeukRwUbaS5VkJqDExduxYOfvss8tnClAvYRi7xiueQ73LdPG1GtOYJUA9tMau5iF0hlGDr8dr/XXDaf121yiFfq9JbdGWBYxgnOEcKqu2dd+aLBsXrhEWfQdmfCjHVDrZ7lNt7LVZjoXSFq08eU0CJLBzBNwZChoUSZ4hJQq/25FaO4oacgcJKTYqOjsVH1Iw7IvRp/ipUmUXc9KgUMI8gwC+fg03p4kTJ8qJJ54YGa/43bd9qxLTdoC/fbMNGg5na0ygjmZ6IA07c2fbFOLQPOAMY1zv4+98aYvKAu0YedaZIJ/BBY66DgTl9Rl5Gh/6FgxC4KAclUrq1trZ7FM1hdoqx0JqiypLnkmABLJDgAZFgOOcOXOiO1aJUsUGN6wvM36HQo/RRKvQI5wq+qGXGsLgeSgGmI51FQxdQIjtNn1xxL0AaFBEIuR/SWNiyZIlMmHCBGnfvr2gPmGWy+fXr8BsfbftQO/bs8+Y0LqJdRKhL7jDmIbyjMOXBuL1fbfB5i0f2iLyq32EO8NiOapLlzvDacPg2vYLlKNLJ3d9am2WY6G0xcq1hb+QAAlkg4BrUHCXpyTVJk2apLhsWAXGKj72d3cb2bhRVys8GBGuYod4MZIJQwPKhU1Tn7Vp292lcB+KGA8SAAHMTHz66acyfvz4aJFzq1atKi3y95FC3YPh4dYtN6zPmNDfMJvg1m19XsP4FmYjjLoJuu5Ttt7bdmF/r2ltUY0imy/lgDPyrv0FZiVCO15hwTVcm8AO/QLYuoMQNl5cU44JImC8s31qbZVjobRFt23wbxIggdwRoMuThy06W3VBsAqMdsJQmuy6CKvYpHNZcJPDs5hOT+cPHcoT4tN8XXTRRfLll1+6SfDvAiOAnZIuv/xyOe644zJSQIEHSihG1N0NB1x0Wtfszkq+39zndCci+5wNo+m7a4VC9V7TrKlt0TWKbFnVcHLzbsNon4D+IVNDAs8rR8oxO31qbZRjIbVFtDEeJEACuSHAGYo0XFVRcUdR8aLGaJerEIUUHiSDKeVM/aFhiPi2zEQ8qoC4aeOezZf6VrtFVLcKV1lzw82bNy8aKXV3xoBSg4XqONx7O6PAIN5Zs2ZVYqr5Ur/lUL6hACN9V3mqLhnCtWVnZRhai1CTZYjvQ/jqJuSodQeyyhc5ZqMt7qwc0ebBy21vyjMXbZFyTPQ8tk+tbXLMtz51Z9sivgrOgwRI4PshwBkKw1kVUVc50k4YaxqsO0coPKLUexhddP3JoSzg43WhdRImS9HsBQwZnzKWTpmH8mHdKkLKrk3PvdaXK9ws3EWgysVV6N04lIXlirxhJyEcdhZInw0teMd9PKv+6e4aFl9aeEbzShmWpLjXKJdcyBBymjFjRiRSX/yUo9b2zM7V1RYpxwr5gAX71AQP7TvyrU+tkCavSIAEdoYAZygC9EKKKBRXjM5jpMT6OYfCI3o7pewaEzrSHFonodmzypabNsKkMyZ0VgNTvq5PPOLGywAzKKERONxD2VFOd3E4noeR4+Oi+dezjxOejzMm8AxcwHC4I7R2IaHrn+5LC3FQhtUjQyheOHzGBOUYoYmM45reFinHhKzYp1bs5JavfWpCkvyfBEggFwQ4Q5GkipFUdwRdR6IyHQVHVKrouzMKUKI1vrhpXMQBoyNuTUXc6L0+D/cnNw+4h5ciFhrqjINv1kJHQl23LzwPpV0XKtrddnDPPUIKPlwr8IEl38yEPoOPf7n39Z4vX/qypwwTUqgJMoQsYBC6dYxyTMgoX9oi5Zjok9mnpm4mkG/vRff9xL9JgAR2joA7Q0GDIskTIy46Wm9HT12lVhW1tm3bVvqSrRoT7ogsFCgYE1Di3fisOFXBwG+ue5GG05Ehd9YA99MZLWqI+AwNfV5nHnzxYyQVL1UoGLgft9uMKo1WwUcamn/3ZYR7oWdwT9liZsf9grDeg/JKGVbMHtU0GVKOIJA48rktogTa5tgeP4gGf9inJtYY1sT3orY5nkmABLJLgAZFGp6q1Pp2YIHCj9F112BAlKoou0qcxucq1jYbMAR0VgIvptDWkJqGTxnXEXpfvq2h4XsWebFGlDvzgHtIG2WJ21NfyxQqs5bRlwfNv4+TKl8+7qrYWGNC0/exoAyrR4aoG5RjqtHvawc1vS1Sjolejn1qvQSI5Kx3TX0vlmeSFyRAAlkn4BoU/A6FQWzXPuhIt96GkopZBij8rl9/SNGPU5I1XoRRFySsCYAS7B54eenMgU8J0XUZvlEy5FtdlNy1FJqOKuCuKxHS1VkJlBmuWnGzEohP43INAyj+mN0AV7eMPqMAcSF9sMUHBH1s9DlraFCGP4gYq5yqW4aUo7ayVHfBfGuLlGPtkGOh9anuGsYKKfKKBEgg2wRoUCSJqnKKGQa7kxNuWyXZdlDonHVdhKvoa3w+lwDEiWd1xN5nCKigEQ4LmLEjlJuGm37IVx3KfchFKS6fKFtxcXGUrhu35s+eLSdrkOF3GAbu7A2e1fStUYDfv/vuS5l+Qy85Z/bP5blXRspu9XexSXmf07h2VIa9f1gmf7vqAvnbiIdlXOf65WlQhok2UFUZQmCo4/ptFHcRfUj+OytHt51ofJQj5Yg6V6h9KmaaZ86cKRhVLJS2aN/XKS8Q/kECJJB1AjQokkihLLlKLW7h5ePbn11fSgjjds6qwPjiQ/hMZiUQDop4aHZBZz8w2u8b7UQeMKvhzhQgXj0w+4AwoXxCMcv0CBkTeImBH2Y4XEMtjtM///laIumGrWTXXVKNCZTdlVecO00mMjz22KPk29fOlgsfaSBDRoQNHeVBGSZIxMkQMsJ9rYM6a2IZZluObIupAyBo23rsaFukHCvqej73qTAmcPjW8eWiT60JbVHrPs8kQAK5J0CDIskYnZ/riqP4MbJpRzqsou92znEKFuJT96TQaKmmaV133NkFjSM0s5EuD0gDSgK2fQ0ZE1DQsROTVUg0b+45ZExAkccsB7i68YTyaA21fVrXF5E6KckhLcQJA0Vdz7QsOyfDOvJtMqWvN6yTdz/1G5gIovwpQ//XtVWGOMOY6NatW4oM8Ufu5Fjh2x2qY5oZyjFBIsSJctSakn6AASG1H6rJfSr6SNewL5S2WCFNXpEACeSCAA2KJNWQMYHO1zUmdMbCVfRDL2YkgdFBKMJ4SWPkP+RChHBQ5rFuAAaDHdXHs4gDL4BQHHF50AqkLz7XNcR3X3+LOyNPuv7ChkM6OLD2wh7IP+65L14769K9ex/5dPFNIrJGlk49Tx68+Fl5fr1I3WMvlIsv+pnccEiXcteFpnXmy3cfTJPBp78h85BQt1/K8JFDZUz/ztJCJHqB7r9fqbz5+Lly9xUvRPGINJFmQ34lV1x6vvSqV0f+85fTpOuQv8t6EXmib2d5Zuij8sGAdjbblKGhkYkMXWNbH8ez2oZQB6ziGqqTeJZtUQmGz7loi5Sj33C2UsiHPhVfjfYZE4XQFq2seE0CJJAbAjQoqsDVzhpkOuKO6KHkY6ocSrfv5QwFC3HjjFkDjLy708VW2fa5OCGdOLcf3IfihnwgjZDilu7F6OLCKC/idbdyVaMI6diXmLpdYHRfZxjwG+IBp4pZl42JpF6/RX7d6hb5w98myog1U2XzP++TG89YJD97ZbJcsG2h7F5vnvxj4jgZXe8quW/hn2VI222y8vXLZMyPesoR/z1d5o7uIS1kpcwbd5qcsvhi+d308XLWirel076bZMm9Y+S0S3eVPV68RE496Tl5bdIA6Tmsjgyc8bDce0TrlKJShhUj/5nLMAVh9Ic+q25QakzgZq9evVLqSuWnK35hW6xgoVe5a4uaQsWZckywyK8+tUJ+uCoUGaaWmn+RAAnkigANigzJ6si/b8Gv3nNH3PGygYKO2QY8pwq0JonnsPMRwmH/bnyJG4p5gwYNNEh0VteMCmU75Xb0hxoCIbcfVdxwDhkTWFOBPIXicFOFkaM7N9k8Iw58mA8zE+7MD9LXmRc8j7D4BwWzT58+lcouzc6R394wTDosf0uK6u8rx13ykGz5rJecdf8L8pPLustBy1+V0a+cJpe9e74MaYu1FrtIm6P/IHc+uUK6Dpkgtw56RCa0nibPjK8vh97fV/b87E3plFx43+G8f8jR978hs1dcKEc1XyXLV22UurKnNGravLyoyC9lmLrzWJVlmKSJ5+wIus5UoI5ksoOYCgX1BTJhW1QiiXVZOW+LlGMFcLO4G/U6r/rUZN4LoS2mCIx/kAAJ5JQADYoM8MaN/Kty4xoTUJbQYWN03n3ZQJHWxdZQrl1DQ7NklVkoXDA4fIcaE246GhbxYKcoHKFRYJRDF2i7RoDGY89aPjvTgPv4HfGgXL78Im4YH/PmzYsMraAhoYkdeKjsU7w+Mrowu7N58xrZ1rixlD7zjqy8vb+8/fDbsq3HYOndxi7cLpbG7TvJgTJbFi/fJNJ5uJzz2lEyZNWLsvCvX8mT770nHZvMkQeunCPz5GTpsGGdLFixQDrt2QSONZpyuZ8/ZViOJLqosgyTj8NgRV2EHNWY0JmK1BTCf7EtVmbzvbVFyrEcfl73qSLRduCF0BZdT4JyAfKCBEgg6wRoUKRBapV1d90DpoxVCbdGge6e5C7aRXh1BcI9uzbDzYYqCVBmXfcnGxauH3EuTPbF53O3QlzWCLDlsOnYa6sMWlcnpAVDCa5dobLZ/MSVqzy9rZvli+Ur5PiSkqicy5a9Jbs1LBKp20Rk+7/k83e/EalbHtq5WC2ffL5WPvr0PflkyqVyyV2fy3qsrzh7D5HVv5Q7Z3SS3/adI++9/bFcP7irNHhv1/LnKcMsyjDp9ocRdBjGqK9oN1U1JtgWy6tn+cX32hYpx4i77cPysU/F4FGhtMXyhsILEiCBnBOgQRFArC8NnEMj/xhpx0I3PRAWSg9cnNwZBSio6MShbKdTpHXWwzVINB17xiyAbyYAYbQMuA69+BBGF+WFjACbXpzvOpRExIe0Qgfct3CE8qPPlZZulY+WfyPy3brIONm2eWPEtkePA2Td+0nFv6i1dDikgcj7+pR73kNaFq2X7z64X+65S6Ttg+/Jp6d3kESl3yb/+cv9skiKpMu+B8oeezST/0SPl8mXy5bKx7KMMnRxJv/OVIYIjvqC+qxtAjuHoY24M3qBpKKftR7jzLZYQer7aouUYwVzrYv4JdSHIUxN7FORr1mzZkWFwfupUNtihTR5RQIkkE0CNCg8NDGTAHclHCEXIfex0IwC4oIChfsHH3xwUPlHfOjwoZRjBLcqCpebF41L3ZziXnwI07Bhw0rbuvri1FF7n++6Ko4wluwibI0HHPCRPDujoffcMzi88cZMKS0rE/l8k3z4n61S94OEEtqy5VZZ8PFaKT7zBBnYtJU07HuYFE96S2av/Kn0aqduT9tk3ZLFskBayjF71Je2xV/LIimRIV33SBoTSPE72bguufA7mYFvvi2VUvlaSrd+J7379C5fz0EZJgBVVYYwPLCWBh/SgiGANlBVYwJpsi26LSThsoK+4vtoi5Rjgj/6pXzuU2fMmBEVBH10obbFyi2Jv5AACWSLAA0KhyQ6Wowu6TaoPuXYeSQagfW5cNhZidDOTBqXVZxCo7AaNt05kxcf4rAvx7g40xk6uL9o0aJoLYhv/YVy0MXYcWnBMEFcdeuKRN+hWP+kTLyqldx50znSrl2pLL73DDl90iD59bwesqcUiRx1sYzrd66MvvJA6XQLFmYXydr5o2TYT9+QogsnyYSTu0rzTYPkzOLR8uxDs2X4uJOkpGhztBPUlaPmy3o5IMrOihWrZO3WRtJJtkjrffeVrV9vlXoNGshyM7NEGX5cvqA+Exmi7cCtCd+h0Fk311BGvbcL+m28bIuWRuK6Otoi5ZjZbC8kVJP7VOQvzpio7W2xcmviLyRAAtkkQIPC0FSlJxNXI33Mt0gUHXOmsxKIZ0cUJ03fPWdiTCAMRn03b94cvWDijCY1dPCMz9DR9BAHRkvtgXs645JudsYyS6wv6SZvvX29SNfBcsXJb8mLx94gQ9eLFA+6Ri6a0k+O/Ph1kY59RRr3leH3PSMdHrlVxh54hZyHDBzwX3La7/8k84ceH32HQpqeJb+eukRk9JlyZPNtItJROo8aJVf+TxvZ49Q/yZtrVsm7330uR/a6QK76xQg57Yg28uBR4+W2O46VvZctTTuzhCQpw8Q2lFrv7RohGInuzIStG9ZtUOsP26KSqDhXX1vcP8oE5Rjv5lTz+9T9IxfEQmyLFa2IVyRAArkiUKesDH4lqQdcFDZs2JD6Yy3/C50sXI2gFIcWJkNptCPw6gpgFW28dLEwGeEwGhsafVWcUBJmzpwpVTFi9FkoXXAjsmsoMLsC39iQm5PuMAUDIBRG49eyhGZr4uICK93JCv66IQ6qWKIs4I51HDasZa75CbGlDFVyFWdlVp0yRG4ox4rdw1Q6ce1Hw+iZcmSfyj5VW0P82fdejH+Cd0mABHaEgGsr0KBIUsQLG2sJrMFgAcN40J0xrAIPgwAKsFWMfX7NNi73Gs/GzRK44fF3SHlGXDjc+PC7GkBwPYpbgJ1JWZSHzxBS5QfuLmDh5gX5QxpwhYKPPZgjT+4uWlFBkmFRXt/XwzUMzpRhBY2aJkPkDHmiHBMc8rUtUo6pbSxf5VhobbFCarwiARLIFgEaFFUkaTtejLT7lF4dOUJYhAkZJVVM2hvcuj1kmhZGbOB6BIMJrkdx+bOjpr6weh+Zw32Xhy7cDhktYJSpIYE0ND0YJb78eCE5P1KGqR+mU6bflwwpx4oKmc9tkXKsHXLU9l/ofWqFNHlFAiSwIwRoUFSBGjpe+MVCAQ+5L6mCEBqN1xmMKiQbDKpphdxX3AeRfyxwxlqJOFcufc7OOmAGw84sQCmHUYI86OJqex9xYPQZ992Ft7gHDogfbmXpZiQ0P/j4HcKHjBPMSGh6bl40DsqwwtWmOmQIYxtywuwe5Zi/bZFyTPQo7FMTgzz5/F7UdwPPJEACO0fANSi4KNvDE4pXuqlsVc7i1l1A2YWSjTUW7ki+J9ngT0hLXUUyMQzw0oMCByUALkkdO3ZMMQ7chOwMi5tXpG1nFLBLiG+GA/kDi9B9xIP1Hna9iZsP+/fUqVOjP938aBhdDB/nUkUZJmhVlwy1/mNmjHLM37ZIOSaUaPap+f1e1HcHzyRAArkhwDUUDlco41hMHDcdrAo4Hg254ehL2DdaDwUPo/1Q9H3Kuc2SrkeImyXR8GpI4Ky77IRG7vGMKpp4UfrC4z62QcS5pKQkZfG3pomzGhOZGgv2WfcaaWl8MBbAyB42TyGXL8owdVaiumSINS+QF3Zxcush5Whrdc1ui5Tjx5Hrpa+PTJVizZajDn4VWp/qyoh/kwAJZIcAZygCHKHgpBvRxqMwFGAMhFycNAyU4pAxoXuV292M3GwhP4gj3UJkPGcNCeyU1KdPn5Sdkty49Rndhck3eqwKH8LGfdxPlX+fMYE4YHxlOjuDsJhKh/LpKwPKqVPtvh2qKMPdU0Rd3TLEbJWvjlOOKWIqXyeEX2tiW6Qc2adi84yQyyLqbU19L2b67kltkfyLBEhgRwhwhiJJbdasWbGzElDOYEjoKE9oa9l0MxNqTPgUYhUgXIwwa5BuVkLXJSBN35arGp89u0q3zx3KKqKZ5NNnTCBNNYjwQbh0hy7mxiig72vaej/0UstkVoIyrCwFrWvfhwyROuVYIYN8bYuUY4UMcZWvciyEtjhgwIBUYfEvEiCBrBHgDEUAZdu2bYNbqerOSng0pHjh3s4aE0gHSjhG6uPWSriGhG8031dMHUWCoRJa64C08S0L+L3HGRO60BbcfG5bSAv/wCvuwMsYsw5IFy5MdktePIf7apiE7tvF4qHtcCnDylL4vmRIOVZmn49tkXKsHXIspD61ssT4CwmQQK4IcIYiDVldw5BuZyUoCFB807k5hZR0uFthVgKuVIjD9TlHNvEi0BHlTGck8Jw1VDDC7/rQKgI1JuLcuezLCLMJvhmOOBaaFs7W9QVldt1jkB91y/KtVbFKGQwwn2GDdChDSz3VSMu1DJEy5VjBP1/bIuVYIUNc5asc2RZT5ci/SIAEdpyAO0NBg2LHWfJJEiABEiABEiABEiABEig4Aq5BUVRwBFhgEiABEiABEiABEiABEiCBrBGgQZE1lIyIBEiABEiABEiABEiABAqPAA2KwpM5S0wCJEACJEACJEACJEACWSNAgyJrKBkRCZAACZAACZAACZAACRQeARoUhSdzlpgESIAESIAESIAESIAEskaABkXWUDIiEiABEiABEiABEiABEig8AjQoCk/mLDEJkAAJkAAJkAAJkAAJZI0ADYqsoWREJEACJEACJEACJEACJFB4BGhQFJ7MWWISIAESIAESIAESIAESyBoBGhRZQ8mISIAESIAESIAESIAESKDwCNCgKDyZs8QkQAIkQAIkQAIkQAIkkDUCNCiyhpIRkQAJkAAJkAAJkAAJkEDhEaBBUXgyZ4lJgARIgARIgARIgARIIGsEaFBkDSUjIgESIAESIAESIAESIIHCI0CDovBkzhKTAAmQAAmQAAmQAAmQQNYI0KDIGkpGRAIkQAIkQAIkQAIkQAKFR4AGReHJnCUmARIgARIgARIgARIggawRoEGRNZSMiARIgARIgARIgARIgAQKjwANisKTOUtMAiRAAiRAAiRAAiRAAlkjQIMiaygZEQmQAAmQAAmQAAmQAAkUHgEaFIUnc5aYBEiABEiABEiABEiABLJGgAZF1lAyIhIgARIgARIgARIgARIoPAI0KApP5iwxCZAACZAACZAACZAACWSNAA2KrKFkRCRAAiRAAiRAAiRAAiRQeARoUBSezFliEiABEiABEiABEiABEsgaARoUWUPJiEiABEiABEiABEiABEig8AjQoCg8mbPEJEACJEACJEACJEACJJA1AjQosoaSEZEACZAACZAACZAACZBA4RGgQVF4MmeJSYAESIAESIAESIAESCBrBGhQZA0lIyIBEiABEiABEiABEiCBwiNAg6LwZM4SkwAJkAAJkAAJkAAJkEDWCNCgyBpKRkQCJEACJEACJEACJEAChUeABkXhyZwlJgESIAESIAESIAESIIGsEaBBkTWUjIgESIAESIAESIAESIAECo8ADYrCkzlLTAIkQAIkQAIkQAIkQAJZI0CDImsoGREJkAAJkAAJkAAJkAAJFB4BGhSFJ3OWmARIgARIgARIgARIgASyRqBOWVlZmY2tadOm9k9ekwAJkAAJkAAJkAAJkAAJkEAlAhs2bIh+q2RQVArJH0iABEiABEiABEiABEiABEggQIAuTwEw/JkESIAESIAESIAESIAESCA9ARoU6RkxBAmQAAmQAAmQAAmQAAmQQIAADYoAGP5MAiRAAiRAAiRAAiRAAiSQngANivSMGIIESIAESIAESIAESIAESCBA4P8AWlNmWh02VRYAAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An air molecule is situated at point X in the pipe at <em>t</em> = 0. Describe the motion of this air molecule during one complete cycle of the standing wave beginning from <em>t</em> = 0.</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 speed of sound <em>c</em> for longitudinal waves in air is given by</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = \sqrt {\frac{K}{\rho }} ">
<mi>c</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mi>K</mi>
<mi>ρ</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>ρ</em> is the density of the air and <em>K</em> is a constant.</p>
<p>A student measures <em>f</em> to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m<sup>–3</sup>. Determine, in kg m<sup>–1</sup> s<sup>–2</sup>, the value of <em>K</em> for air.</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>Demonstrate, using a second ray, that the image appears to come from the position indicated.</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 the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.</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>«air molecule» moves to the right and then back to the left ✔</p>
<p>returns to X/original position ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 2 × 1.4 = «2.8 m» ✔</p>
<p><em>c</em> = «<em>f λ</em> =» 120 × 2.8 «= 340 m s<sup>−1</sup>» ✔</p>
<p><em>K</em> = «<em>ρc</em><sup>2</sup> = 1.3 × 340<sup>2</sup> =» 1.5 × 10<sup>5</sup> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>construction showing formation of image ✔</p>
<p><em>Another straight line/ray from image through the wall with line/ray from intersection at wall back to transmitter. Reflected ray must intersect boat.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>interference pattern is observed</p>
<p><em><strong>OR</strong></em></p>
<p>interference/superposition mentioned ✔</p>
<p><br>maximum when two waves occur in phase/path difference is nλ</p>
<p><em><strong>OR</strong></em></p>
<p>minimum when two waves occur 180° out of phase/path difference is (n + ½)λ ✔</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.</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>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;" 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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>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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"></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>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>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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"></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 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><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 src="data:image/png;base64,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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>Cold milk enters a small sterilizing unit and flows over an electrical heating element.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The temperature of the milk is raised from 11 °C to 84 °C. A mass of 55 g of milk enters the sterilizing unit every second.</p>
<p style="padding-left: 210px;">Specific heat capacity of milk = 3.9 kJ kg<sup>−1 </sup>K<sup>−1</sup></p>
</div>
<div class="specification">
<p>The milk flows out through an insulated metal pipe. The pipe is at a temperature of 84 °C. A small section of the insulation has been removed from around the pipe.</p>
<p style="text-align: center;"><img 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rkbkXqgQKlwa9rQVzBd7wMXtITH4Ccw1k+Lkq0mHK+yK6Nq1bfxAw7vPSQq9ELfbq6ipgYuPqFYfeQ0jswdAqmkrqwnPsH7236G39gnMNijpSgRj/nQUAzyru12X8RnyxaK16Bi30HjiSGvxiHaNxeGWeKzUP5R8ELoa1HQe4stFXUGh46Bn/NrQERUjYbvUfnkX1h5tD+WyGeraxGODxEVshAZReKvmPUYkieMQ2z2cPls1mLJxa7p/yNOFMff9tlWzWfRV+EfvRWZiXpRU4/EzDzkRD+E/7HfVXEdZ41vICRsOc6P3STObk+L7Z4Pzx3Tnc6y6+Msmm6L9Tvs23QAGOiP7q5lb2ENXP3/jNHlSaU1vMPXi/fUCgw8swtGoxHGTQmYEPI6cpQa5bz7oqd8sJaIENCtNx7S1u1A2qq9K9oqt6FpC7cOrZSF2qu+jY4IGDkU2pL3MWnaImwyfvarA7HGOxybLUfw74HnsVnaN8YNMEwIRVyOQ5dUTaw/Iu/QD077TnC5H30fuhcwn8SZ8m3Uor1ra+W2eOx2buig3CYiupWGDypax7PegQgd2w8o+RJfHb8MXDiCveIPo/ah3ugmnZGJc0MfEQaOWPZi7pD29vvXSR3OoqtTtB/LZqQCI2YiPqynOLuVmig7y16GWR+ZlfH3+jmLpttgLcFPlioOqG1d0d4hH1jz0xEX3B/DwmZjy6mr0tEZ41b8A4HK+nId3NDO8ZPg1M6d1xKe+tnYnLwU0zvuwdSoZzDMV+c0H6SOrGeREfd/4TvsGczYclK00Rr3j5uL+EB3pcItlL0GzvtOtOPaXqTFkgIUXv51YYqISNLwQaWVG1zblj1MC7Rzu0e5LXTwx8gRnihJeRXTDBtgzCgb8rlddTiLrob1fB4OlWjh/UgPe9CRlZ1ll8BsPle+jfVxFk23QaPFPTpxMLxQiEuOx8LLRbh4TbktDU0seRNJ3wUj8Yu9WB09Fnr9KAzu9FtcUGpUq1I7auEK7yF6hM/9WO55TE+eg9Gn/4WoZ5fjM6l3sk6sKPpsJSYlnceIxP04vHoaRuv10A/WiX1ayyde3WsgThaKLooAo3WHW/nnnojo9t3ZvyQaHfQL1yM58QV03PEmosKGwtd5Pkgd1fosuhrWSwWwoJU4UWxbeecoZ9kl5wtxWSmiO0RzHwaO7uc0vGBF8fGDyC7vaLmCwvNFTkMTos6ZkzArS+X2mXC0/GAvDuKmT7CpxAuP9dWp9Oo1KbSMw0sTh4s35Ankna/qsyKex1ET9ilLlVlxubAAJfDGIz07VLzPi8+JIF7LoR/N7+DVSxri+QqHHT+rxafwVbY0JNQVneReUiKiX+fO/yVx8cYQfQTmbj8GS+4eJMcPx2nDFPnKg7rP9fgVZ9EKTTt36HBNnCheFn/OHShn2dqObhW9KHSHtMYDgU9gBD7EWws2y/M1rPl78PbMZchVagDtoOv5AJDz/7AlR7oC5TryTR9gwVsfigM0cO1iUUXgLKnczkJRByNiMHnw7Qw/NgDpCp2JAZUnohcfw/YtmYDvw+j9+7bo0LMf/HAYq5an4Zj8PL5A0rrt8nO9mQYuuj/AFwewYcshuYdQntS+4B2kyDunEEXlwzYFOHAqH4UnTiiXdJdpj8GTY8RrkIoZcR/KjykPJ70dD0OuL6Jn6eHNnEJE9UBdf0qk0BI+ERMD3VFyKA/nK/1hLFOIo1nVDeTU4Sy6GpqOXuglDfF8ccThD3PZ2boW3t6/l+et0J2l8QzBws1LEXR+njxfwytgEW4E6cXBt4wb/P/2FhJDS2HQPwidrisCZubC++/zES3NJXJ8f2n/iIdK31PamYGzQUuxeWEIPNXy6dDoEDJrJRKDzmDGMF/7VWa+o7Gh48swJk2EvzT/y/sZrEp9HQP3zcBw6XkMfQ83Bgx32B+ORFDxD8eSxKcAw+PwFe15BcTjqPckJEYPrOil6fAIXogJwjVRp/fItTha3ntlZ38N1mF6x43yY+q8AjDp7FAkGlfgZX83pRYR0a8kfYV+vTmXZovo0snWJyHb9ovNYkuL6GXr0ucdW/YvynpRei5tsq1Ll0BbQvYl240zabYXuv/BFjQzzfbtpRti/Q3bpaPJtgipLCHTdsl2xfbtmmdE/f62iDXfiOVrtnOZK8T6TuVtVH7Mn2zZCXqxTi/W/STaE/Wz19lmBv1BlHWydZ+5x/ZzpW04Yzv+7RnbaYdtku5zJi3K1r38McVWndtte0NqI2ixLVvazkqPWaaq50uNSn5detki0ixKwa3wNSMiUrs7es6o8RyBWesXlJ8V63Q6+A7fiI4z1yHp5f5wkSbHhr2D1Jhe2BcXJM78umLovy5hwOi+SgvOanMW3UKcKD6DmMCfRJ0AjEw67DSBt+wKixfRccNo5WxTOsteUH72WhsFBQW4cuWKskT16yIyYgdB12Miko5VDIUYl7yHndqhGBnQ0V5GRER3Pf5TwgayYsUKtGvXDuPGjVNKqD5Z803Y/MEyzDDsUOZhaOEbOgOvhY/GEOmLxWpF+kLBOv6jPiIialQMKg1E6lF5/HE9/v3vD9CpUyellIiIiOqC8/IbiLu7O6Kjp2HZsmVKCREREdUVg0oDCgoKwvHjx7F//36lhIiIiOqCQz8N7Ouvv0ZU1EvYvn0H2rRpo5QSERFRbbBHpYH16dMHAwcOQmpqqlJCREREtcUelUYgTaz18+uNzz//khNriYiI6oA9Ko1AmlibmLiUE2uJiIjqiEGlkXBiLRERUd0xqDQSaSJtbGwsFi1axG+sJSIiqiUGlUYkTazt1q0bduzYoZQQERFRTTiZtpGVTazNyTkoz10hIiKi6qk6qEj/zp7qn8VyWrlF9Ovxc1r/+BklqqD6oPLhh/9RlpqOa9euYd68uQgNDZOHghrTU089wT+CVK+a6uf0TuFnlKgyzlG5A1q1aiWHlJSUZDm0EBERUdUYVO4QqSdF+vK3zMwvlRIiIiJyxqByB40d+zSWLl2CoqIipYSIiIgcMajcQa6uroiIiMSGDR8oJUREROSIQeUOe/TRITh06JD8rbVERERUGYPKHSZNrH3hhYmcWEtERFQFBhUVePDBBzmxloiIqAoMKirx+OOjObGWiIjICYOKStx7772cWEtEROSEQUVFyibWnj79vVJCRETUvDGoqEjZxNp3331XKSEiImreGFRUpmxi7X//+5lSQkRE1HwxqKiQNLF248aNnFhLRETNHoOKCkkTa0eNGoWPP/5YKSEiImqeGFRUSppY+8UXn3NiLRERNWsMKirFibVEREQMKqrGibVERNTcMaio3IgRIzixloiImi0GFZXr3LkLnnzySf7DQiIiapYYVO4Cf/rTYPlKICIiouaGQYWIiBrZ9zBG9obOLwGmUqWIqBoMKkRE1Mi6QL/6ICw50+DfQikiqgaDChEREakWgwoREdWjUuQbp0CnC4dhUyIie3QWt8VPcCxSTPmwynWchn7yjYjU9Ua4IQWJkQH2+rpRiE3JQr79DjJrfhZSYkcp6zujR2Qi0s28IrKpY1AhIqIGsBuG2FwMMubCkpeJ5ICDiNVPwmJTobLeWQE+MSzBwUFrkGs5iczkh5EdOw7hi7NQLK0uzsLi8HGYd/4xpGaelNtc4bkL40PegPHsdbkFapoYVIiIqAF4YsT8mQjzcRVHGk8MeTUO0b65WJWag+r6QLQjZiI+rCdc0BIeQ6ZgXrQvcld9jANFl2H+aBEMuf0wfXo4+nu0tLcZ8wpCkYoZy/ZX2ybd/RhUiIioAXjjkZ4dKg4yLvej70P3omSrCcervNJHC+9HesCj/A6u6Na3F7QlX+Kr49/h8N5DgPtD6H1/a2W94PoA+g90r6FNagoYVIiIqAHcA7d2jpf0tIZre61yuyqt0MGtrcNBSYO2rm6iVLhRgsIL14CCBOi7KnNe5J8/ImpngVybmi4GFSIiagRXUXSxRLldG1ZcLiqE/J3cv9XCrYOILH5zkJ53GhaL0w8vc27SGFSIiKgB5CDrqMPE2aJvsGtTHrSP+aNblaGiAPuyTjjMNSmAadcnKNE+jL7d7kPPQb1Ek7uw78RVZb1gPYakEB/oQpJgdrg6iJoWBhUiImoAeUh5KxFG6fJh61lkLHwHKRiD+ZMHwFWp4awk5R0sMB5DMa4jP2Ml3kq5jhHzIzHYtS0eCHwCI7SfYsGCJGTlX5euVUbW0rexIMcX0bP08ObRrMniS0tERA3AE4EP/YyVw3yh8wrApLPDsWbzbOg9Wyrrb6YN9EXpyhD46roiYNIpBK1Zj4V6nXyg0njqsXxPGmZ23IoxAV1Fm/0wZpsHZhpX4GV/N3sD1CT9xiYot1VHmixF9U8a0yWqL/yc1r+7+zMqfeHbVAREmRFtTEW0v4tSXgPpC98CpuBA9Gbx4w9ONyFHqg4qRER0t2FQofrFHhUiIpVRW4/KlStX0KZNG2UJOHPmDObMmYOtWz9GevoeeHt7K2skDCpUv9ijQkREN1mwYAF+/vlnrFuXLC/n5ByEu7u7fFsKLqdPn0bnzp0rBRiihsCgQkTUDBmNRpw7dw7ff/899u3bi9Wr36vUM7J//37ce++9DCN0xzGoEBE1QV9//TVOnTpVHkbGjx9fKYhIQcXFRYv77vPC7373u/LeEiK1YVAhIroLSfNELl++jMOHD6O4uBhdu3bFgAEDlLXAihUr0K5dOxFGXNCzZ0+GEbprMagQEalUQUEBfvzxR3z3XZ7c8+HYIyIFEamnxNfXVw4jgwcPZhChJolBhYjoDioLI1LvSJ8+fZRS+2TWbdu2YuDAQejSpQv+8pe/OF1dQ9Q8MKgQETUw6SoZKZB06tRJKQF2796F558fL98eNy4MAQEB0Ov18jIRVWBQISJqQNIQzfz5czFv3lsikIxTSu09KdLVNLyihqhmDCpERESkWg30TwmlbyacAp0uCAZTsf1bB3Wd4WcwiTVO64iIiIiq0UBBpQU89Ethseyo3dcnExEREVWhgYIKERER0a9Xi6DyPYyRvaELjsX7hgj00HWW/1lgj8iVyDIfRnp5mQ+CY40wF1vFfeo2vGPNT0dcsI94jDnIyL+ulFJNpK+3lq4kICIiaspq36OS+xE2/vQM9uRZkGt8FfftnIMxw8bjg99GiLKTyEwOBVKm45WPzJCiSq0VH0by6zOQhFAkJ72KIR4tlRVUkwsXLiA4OEgOLERERE1V7YOK9im8FjMUHhoNXPyCMNZPK8qCMS78EVHWEh6DRiDIvQQ5e4/ggnKXWyo6iKSp4xF3OoQhpY6k71uQ/onYokWLMHPmTPlSRyIioqam9kGllRtc2yrVNW3h1qEVMNAf3V1r30Rlh2EIexJxO1si9LWJDCm3QfqWyo0bN8pfFPX443r5n4wRERE1JbX4HhVpjspjiDoQDuOBafBv4VCGeGSu1sNDKio1wdAvRPwsFWUjAeNUBESZEW1MRbTnbkQGTMGB6M3ipzcuyuvEQVXrA99Op5HbYjKMH02Bv0vVoUeaE0O1k5NzkP/vg4iImg4pqNTMYkuL6GXr0ucdW/YvSlFZWUSa7ZxSYvsl25bQp5NS9ovtXNpkW5cugbaE7Es2sWCL6NLJ1ichW6wpWzfQNnPPedul7MW2oC5/sI1ac9R2Q2mKau/bb7+1PfHEE7YZM2bYfvzxR6WUiIioabjdcZt6oEV717Zw8dNj4oj/g5wFy7H5LK/4qS3pih/pq7kjIyMwdepUzJs3jz0pRETU5NzBoKLQ6BASNxMjkIoZ8dtwtk6XDDVfs2fPRlFREbZv34EBAwYopURERE3LnQ8qgsZzCCZM6I+SbWvxYU6hUko1kXpQpk+fzn9oRkRETRr/KSERERGplip6VIiIiIiqwqBCREREqsWgQkRERKrFoEJERESqxaBCREREqsWgQkRERKrFoEJERESqxaBCREREqsWgQkRERKrFoEJERESqxaBCREREqqXq//Wj03VWbhERNR8Wy2nlFhHxnxISERGRarFHpRni2RrVJ35O6x8/o0QVVB9UPvzwP8oS1YennnqCfwSpXvFzWr/4GSWqjJNpiYiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVOgudx35pvWIDfaBTtdZ/ukRmQCjKR9WpcbNSpFvnFJev+InCAZTsVJHsObDlBKL4LL1PSKQmFVTu0REVN8YVOjuVrQfS56NR/ZDC5Cea4ElLxMrPPcgSv8Kks1XlUrOCnE0Kwfwm4P0vNOwWMp+diDa36W8jmnxJDz7aXcsVtpNfuICFo6ZhMWmQqUOERE1NAYVuotZUWT6BJtK+mFseDC8XcTbWeOJwaFj4IdD2Hv4B6WeE+uPyDv0A7S9vNCxmk+A1WzELMMPGD3uf+GjtDsk5hWEarOw9tOTKFXqERFRw2JQobvYZRz/6kuUaB+AV8eWSpl4U9/fG0PdC7Av6wSKlLJKis/BbG6Fgf0fgKtSVNlVnNi3CznaP2O4v7tSJrgOwdwjp5ET7Y8WSlHFMNIoxL7/T0T2cBwmOoZj6YkVZcFxMJqr3CIiIqoGgwrdxa6i6GIJ0MoNrm0d3soaLe7RaVFyvlBEmZuVHjdha0lrlG6JQY+y+SfBsUgpn9dSiks/XRTttkThN6scgoZjHWdfIWXjNYzbcxKW3DRE37cXC8cMg/6DlnhBlOVlrkU4PkTUK5tg5iQXIqJaY1Chu9gVFJ6voodC0xZuHVopC86u4tTBbBSIWy0GxSFLnptiQe7i7vj02bL5Jz/BcvgcULASM96HHDQslpPIfK0N1uurm6PihdDXJmKIR0vApRdGju0nl40e91f0F2Uaj4ehD/ICcg7g8AUOHBER1RaDCjUzreEdvl4Ej0ysDu8J+9RZDVx8hmDkwBMwzDJW9Hhox2B+/PNy0ABawmPwExjrl4tVqTlVDClp0d61tXK7Bdq53SN++6F/dzd7ERER3RYGFbqLtYFbxypmmVgvo/DCNWWhjiwFuGRV2m11H3QdKua+lPXUlGw14Tg7RYiIGgWDCt3FWsO1vRa4Voiiyw4TP6wl+MlSAm1HN7RViurGBZ2871NuV0Hnjnb85BARNYrf2ATltupIExip/knfGdI0WFGUMQsPh53A9PT3EO5tH3qxmpOgHzYfiN8MY7iPUxq/iIxYPcI2/RnJX87CEFdlrfUYkvQhWNDrX/hy7mCginYr1xmiXDEkXfUzFQFRZkQbU5XvYSkrAxIzF0HvIV0jVAyTYQz0Bm+HsqaBn9P613Q+o0T1QAoqRHetn/fYZnbvZOsekWw7eumGzXbpqC1t5khbl+5RtrQz15RKjm7YLmUvtgV16W+LWPON7ZJcds12bs9sW5DjfW58Z0t7ob+t+wtptjOiWfFAtm/T3qhcR/aL7VzaZFuXLoG2hGx7axVlk21p535Ryi7ZshMCncqIiOhW2IFNdzfXAXhp/QKMPj0Hw3110PkOQ1R2b8xdPwMhnvb5JaWmBPjpeiPS+L1Y0sDFfyKSjDPRc+94+MqXJ3fF0HWu+Pvm2dAr94FGB/3C9Vjq8zGGeUl1fBGypX3lOkRE1OBUPfRDjaOgoADu7g5fbEZUDb5XiKixsUelGbty5QrWrVuHxx/XKyVE1ZNCip9fbxiNRqWEiKjhMag0U19//TWCg4Nw5swZbN++Qyklqp7Uk5KTcxCZmZl48sknYTablTVERA2HQz/NjHRW/O677yI7Oxtz586Ft7e3soao9nbv3oXZs2fjb3+bgDFjxqBNmzbKGiKi+sWg0szwUlKqb489NgorVqxQloiI6heDSjMjddfHxsaiW7duiImJ4cRIui3SkOGcOXPk26+//jo6deok3yYiqm+co9LMSEM9a9euha+vrzyJVurCJ6otaQK2NJn2mWeexpgxo+WeFIYUImpI7FFpxhzPitl1T7cihZTnnnuOvXFE1KgYVEgeDuKkWroVKahIk7HZg0JEjYlBhYiIiFSLc1SIiIhItRhUiIiISLUYVIiIiEi1GFSIiIhItRhUiIiISLUYVIiIiEilgP8PKscAbPcBwG0AAAAASUVORK5CYII="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the power input to the heating element. State an appropriate unit for your answer.</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>Outline whether your answer to (a) is likely to overestimate or underestimate the power input.</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>Discuss, with reference to the molecules in the liquid, the difference between milk at 11 °C and milk at 84 °C.</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>State how energy is transferred from the inside of the metal pipe to the outside of the metal pipe.</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>The missing section of insulation is 0.56 m long and the external radius of the pipe is 0.067 m. The emissivity of the pipe surface is 0.40. Determine the energy lost every second from the pipe surface. Ignore any absorption of radiation by the pipe surface.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe <strong>one</strong> other method by which significant amounts of energy can be transferred from the pipe to the surroundings.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>energy required for milk entering in 1 s = mass x specific heat x 73 ✓</p>
<p>16 kW <em><strong>OR</strong> </em>16000 W ✓</p>
<p> </p>
<p><em><strong>MP1</strong> is for substitution into mcΔT regardless of power of ten.</em></p>
<p><em>Allow any correct unit of power (such as </em>J s<sup>-1</sup><em> OR </em>kJ s<sup>-1</sup><em>) if paired with an answer to the correct power of 10 for <strong>MP2</strong>.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Underestimate / more energy or power required ✓</p>
<p>because energy transferred as heat / thermal energy is lost «to surroundings or electrical components» ✓</p>
<p> </p>
<p><em>Do not allow general term “energy” or “power” for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the temperature has increased so the internal energy / « average » KE «of the molecules» has increased <em><strong>OR</strong></em> temperature is proportional to average KE «of the molecules». ✓</p>
<p>«therefore» the «average» speed of the molecules or particles is higher <em><strong>OR</strong> </em>more frequent collisions « between molecules » <em><strong>OR</strong> </em>spacing between molecules has increased <em><strong>OR</strong> </em>average force of collisions is higher <em><strong>OR</strong> </em>intermolecular forces are less <em><strong>OR</strong> </em>intermolecular bonds break and reform at a higher rate <em><strong>OR</strong> </em>molecules are vibrating faster. ✓</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>conduction/conducting/conductor «through metal» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>e</mi><mi>σ</mi><mi>A</mi><msup><mi>T</mi><mn>4</mn></msup></math> where <em>T</em> = 357 K ✓</p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>2</mn><mi>π</mi><mo> </mo><mi>r</mi><mo> </mo><mi>l</mi></math> « = 0.236 m<sup>2</sup>» ✓</p>
<p><em>P</em> = 87 «W» ✓</p>
<p> </p>
<p><em>Allow 85 – 89 W for <strong>MP3</strong>.</em></p>
<p><em>Allow ECF for <strong>MP3</strong>.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>convection «is likely to be a significant loss» ✓</p>
<p><br>«due to reduction in density of air near pipe surface» hot air rises «and is replaced by cooler air from elsewhere»</p>
<p><em><strong>OR</strong></em></p>
<p>«due to» conduction «of heat or thermal energy» from pipe to air ✓</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates recognized that this was a specific heat question and set up a proper calculation, but many struggled to match their answer to an appropriate unit. A common mistake was to leave the answer in some form of an energy unit and others did not match the power of ten of the unit to their answer (e.g. 16 W).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that this was an underestimate of the total energy but failed to provide an adequate reason. Many gave generic responses (such as "some power will be lost"/not 100% efficient) without discussing the specific form of energy lost (e.g. heat energy).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered. Most HL candidates linked the increase in temperature to the increase in the kinetic energy of the molecules and were able to come up with a consequence of this change (such as the molecules moving faster). SL candidates tended to focus more on consequences, often neglecting to mention the change in KE.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates recognized that heat transfer by conduction was the correct response. This was a "state" question, so candidates were not required to go beyond this.</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates at both levels were able to recognize that this was a blackbody radiation question. One common mistake candidates made was not calculating the area of a cylinder properly. It is important to remind candidates that they are expected to know how to calculate areas and volumes for basic geometric shapes. Other common errors included the use of T in Celsius and neglecting to raise T ^4. Examiners awarded a large number of ECF marks for candidates who clearly showed work but made these fundamental errors.</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A few candidates recognized that convection was the third source of heat loss, although few managed to describe the mechanism of convection properly for MP2. Some candidates did not read the question carefully and instead wrote about methods to increase the rate of heat loss (such as removing more insulation or decreasing the temperature of the environment).</p>
<div class="question_part_label">d.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.</p>
<p style="text-align: center;"><img 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"></p>
<p>The following data are available for the lamps when at their working temperature.</p>
<p> </p>
<p style="padding-left: 90px;">Lamp specifications 24 V, 5.0 W</p>
<p style="padding-left: 90px;">Power supply emf 24 V</p>
<p style="padding-left: 90px;">Power supply maximum current 8.0 A</p>
<p style="padding-left: 90px;">Length of each rod 12.5 m</p>
<p style="padding-left: 90px;">Resistivity of rod metal 7.2 × 10<sup>–7</sup> Ω m</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.</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>Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.</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>One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline <strong>one</strong> other electrical advantage of this system compared to one in which the lamps are connected in series.</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><em><strong>ALTERNATIVE 1:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt {\frac{{\rho l}}{{\pi {\text{R}}}}} ">
<mi>r</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>l</mi>
</mrow>
<mrow>
<mi>π</mi>
<mrow>
<mtext>R</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{\pi \times 0.1}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mi>π</mi>
<mo>×</mo>
<mn>0.1</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{0.1}}">
<mi>A</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mn>0.1</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current in lamp = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{{24}}">
<mfrac>
<mn>5</mn>
<mrow>
<mn>24</mn>
</mrow>
</mfrac>
</math></span> «= 0.21» «A»</p>
<p><em><strong>OR</strong></em></p>
<p><em>n</em> = 24 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{5}}">
<mfrac>
<mn>8</mn>
<mrow>
<mn>5</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>so «38.4 and therefore» 38 lamps ✔</p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>when adding more lamps in parallel the brightness stays the same ✔</p>
<p>when adding more lamps in parallel the pd across each remains the same/at the operating value/24 V ✔</p>
<p>when adding more lamps in parallel the current through each remains the same ✔</p>
<p>lamps can be controlled independently ✔</p>
<p>the pd across each bulb is larger in parallel ✔</p>
<p>the current in each bulb is greater in parallel ✔</p>
<p>lamps will be brighter in parallel than in series ✔</p>
<p>In parallel the pd across the lamps will be the operating value/24 V ✔</p>
<p> </p>
<p><em>Accept converse arguments for adding lamps in series:</em></p>
<p><em>when adding more lamps in series the brightness decreases</em></p>
<p><em>when adding more lamps in series the pd decreases</em></p>
<p><em>when adding more lamps in series the current decreases</em></p>
<p><em>lamps can’t be controlled independently</em></p>
<p><em>the pd across each bulb is smaller in series</em></p>
<p><em>the current in each bulb is smaller in series</em></p>
<p> </p>
<p><em>in series the pd across the lamps will less than the operating value/24 V</em></p>
<p><em>Do not accept statements that only compare the overall resistance of the combination of bulbs.</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>