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<h2>SL Paper 2</h2><div class="specification">
<p>The Rotor is an amusement park ride that can be modelled as a vertical cylinder of inner radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> rotating about its axis. When the cylinder rotates sufficiently fast, the floor drops out and the passengers stay motionless against the inner surface of the cylinder. The diagram shows a person taking the Rotor ride. The floor of the Rotor has been lowered away from the person.</p>
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" width="291" height="330"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw and label the free-body diagram for the person.</p>
<p> </p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The person must not slide down the wall. Show that the minimum angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi></math> of the cylinder for this situation is</p>
<p style="text-align: center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><msqrt><mfrac><mi>g</mi><mrow><mi>μ</mi><mi>R</mi></mrow></mfrac></msqrt></math></p>
<p style="text-align: left;">where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> is the coefficient of static friction between the person and the cylinder.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The coefficient of static friction between the person and the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>40</mn></math>. The radius of the cylinder is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. The cylinder makes <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math> revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">arrow downwards labelled weight/W/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>g</mi></math> </span><span class="fontstyle0">and arrow upwards labelled friction/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">arrow horizontally to the left labelled </span><span class="fontstyle4">«</span><span class="fontstyle0">normal</span><span class="fontstyle4">» </span><span class="fontstyle0">reaction/</span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><img src="data:image/png;base64,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"></p>
<p><em><span class="fontstyle0"><br>Ignore point of application of the forces but do not allow arrows that do not touch the object.</span></em></p>
<p><em><span class="fontstyle0">Do not allow horizontal force to be labelled ‘centripetal’ or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">See <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>μ</mi><mi>N</mi></math> </span><span class="fontstyle2"><em><strong>AND</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mi>m</mi><mi>R</mi><msup><mi>ω</mi><mn>2</mn></msup></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle4">«</span><span class="fontstyle0">substituting for N</span><span class="fontstyle4">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><mi>R</mi><mo>=</mo><mi>m</mi><mi>g</mi></math> </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span class="fontstyle0">ALTERNATIVE 1</span></strong></em></p>
<p><span class="fontstyle0">minimum required angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><msqrt><mfrac><mrow><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>40</mn><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn></mrow></mfrac></msqrt><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>6</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">actual angular velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mfenced><mstyle displaystyle="true"><mfrac><mn>60</mn><mn>28</mn></mfrac></mstyle></mfenced></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math></span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">actual angular velocity is greater than the minimum, so the person does not slide </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><span class="fontstyle3"><em><strong>ALTERNATIVE 2</strong></em></span></p>
<p><span class="fontstyle0">Minimum friction force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>m</mi><mi>g</mi><mo>=</mo><mo>«</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>»</mo></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">Actual friction force <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>μ</mi><mi>m</mi><mi>R</mi><msup><mi>ω</mi><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>×</mo><mn>3</mn><mo>.</mo><mn>5</mn><msup><mfenced><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mfrac><mn>28</mn><mn>60</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>»</mo><mo>=</mo><mn>12</mn><mo>.</mo><mn>0</mn><mo> </mo><mi mathvariant="normal">m</mi></math> </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">Actual friction force is greater than the minimum frictional force so the person does not slide </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle4">Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">2</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">7</mn></math> from </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn><mo mathvariant="italic"> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">2</mn></mrow></msup></math>.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A football player kicks a stationary ball of mass 0.45 kg towards a wall. The initial speed of the ball after the kick is 19 m s<sup>−1</sup> and the ball does not rotate. Air resistance is negligible and there is no wind.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In practice, air resistance affects the ball. Outline the effect that air resistance has on the vertical acceleration of the ball. Take the direction of the acceleration due to gravity to be positive.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>40</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The radius of the ball is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>11</mn><mo> </mo><mtext>m</mtext></math>. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Δ</mtext><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn><mo> </mo><mtext mathvariant="bold-italic">OR </mtext><mi>a</mi><mo> </mo><mo>=</mo><mfrac><mn>19</mn><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>F</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>19</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>055</mn></mrow></mfrac><mo>»</mo><mn>160</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em>Allow <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong> if 19 sin22 <strong>OR</strong> 19 cos22 used.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>horizontal speed =</mtext><mo> </mo><mn>19</mn><mo>×</mo><mi>cos</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mn>17</mn><mo>.</mo><mn>6</mn><msup><mtext> m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>time</mtext><mo>=</mo><mo>«</mo><mfrac><mtext>distance</mtext><mtext>speed</mtext></mfrac><mo>=</mo><mfrac><mn>11</mn><mrow><mn>19</mn><mo> </mo><mi>cos</mi><mo> </mo><mn>22</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>62</mn><mo> </mo><mo>«</mo><mtext>s</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP2</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>initial vertical speed</mtext><mo>=</mo><mn>19</mn><mo>×</mo><mi>sin</mi><mo> </mo><mn>22</mn><mo> </mo><mo>«</mo><mo>=</mo><mo> </mo><mn>7</mn><mo>.</mo><mn>1</mn><mo> </mo><msup><mtext>m s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>7</mn><mo>.</mo><mn>12</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>624</mn><mo>-</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>624</mn><mn>2</mn></msup><mo>=</mo><mo>»</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>«</mo><mtext>m</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p>ball does not hit wall <em><strong>OR</strong> </em>2.5 «m» > 2.4 «m» <strong>✓</strong></p>
<p><em><br>Allow <strong>ECF</strong> from (b)(i) and from <strong>MP1</strong> </em></p>
<p><em>Allow g = 10 m s<sup>−2</sup></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>air resistance opposes «direction of» motion<br><em><strong>OR</strong></em><br>air resistance opposes velocity <strong>✓</strong></p>
<p>on the way up «vertical» acceleration is increased <em><strong>OR</strong> </em>greater than g <strong>✓</strong></p>
<p>on the way down «vertical» acceleration is decreased <em><strong>OR</strong> </em>smaller than g <strong>✓</strong></p>
<p><em><br>Allow deceleration/acceleration but meaning must be clear</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><strong>✓</strong></p>
<p><em><br>Unit must be seen for mark</em></p>
<p><em>Accept Hz</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>π</mi><mo> </mo><mo>«</mo><mtext>rad</mtext><mo>»</mo><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton is moving in a region of uniform magnetic field. The magnetic field is directed into the plane of the paper. The arrow shows the velocity of the proton at one instant and the dotted circle gives the path followed by the proton.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The speed of the proton is 2.0 × 10<sup>6</sup> m s<sup>–1</sup> and the magnetic field strength <em>B</em> is 0.35 T.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the path of the proton is a circle.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the radius of the path is about 6 cm.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the time for <strong>one</strong> complete revolution.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the kinetic energy of the proton is constant.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">magnetic force is to the left «at the instant shown»<br><em><strong>OR</strong></em><br>explains a rule to determine the direction of the magnetic force ✔</span></p>
<p><span style="background-color: #ffffff;">force is perpendicular to velocity/«direction of» motion<br><em><strong>OR</strong></em><br>force is constant in magnitude ✔</span></p>
<p><span style="background-color: #ffffff;">force is centripetal/towards the centre ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept reference to acceleration instead of force</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mi>v</mi><mi>B</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>R</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></mrow></mfrac></math> <em><strong>OR</strong></em> 0.060 « m »</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award MP2 for full replacement or correct answer to at least 2 significant figures</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>v</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> « s » ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br>work done by force is change in kinetic energy ✔<br>work done is zero/force perpendicular to velocity ✔ <br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Award <strong>[2]</strong> for a reference to work done is zero hence E<sub>k</sub> remains constant</em><br></span></p>
<p> </p>
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br>proton moves at constant speed ✔<br>kinetic energy depends on speed ✔<br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Accept mention of speed or velocity indistinctly in MP2</em><br></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A student uses a load to pull a box up a ramp inclined at 30°. A string of constant length and negligible mass connects the box to the load that falls vertically. The string passes over a pulley that runs on a frictionless axle. Friction acts between the base of the box and the ramp. Air resistance is negligible.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The load has a mass of 3.5 kg and is initially 0.95 m above the floor. The mass of the box is 1.5 kg.</p>
<p>The load is released and accelerates downwards.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline <strong>two</strong> differences between the momentum of the box and the momentum of the load at the same instant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The vertical acceleration of the load downwards is 2.4 m s<sup>−2</sup>.</p>
<p>Calculate the tension in the string.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the speed of the load when it hits the floor is about 2.1 m s<sup>−1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The student then makes the ramp horizontal and applies a constant horizontal force to the box. The force is just large enough to start the box moving. The force continues to be applied after the box begins to move.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Explain, with reference to the frictional force acting, why the box accelerates once it has started to move. </p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>direction of motion is different / <em><strong>OWTTE</strong> </em>✓</p>
<p><em>mv</em> / magnitude of momentum is different «even though <em>v</em> the same» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>ma = mg − T</em> «3.5 x 2.4 = 3.5<em>g − T</em> »</p>
<p><em><strong>OR</strong></em></p>
<p><em>T </em>= 3.5(<em>g − </em>2.4) ✓</p>
<p>26 «N» ✓</p>
<p> </p>
<p><em>Accept 27 N from g = 10 m s<sup>−2</sup></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>proper use of kinematic equation ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfenced><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfenced></msqrt><mo>=</mo><mn>2</mn><mo>.</mo><mn>14</mn></math> «m s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Must see either the substituted values <strong>OR</strong> a value for v to at least three s.f. for <strong>MP2</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mfrac><mi>v</mi><mi>r</mi></mfrac></math> to give 84 «rad s<sup>−1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>025</mn></math> to give 84 «rad s<sup>−1</sup>» ✓</p>
<p> </p>
<p>quoted to 2sf only✓</p>
<p> </p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><msup><mi>u</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>s</mi><mo>⇒</mo><mn>0</mn><mo>=</mo><mn>2</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>a</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></math>» leading to <em>a </em>= 6.3 «m s<sup>-2</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi></mrow></mfenced><mi>t</mi></math> » leading to <em>t</em> = 0.33 « s » ✓</p>
<p><em><br></em><em>F</em><sub>net</sub> = « <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>6</mn><mo>.</mo><mn>3</mn></math> = » 9.45 «N» ✓</p>
<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>
<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>kinetic energy initial = work done to stop 0.5 x 1.5 x (2.1)<sup>2</sup> = <em>F</em><sub>NET</sub> x 0.35 ✓</p>
<p><em>F</em><sub>net</sub> = 9.45 «N» ✓</p>
<p>Weight down ramp = 1.5 x 9.8 x sin(30) = 7.4 «N» ✓</p>
<p>friction force = net force – weight down ramp = 2.1 «N» ✓</p>
<p> </p>
<p><em>Accept 1.95 N from g = 10 </em>m s<sup>-2</sup><em>.</em><br><em>Accept 2.42 N from u = 2.14 </em>m s<sup>-1</sup><em>.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>static coefficient of friction > dynamic/kinetic coefficient of friction / μ<sub>s</sub> > μ<sub>k</sub> ✓</p>
<p>«therefore» force of dynamic/kinetic friction will be less than the force of static friction ✓</p>
<p><br>there will be a net / unbalanced forward force once in motion «which results in acceleration»</p>
<p><em><strong>OR</strong></em></p>
<p>reference to net F = ma ✓</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many students recognized the vector nature of momentum implied in the question, although some focused on the forces acting on each object rather than discussing the momentum.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some students simply calculated the net force acting on the load and did not recognize that this was not the tension force. Many set up a net force equation but had the direction of the forces backwards. This generally resulted from sloppy problem solving.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was a "show that" questions, so examiners were looking for a clear equation leading to a clear substitution of values leading to an answer that had more significant digits than the given answer. Most candidates successfully selected the correct equation and showed a proper substitution. Some candidates started with an energy approach that needed modification as it clearly led to an incorrect solution. These responses did not receive full marks.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This SL only question was generally well done. Despite some power of 10 errors, many candidates correctly reported final answer to 2 sf.</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates struggled with this question. Very few drew a clear free-body diagram and many simply calculated the acceleration of the box from the given information and used this to calculate the net force on the box, confusing this with the frictional force.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was an "explain" question, so examiners were looking for a clear line of discussion starting with a comparison of the coefficients of friction, leading to a comparison of the relative magnitudes of the forces of friction and ultimately the rise of a net force leading to an acceleration. Many candidates recognized that this was a question about the comparison between static and kinetic/dynamic friction but did not clearly specify which they were referring to in their responses. Some candidates clearly did not read the stem carefully as they referred to the mass being on an incline.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The Moon has no atmosphere and orbits the Earth. The diagram shows the Moon with rays of light from the Sun that are incident at 90° to the axis of rotation of the Moon.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A black body is on the Moon’s surface at point A. Show that the maximum temperature that this body can reach is 400 K. Assume that the Earth and the Moon are the same distance from the Sun.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another black body is on the Moon’s surface at point B.</p>
<p>Outline, without calculation, why the aximum temperature of the black body at point B is less than at point A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The albedo of the Earth’s atmosphere is 0.28. Outline why the maximum temperature of a black body on the Earth when the Sun is overhead is less than that at point A on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why a force acts on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why this force does no work on the Moon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> = <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {\frac{{1360}}{\sigma }} \right)^{0.25}}">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>1360</mn>
</mrow>
<mi>σ</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mn>0.25</mn>
</mrow>
</msup>
</mrow>
</math></span> </span>✔</p>
<p>390 «K» ✔</p>
<p><em>Must see 1360 (from data booklet) used for MP1.</em></p>
<p><em>Must see at least 2 s.f</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy/Power/Intensity lower at B ✔</p>
<p>connection made between energy/power/intensity and temperature of blackbody ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(28 %) of sun’s energy is scattered/reflected by earth’s atmosphere <em><strong>OR</strong></em> only 72 % of incident energy gets absorbed by blackbody ✔</p>
<p><em>Must be clear that the energy is being scattered by the atmosphere.</em></p>
<p><em>Award <strong>[0]</strong> for simple definition of “albedo”</em>.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gravitational attraction/force/field «of the planet/Moon» ✔</p>
<p><em>Do not accept “gravity”</em>.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the force/field and the velocity/displacement are at 90° to each other<em><strong> OR</strong></em> there is no change in GPE of the moon ✔</p>
<p><em>Award <strong>[0]</strong> for any mention of no net force on the satellite.</em></p>
<p><em>Do not accept acceleration is perpendicular to velocity.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. A significant portion attempted to apply Wein’s Law and simply stated that a particular wavelength was the peak and then used that to determine the temperature. Some did use the solar constant from the data booklet and were able to calculate the correct temperature. As part of their preparation for the exam candidates should thoroughly review the data booklet and be aware of what constants are given there. As with all “show that” questions candidates should be reminded to include an unrounded answer.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This is question is another example of candidates not thinking beyond the obvious in the question. Many simply said that point B is farther away, or that it is at an angle. Some used vague terms like “the sunlight is more spread out” rather than using proper physics terms. Few candidates connected the lower intensity at B with the lower temperature of the blackbody.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was assessing the understanding of the concept of albedo. Many candidates were able to connect that an albedo of 0.28 meant that 28 % of the incident energy from the sun was being reflected or scattered by the atmosphere before reaching the black body.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Define<em> gravitational field strength.</em></p>
<p>(ii) State the SI unit for gravitational field strength.</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>A planet orbits the Sun in a circular orbit with orbital period <em>T</em> and orbital radius <em>R</em>. The mass of the Sun is <em>M</em>.</p>
<p>(i) Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \sqrt {\frac{{4{\pi ^2}{R^3}}}{{GM}}} ">
<mi>T</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
</mfrac>
</msqrt>
</math></span>.</p>
<p>(ii) The Earth’s orbit around the Sun is almost circular with radius 1.5×10<sup>11</sup> m. Estimate the mass of the Sun.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>(i) «gravitational» force per unit mass on a «small <strong>or</strong> test» mass </p>
<p> </p>
<p>(ii) N kg<sup>–1 </sup></p>
<p><em>Award mark if N kg<sup>-1</sup> is seen, treating any further work as neutral.<br>Do not accept bald m s<sup>–2</sup></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i<br>clear evidence that <em>v</em> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v^2} = \frac{{4{\pi ^2}{R^2}}}{{{T^2}}}">
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> is equated to orbital speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{GM}}{R}} ">
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>R</mi>
</mfrac>
</msqrt>
</math></span><br><em><strong>OR</strong></em><br>clear evidence that centripetal force is equated to gravitational force<br><em><strong>OR</strong></em><br>clear evidence that <em>a</em> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = \frac{{{v^2}}}{R}">
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
</math></span> etc is equated to <em>g</em> in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="g = \frac{{GM}}{{{R^2}}}">
<mi>g</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> with consistent use of symbols<br><em>Minimum is a statement that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{GM}}{R}} ">
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mi>R</mi>
</mfrac>
</msqrt>
</math></span> is the orbital speed which is then used in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \frac{{2\pi R}}{T}">
<mi>v</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mi>R</mi>
</mrow>
<mi>T</mi>
</mfrac>
</math></span></em><br><em>Minimum is F<sub>c</sub> = F<sub>g</sub> ignore any signs.</em><br><em>Minimum is g = a.</em></p>
<p>substitutes and re-arranges to obtain result<br><em>Allow any legitimate method not identified here.</em><br><em>Do not allow spurious methods involving equations of shm etc</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" \ll T = \sqrt {\frac{{4{\pi ^2}R}}{{\left( {\frac{{GM}}{{{R^2}}}} \right)}}} = \sqrt {\frac{{4{\pi ^2}{R^3}}}{{GM}}} \gg ">
<mo>≪</mo>
<mi>T</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>R</mi>
</mrow>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</msqrt>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
</mfrac>
</msqrt>
<mo>≫</mo>
</math></span></p>
<p>ii<br>«<em>T </em>= 365 × 24 × 60 × 60 = 3.15 × 10<sup>7 </sup>s»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M = \, \ll \frac{{4{\pi ^2}{R^3}}}{{G{T^2}}} = \gg \,\, = \frac{{4 \times {{3.14}^2} \times {{\left( {1.5 \times {{10}^{11}}} \right)}^3}}}{{6.67 \times {{10}^{ - 11}} \times {{\left( {3.15 \times {{10}^7}} \right)}^2}}}">
<mi>M</mi>
<mo>=</mo>
<mspace width="thinmathspace"></mspace>
<mo>≪</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=≫</mo>
<mspace width="thinmathspace"></mspace>
<mspace width="thinmathspace"></mspace>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>3.14</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>11</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>3.15</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><br>2×10<sup>30</sup>«kg»</p>
<p><em>Allow use of 3.16 x 10<sup>7</sup> s for year length (quoted elsewhere in paper).</em><br><em>Condone error in power of ten in MP1.</em><br><em>Award<strong> [1 max]</strong> if incorrect time used (24 h is sometimes seen, leading to 2.66 x 10<sup>35</sup> kg).</em><br><em>Units are not required, but if not given assume kg and mark POT accordingly if power wrong.</em><br><em>Award <strong>[2]</strong> for a bald correct answer.</em><br><em>No sf penalty here.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>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>The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground. Point B is 20 m above level ground.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.</p>
</div>
<div class="specification">
<p>At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the safety net with speed 9.6 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The dot on the following diagram represents the skier as she passes point B.<br>Draw and label the vertical forces acting on the skier.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The skier reaches point C with a speed of 8.2 m s<sup>–1</sup>. She stops after a distance of 24 m at point D.</p>
<p>Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the impulse required from the net to stop the skier and state an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}{v^2} = 0.24\,{\text{gh}}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>0.24</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>gh</mtext>
</mrow>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 11.9">
<mi>v</mi>
<mo>=</mo>
<mn>11.9</mn>
</math></span> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Award GPE lost = 65 × 9.81 × 30 = «19130 J»</em></p>
<p><em>Must see the 11.9 value for MP2, not simply 12.</em></p>
<p><em>Allow g = 9.8 ms<sup>–2</sup>.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>internal energy is the total KE «and PE» of the molecules/particles/atoms in an object</p>
<p>temperature is a measure of the average KE of the molecules/particles/atoms</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if there is no mention of molecules/particles/atoms.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arrow vertically downwards from dot labelled weight/W/mg/gravitational force/F<sub>g</sub>/F<sub>gravitational</sub> <strong><em>AND</em></strong> arrow vertically upwards from dot labelled reaction force/R/normal contact force/N/F<sub>N</sub></p>
<p>W > R</p>
<p> </p>
<p><em>Do not allow gravity.</em><br><em>Do not award MP1 if additional ‘centripetal’ force arrow is added.</em><br><em>Arrows must connect to dot.</em><br><em>Ignore any horizontal arrow labelled friction.</em><br><em>Judge by eye for MP2. Arrows do not have to be correctly labelled or connect to dot for MP2.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>= 468 «N»</p>
<p>W/640 N (weight) is larger than the centripetal force required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>recognition that centripetal acceleration is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>a = 7.2 «ms<sup>–2</sup>»</p>
<p><em>g</em> is larger than the centripetal acceleration required, so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p>recognition that to lose contact with the ground centripetal force ≥ weight</p>
<p>calculation that v ≥ 14 «ms<sup>–1</sup>»</p>
<p>comment that 12 «ms<sup>–1</sup>» is less than 14 «ms<sup>–1</sup>» so the skier does not lose contact with the ground</p>
<p> </p>
<p><em><strong>ALTERNATIVE 4</strong></em></p>
<p>recognition that centripetal force is required / <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span> seen</p>
<p>calculation that reaction force = 172 «N»</p>
<p>reaction force > 0 so the skier does not lose contact with the ground</p>
<p> </p>
<p> </p>
<p><em>Do not award a mark for the bald statement that the skier does not lose contact with the ground.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>0 = 8.2<sup>2 </sup>+ 2 × <em>a</em> × 24 therefore <em>a</em> = «−»1.40 «m s<sup>−2</sup>»</p>
<p>friction force = <em>ma </em>= 65 × 1.4 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br><em>KE</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> = 0.5 x 65 x 8.2<sup>2</sup> = 2185 «J»</p>
<p>friction force = KE/distance = 2185/24 = 91 «N»</p>
<p>coefficient of friction = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{91}}{{65 \times 9.81}}">
<mfrac>
<mrow>
<mn>91</mn>
</mrow>
<mrow>
<mn>65</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
</math></span> = 0.14</p>
<p> </p>
<p><em>Allow ECF from MP1.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«76 × 9.6»= 730<br>Ns <em><strong>OR</strong></em> kg ms<sup>–1</sup></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>safety net extends stopping time</p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta p}}{{\Delta t}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>p</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> therefore <em>F</em> is smaller «with safety net»</p>
<p><em><strong>OR</strong></em></p>
<p>force is proportional to rate of change of momentum therefore <em>F</em> is smaller «with safety net»</p>
<p> </p>
<p><em>Accept reverse argument.</em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A planet is in a circular orbit around a star. The speed of the planet is constant.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why a centripetal force is needed for the planet to be in a circular orbit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the nature of this centripetal force.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the gravitational field of the planet.</p>
<p>The following data are given:</p>
<p style="padding-left:180px;">Mass of planet <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup></math> kg<br>Radius of the planet <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></math> m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«circular motion» involves a changing velocity <strong>✓</strong></p>
<p>«Tangential velocity» is «always» perpendicular to centripetal force/acceleration <strong>✓</strong></p>
<p>there must be a force/acceleration towards centre/star <strong>✓</strong></p>
<p>without a centripetal force the planet will move in a straight line <strong>✓</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gravitational force/force of gravity ✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><msup><mi>R</mi><mn>2</mn></msup></mfrac></math> ✓</p>
<p>6.4 «Nkg<sup>−1</sup> or ms<sup>−2</sup>» ✓</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>An electron moves in circular motion in a uniform magnetic field.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_18.05.11.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/05"></p>
<p>The velocity of the electron at point P is 6.8 × 10<sup>5</sup> m s<sup>–1</sup> in the direction shown.</p>
<p>The magnitude of the magnetic field is 8.5 T.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the magnetic field.</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>Calculate, in N, the magnitude of the magnetic force acting on the electron.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the electron moves at constant speed.</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>Explain why the electron moves on a circular path.</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>out of the page plane / ⊙</p>
<p> </p>
<p><em>Do not accept just “up” or “outwards”.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.60 × 10<sup>–19</sup> × 6.8 × 10<sup>5</sup> × 8.5 = 9.2 × 10<sup>–13</sup> <strong>«</strong>N<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the magnetic force does not do work on the electron hence does not change the electron’s kinetic energy</p>
<p><strong><em>OR</em></strong></p>
<p>the magnetic force/acceleration is at right angles to velocity</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the velocity of the electron is at right angles to the magnetic field</p>
<p>(therefore) there is a centripetal acceleration / force acting on the charge</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></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>Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the intensity of the solar radiation at the location of Titan is 16 W m<sup>−2</sup></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>Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the <strong>average </strong>intensity of solar radiation <strong>absorbed</strong> by the whole surface of Titan is 3.1 W m<sup>−2</sup></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the equilibrium surface temperature of Titan is about 90 K.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The orbital radius of Titan around Saturn is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and the period of revolution is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>.</p>
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>T</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mi>R</mi><mrow><mo> </mo><mn>3</mn></mrow></msup></mrow><mrow><mi>G</mi><mi>M</mi></mrow></mfrac></math> where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math> is the mass of Saturn.</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 orbital radius of Titan around Saturn is 1.2 × 10<sup>9 </sup>m and the orbital period is 15.9 days. Estimate the mass of Saturn.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>incident intensity <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1360</mn><mrow><mn>9</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>7</mn><mo>≈</mo><mn>16</mn></math> «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow the use of 1400 for the solar constant.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>exposed surface is ¼ of the total surface ✓</p>
<p>absorbed intensity = (1−0.22) × incident intensity ✓</p>
<p>0.78 × 0.25 × 15.7 <em><strong>OR </strong> </em>3.07 «W m<sup>−2</sup>» ✓</p>
<p> </p>
<p><em>Allow 3.06 from rounding and 3.12 if they use 16</em> W m<sup>−2</sup>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>σT </em><sup>4</sup> = 3.07</p>
<p><em><strong>OR</strong></em></p>
<p><em>T</em> = 86 «K» ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct equating of gravitational force / acceleration to centripetal force / acceleration ✓</p>
<p>correct rearrangement to reach the expression given ✓</p>
<p> </p>
<p><em>Allow use of <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><mi>R</mi></mfrac></msqrt><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>T</mi></mfrac></math> for <strong>MP1</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"><mi>T</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></math> «s» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfrac><mrow><mn>4</mn><msup><mi mathvariant="normal">π</mi><mn>2</mn></msup><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfenced><mn>3</mn></msup></mrow><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><msup><mfenced><mrow><mn>15</mn><mo>.</mo><mn>9</mn><mo>×</mo><mn>24</mn><mo>×</mo><mn>3600</mn></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>26</mn></msup><mo> </mo></math>«kg» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.</p>
<p style="text-align: center;"><img 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"></p>
<p>The mass of ions ejected each second is 6.6 × 10<sup>–6 </sup>kg and the speed of each ion is 5.2 × 10<sup>4</sup> m s<sup>–1</sup>. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.</p>
</div>
<div class="specification">
<p>An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.</p>
</div>
<div class="specification">
<p>In practice, the ions leave the spacecraft at a range of angles as shown.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the initial acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the maximum speed of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why scientists sometimes use estimates in making calculations.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ions are likely to spread out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by the gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>change in momentum each second = 6.6 × 10<sup>−6</sup> × 5.2 × 10<sup>4</sup> «= 3.4 × 10<sup>−1 </sup>kg m s<sup>−1</sup>» ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}">
<mfrac>
<mrow>
<mn>3.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>740</mn>
</mrow>
</mfrac>
</math></span> =» 4.6 × 10<sup>−4</sup> «m s<sup>−2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>(considering the acceleration of the spacecraft)</p>
<p>time for acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «4.6 × 10<sup>6</sup>» «s» ✔</p>
<p>max speed = «answer to (a) × 4.6 × 10<sup>6</sup> =» 2.1 × 10<sup>3</sup> «m s<sup>−1</sup>» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>(considering the conservation of momentum)</p>
<p>(momentum of 30 kg of fuel ions = change of momentum of spacecraft)</p>
<p>30 × 5.2 × 10<sup>4 </sup>= 710 × max speed ✔</p>
<p>max speed = 2.2 × 10<sup>3 </sup>«m s<sup>−1</sup>» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>problem may be too complicated for exact treatment ✔</p>
<p>to make equations/calculations simpler ✔</p>
<p>when precision of the calculations is not important ✔</p>
<p>some quantities in the problem may not be known exactly ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ions have same (sign of) charge ✔</p>
<p>ions repel each other ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the forces between the ions do not affect the force on the spacecraft. ✔</p>
<p>there is no effect on the acceleration of the spacecraft. ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force per unit mass ✔</p>
<p>acting on a small/test/point mass «placed at the point in the field» ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>satellite has a much smaller mass/diameter/size than the planet «so approximates to a point mass» ✔ </p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>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 proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the magnetic force <em>F</em> on the proton. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the velocity vector <em>v</em> of the proton.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The speed of the proton is 2.16 × 10<sup>6</sup> m s<sup>-1</sup> and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>F</em> towards centre ✔</span></p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>v</em> tangent to circle and in the direction shown in the diagram ✔</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="qvB = \frac{{m{v^2}}}{R} \Rightarrow » R = \frac{{mv}}{{qB}}/\frac{{1.673 \times {{10}^{ - 27}} \times 2.16 \times {{10}^6}}}{{1.60 \times {{10}^{ - 19}} \times 0.042}}">
<mi>q</mi>
<mi>v</mi>
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
<mo stretchy="false">⇒</mo>
<mrow>
<mo>»</mo>
</mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi>q</mi>
<mi>B</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>1.673</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>2.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.042</mn>
</mrow>
</mfrac>
</math></span> </span> <span style="background-color:#ffffff;">✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.538 «m»✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.54 «m» ✔<br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered although usually to 3 sf. Common mistakes were to substitute 0.042 for F and 1 for q. Also some candidates tried to answer in terms of electric fields.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Airboats are used for transport across a river. To move the boat forward, air is propelled from the back of the boat by a fan blade.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>An airboat has a fan blade of radius 1.8 m. This fan can propel air with a maximum speed relative to the boat of 20 m s<sup>−1</sup>. The density of air is 1.2 kg m<sup>−3</sup>.</p>
</div>
<div class="specification">
<p>In a test the airboat is tied to the river bank with a rope normal to the bank. The fan propels the air at its maximum speed. There is no wind.</p>
</div>
<div class="specification">
<p>The rope is untied and the airboat moves away from the bank. The variation with time <em>t</em> of the speed <em>v</em> of the airboat is shown for the motion.<br><br></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why a force acts on the airboat due to the fan blade.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that a mass of about 240 kg of air moves through the fan every second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the tension in the rope is about 5 kN.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the distance the airboat travels to reach its maximum speed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the mass of the airboat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The fan is rotating at 120 revolutions every minute. Calculate the centripetal acceleration of the tip of a fan blade.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>there is a force «by the fan» on the air / air is accelerated «to the rear» ✓</p>
<p>by Newton 3 ✓</p>
<p>there is an «equal and» opposite force on the boat ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>air gains momentum «backward» ✓</p>
<p>by conservation of momentum / force is rate of change in momentum ✓</p>
<p>boat gains momentum in the opposite direction ✓</p>
<p> </p>
<p><em>Accept a reference to Newton’s third law, e.g. N’3, or any correct statement of it for <strong>MP2</strong> in <strong>ALT 1</strong>.</em></p>
<p><em>Allow any reasonable choice of object where the force of the air is acting on, e.g., fan or blades.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><msup><mi>R</mi><mn>2</mn></msup></math> <em><strong>OR</strong></em> «mass of air through system per unit time =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>v</mi><mi>ρ</mi></math> seen ✓</p>
<p>244 «kg s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Accept use of Energy of air per second = 0.5 ρΑv<sup>3</sup> = 0.5 mv<sup>2</sup> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«force = Momentum change per sec = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>v</mi><mn>2</mn></msup><mi>ρ</mi></math> = » 244 x 20 <em><strong>OR</strong> </em>4.9 «kN» ✓</p>
<p> </p>
<p><em>Allow use of 240</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that area under the graph is distance covered ✓</p>
<p>«Distance =» 480 - 560 «m» ✓</p>
<p> </p>
<p><em>Accept graphical evidence or calculation of correct geometric areas for <strong>MP1</strong>.</em></p>
<p><em><strong>MP2</strong> is numerical value within range.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculation of acceleration as gradient at <em>t</em> = 0 «= 1 m s<sup>-2</sup>» ✓</p>
<p>use of <em>F=ma <strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4900</mn><mn>1</mn></mfrac></math> </strong></em>seen ✓</p>
<p>4900 «kg» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be shown on the graph.</em></p>
<p><em>Allow an acceleration in the range 1 – 1.1 for <strong>MP2</strong> and consistent answer for <strong>MP3</strong></em></p>
<p><em>Allow ECF from <strong>MP1</strong>.</em></p>
<p><em>Allow use of average acceleration = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>40</mn></mfrac></math></em></p>
<p><em>or assumption of constant force to obtain 11000 «kg» for <strong>[2]</strong></em></p>
<p><em>Allow use of 4800 or 5000 for <strong>MP2</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATE 1</em></strong></p>
<p>« <em>ω</em> = » 4<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi></math> rad s<sup>−1</sup> ✓</p>
<p>« <em>a = r ω</em><sup>2</sup>= » 280 « m s<sup>−2</sup> » ✓</p>
<p> </p>
<p><em><strong>ALTERNATE 2</strong></em></p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi><mi>r</mi></mrow><mi>T</mi></mfrac></math> » = 22.6 m s<sup>−1</sup> ✓</p>
<p>« <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>r</mi></mfrac></math>»= 280 « m s<sup>−2</sup> » ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> for wrong ω (120 gives 2.6 x 10<sup>4 </sup></em>« m s<sup>−2</sup> »<em>)</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> for wrong T (2 s gives 18 </em>« m s<sup>−2</sup> »<em>)</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority succeeded in making use of Newton's third law to explain the force on the boat. The question was quite well answered but sequencing of answers was not always ideal. There were some confusions about the air hitting the bank and bouncing off to hit the boat. A small number thought that the wind blowing the fan caused the force on the boat.</p>
<p>bi) This was generally well answered with candidates either starting from the wind turbine formula given in the data booklet or with the mass of the air being found using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi><mi>A</mi><mi>v</mi></math>.</p>
<p>1bii) Well answered by most candidates. Some creative work to end up with 240 was found in scripts.</p>
<p>1ci) Many candidates gained credit here for recognising that the resistive force eventually equalled the drag force and most were able to go on to link this to e.g. zero acceleration. Some had not read the question properly and assumed that the rope was still tied. There was one group of answers that stated something along the lines of "as there is no rope there is nothing to stop the boat so it can go at max speed.</p>
<p>1cii) A slight majority did not realise that they had to find the area under the velocity-time graph, trying equations of motion for non-linear acceleration. Those that attempted to calculate the area under the graph always succeeded in answering within the range.</p>
<p>1ciii) Use of the average gradient was common here for the acceleration. However, there also were answers that attempted to calculate the mass via a kinetic energy calculation that made all sorts of incorrect assumptions. Use of average acceleration taken from the gradient of the secant was also common.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.</p>
<p style="text-align: center;"><img 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"></p>
<p>The satellite is orbiting the Earth at a distance of 6600 km from the centre of the Earth.</p>
</div>
<div class="specification">
<p>The satellite carries an experiment that measures the peak wavelength emitted by different objects. The Sun emits radiation that has a peak wavelength <em>λ</em><sub>S</sub> of 509 nm. The peak wavelength <em>λ</em><sub>E</sub> of the radiation emitted by the Earth is 10.1 μm.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the orbital period for the satellite.</p>
<p>Mass of Earth = 6.0 x 10<sup>24</sup> kg</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>Determine the mean temperature of the Earth.</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>Suggest how the difference between <em>λ</em><sub>S</sub> and <em>λ</em><sub>E</sub> helps to account for the greenhouse effect.</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>Not all scientists agree that global warming is caused by the activities of man.</p>
<p>Outline how scientists try to ensure agreement on a scientific issue.</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{m{v^2}}}{r} = G\frac{{Mm}}{{{r^2}}}">
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mi>G</mi>
<mfrac>
<mrow>
<mi>M</mi>
<mi>m</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>leading to <em>T</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4{\pi ^2}{r^3}}}{{GM}}">
<mfrac>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mi>G</mi>
<mi>M</mi>
</mrow>
</mfrac>
</math></span></p>
<p><em>T</em> = 5320 «s»</p>
<p><em><strong>Alternative 2</strong></em></p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {\frac{{G{M_E}}}{r}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>G</mi>
<mrow>
<msub>
<mi>M</mi>
<mi>E</mi>
</msub>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</msqrt>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{6.67 \times {{10}^{ - 11}} \times 6.0 \times {{10}^{24}}}}{{6600 \times {{10}^3}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>6.67</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>11</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6600</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <em><strong>or </strong></em>7800 «ms<sup>–1</sup>»</p>
<p>distance = 2<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span><em>r</em> = 2<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> x 6600 x 10<sup>3</sup> «m» or 4.15 x 10<sup>7</sup> «m»</p>
<p>«<em>T</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{d}{v} = \frac{{4.15 \times {{10}^7}}}{{7800}}">
<mfrac>
<mi>d</mi>
<mi>v</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4.15</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>7800</mn>
</mrow>
</mfrac>
</math></span>» = 5300 «s»</p>
<p><em>Accept use of ω instead of v</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.90 \times {{10}^{ - 3}}}}{{{\lambda _{{\text{max}}}}}} = ">
<mfrac>
<mrow>
<mn>2.90</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>λ</mi>
<mrow>
<mrow>
<mtext>max</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.90 \times {{10}^{ - 3}}}}{{10.1 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>2.90</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>10.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>= 287 «K» <em><strong>or</strong> </em>14 «°C»</p>
<p><em>Award <strong>[0]</strong> for any use of wavelength from Sun </em></p>
<p><em>Do not accept 287 °C</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength of radiation from the Sun is shorter than that emitted from Earth «and is not absorbed by the atmosphere»</p>
<p>infrared radiation emitted from Earth is absorbed by greenhouse gases in the atmosphere</p>
<p>this radiation is re-emitted in all directions «including back to Earth»</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peer review</p>
<p>international collaboration</p>
<p>full details of experiments published so that experiments can repeated</p>
<p><em><strong>[Max 1 Mark]</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>