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<h2>SL Paper 3</h2><div class="specification">
<p>An ideal nuclear power plant can be modelled as a heat engine that operates between a hot temperature of 612°C and a cold temperature of 349°C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the Carnot efficiency of the nuclear power plant.</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>Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).</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 nuclear power plant works at 71.0% of the Carnot efficiency. The power produced is 1.33 GW. Calculate how much waste thermal energy is released per hour.</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>Discuss the production of waste heat by the power plant with reference to the first law and the second law of thermodynamics.</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>correct conversion to K «622 K cold, 885 K hot»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\eta _{{\rm{Carnot}}}} = 1 - \frac{{{T_{{\rm{cold}}}}}}{{{T_{{\rm{hot}}}}}} = 1 - \frac{{622}}{{885}} = 0.297">
<mrow>
<msub>
<mi>η</mi>
<mrow>
<mrow>
<mrow>
<mi mathvariant="normal">C</mi>
<mi mathvariant="normal">a</mi>
<mi mathvariant="normal">r</mi>
<mi mathvariant="normal">n</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">t</mi>
</mrow>
</mrow>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mrow>
<mrow>
<mi mathvariant="normal">c</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mi mathvariant="normal">d</mi>
</mrow>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mrow>
<mrow>
<mi mathvariant="normal">h</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">t</mi>
</mrow>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>622</mn>
</mrow>
<mrow>
<mn>885</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.297</mn>
</math></span> <em><strong>or</strong></em> 29.7%</p>
<p><em>Award <strong>[1 max]</strong> if temperatures are not converted to K, giving result 0.430.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the Carnot efficiency is the maximum possible</p>
<p>the Carnot cycle is theoretical/reversible/impossible/infinitely slow</p>
<p>energy losses to surroundings «friction, electrical losses, heat losses, sound energy»</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.71 × 0.297 = 0.211</p>
<p><em>Allow solution utilizing wasted power «78.9%».</em></p>
<p>1.33/0.211 × 0.789 = 4.97 «GW»</p>
<p>4.97 GW × 3600 = 1.79 × 10<sup>13</sup> «J» </p>
<p>Award <strong>[2 max]</strong> if 71% used as the overall efficiency giving an answer of 1.96 × 10<sup>12</sup> J.</p>
<p><em>Award <strong>[3]</strong> for bald correct answer.<br></em></p>
<p><em>Watch for ECF from (a).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Law 1: net thermal energy flow is <em>Q</em><sub>IN</sub>–<em>Q</em><sub>OUT</sub></p>
<p><em>Q</em><sub>OUT</sub><em> refers to “waste heat”</em> </p>
<p>Law 1: <em>Q</em><sub>IN</sub>–<em>Q</em><sub>OUT</sub> = ∆<em>Q</em>=∆<em>W</em> as ∆<em>U</em> is zero</p>
<p>Law 2: does not forbid <em>Q</em><sub>OUT</sub>=0</p>
<p>Law 2: no power plant can cover 100% of <em>Q</em><sub>IN</sub> into work</p>
<p>Law 2: total entropy must increase so some <em>Q</em> must enter surroundings </p>
<p><em>OWTTE</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.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A flywheel consists of a solid cylinder, with a small radial axle protruding from its centre.</p>
<p style="text-align: center;"><img 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"></p>
<p>The following data are available for the flywheel.</p>
<table style="width: 396.667px;">
<tbody>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel mass <em>M</em></td>
<td style="width: 208.667px;">= 1.22 kg</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Small axle radius <em>r</em></td>
<td style="width: 208.667px;">= 60.0 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel radius <em>R</em></td>
<td style="width: 208.667px;">= 240 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Moment of inertia</td>
<td style="width: 208.667px;">= 0.5 MR<sup>2</sup></td>
</tr>
</tbody>
</table>
<p><br>An object of mass <em>m</em> is connected to the axle by a light string and allowed to fall vertically from rest, exerting a torque on the flywheel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The velocity of the falling object is 1.89 m s<sup>–1</sup> at 3.98 s. Calculate the average angular acceleration of the flywheel.</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>Show that the torque acting on the flywheel is about 0.3 Nm.</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>(i) Calculate the tension in the string.</p>
<p>(ii) Determine the mass <em>m</em> of the falling object.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\omega _{{\text{final}}}} = \frac{v}{r} = 31.5">
<mrow>
<msub>
<mi>ω</mi>
<mrow>
<mrow>
<mtext>final</mtext>
</mrow>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mi>v</mi>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mn>31.5</mn>
</math></span> «rad s<sup>–1</sup>»</p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega = {\omega _o} + \alpha t">
<mi>ω</mi>
<mo>=</mo>
<mrow>
<msub>
<mi>ω</mi>
<mi>o</mi>
</msub>
</mrow>
<mo>+</mo>
<mi>α</mi>
<mi>t</mi>
</math></span> so» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha = \frac{\omega }{t} = \frac{{31.5}}{{3.98}} = 7.91">
<mi>α</mi>
<mo>=</mo>
<mfrac>
<mi>ω</mi>
<mi>t</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>31.5</mn>
</mrow>
<mrow>
<mn>3.98</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>7.91</mn>
</math></span> «rad s<sup>–2</sup>»</p>
<p><em><strong>ALTERNATIVE 2</strong></em><br><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a = \frac{{1.89}}{{3.98}} = 0.4749">
<mi>a</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.89</mn>
</mrow>
<mrow>
<mn>3.98</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.4749</mn>
</math></span> «m s<sup>–2</sup>»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha = \frac{a}{r} = \frac{{0.4749}}{{0.060}} = 7.91">
<mi>α</mi>
<mo>=</mo>
<mfrac>
<mi>a</mi>
<mi>r</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.4749</mn>
</mrow>
<mrow>
<mn>0.060</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>7.91</mn>
</math></span> «rad s<sup>–2</sup>»</p>
<p><em>Award <strong>[1 max]</strong> for r = 0.24 mm used giving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = 1.98 «rad s<sup>–2</sup>».</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Gamma = \frac{1}{2}{\rm{M}}{{\rm{R}}^{\rm{2}}}\alpha = \frac{1}{2} \times 1.22 \times {0.240^2} \times 7.91">
<mi mathvariant="normal">Γ</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mrow>
<mi mathvariant="normal">M</mi>
</mrow>
</mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mi mathvariant="normal">R</mi>
</mrow>
</mrow>
<mrow>
<mrow>
<mn>2</mn>
</mrow>
</mrow>
</msup>
</mrow>
<mi>α</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1.22</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>0.240</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>7.91</mn>
</math></span></p>
<p>= 0.278 «Nm»</p>
<p><em>At least two significant figures required for MP2, as question is a “Show”.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{F_T} = \frac{\Gamma }{r}">
<mrow>
<msub>
<mi>F</mi>
<mi>T</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mi mathvariant="normal">Γ</mi>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{F_T} = 4.63">
<mrow>
<msub>
<mi>F</mi>
<mi>T</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>4.63</mn>
</math></span> «N»</p>
<p><em>Allow 5 «N» if Γ= 0.3 Νm is used.</em></p>
<p> </p>
<p>ii</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{F_T} = mg - ma">
<mrow>
<msub>
<mi>F</mi>
<mi>T</mi>
</msub>
</mrow>
<mo>=</mo>
<mi>m</mi>
<mi>g</mi>
<mo>−</mo>
<mi>m</mi>
<mi>a</mi>
</math></span> so <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m = \frac{{4.63}}{{9.81 - 0.475}}">
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>4.63</mn>
</mrow>
<mrow>
<mn>9.81</mn>
<mo>−</mo>
<mn>0.475</mn>
</mrow>
</mfrac>
</math></span><br><em>m </em>= 0.496 «kg»</p>
<p><em>Allow ECF</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 horizontal rigid bar of length 2<em>R</em> is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass <em>M</em> is attached to one end of the bar and a container is attached to the other end of the bar.</p>
<p>A point particle of mass <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{M}{3}">
<mfrac>
<mi>M</mi>
<mn>3</mn>
</mfrac>
</math></span> moving with speed <em>v</em> at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.</p>
<p>The mass of the rod and the container can be neglected.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A torque of 0.010 N m brings the system to rest after a number of revolutions. For this case <em>R</em> = 0.50 m, <em>M</em> = 0.70 kg and <em>v</em> = 2.1 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of <em>M</em>, <em>v</em> and <em>R</em>, for the angular momentum of the system about the vertical axis just before the collision.</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>Just after the collision the system begins to rotate about the vertical axis with angular velocity <em>ω</em>. Show that the angular momentum of the system is equal to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}M{R^2}\omega ">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>M</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>ω</mi>
</math></span>.</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>Hence, show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega = \frac{v}{{4R}}">
<mi>ω</mi>
<mo>=</mo>
<mfrac>
<mi>v</mi>
<mrow>
<mn>4</mn>
<mi>R</mi>
</mrow>
</mfrac>
</math></span>.</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>Determine in terms of <em>M</em> and <em>v</em> the energy lost during the collision.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular deceleration of the system is 0.043 rad<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>s<sup>–2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of revolutions made by the system before it comes to rest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{M}{3}vR">
<mfrac>
<mi>M</mi>
<mn>3</mn>
</mfrac>
<mi>v</mi>
<mi>R</mi>
</math></span></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><em>evidence of use of:</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="L = I\omega = \left( {M{R^2} + \frac{M}{3}{R^2}} \right)\omega ">
<mi>L</mi>
<mo>=</mo>
<mi>I</mi>
<mi>ω</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>M</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mi>M</mi>
<mn>3</mn>
</mfrac>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mi>ω</mi>
</math></span></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of use of conservation of angular momentum, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{MvR}}{3} = \frac{4}{3}M{R^2}\omega ">
<mfrac>
<mrow>
<mi>M</mi>
<mi>v</mi>
<mi>R</mi>
</mrow>
<mn>3</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>M</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>ω</mi>
</math></span></p>
<p>«rearranging to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega = \frac{v}{{4R}}">
<mi>ω</mi>
<mo>=</mo>
<mfrac>
<mi>v</mi>
<mrow>
<mn>4</mn>
<mi>R</mi>
</mrow>
</mfrac>
</math></span>»</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial KE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{M{v^2}}}{6}">
<mfrac>
<mrow>
<mi>M</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>6</mn>
</mfrac>
</math></span></p>
<p>final KE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{M{v^2}}}{{24}}">
<mfrac>
<mrow>
<mi>M</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>24</mn>
</mrow>
</mfrac>
</math></span></p>
<p>energy loss = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{M{v^2}}}{8}">
<mfrac>
<mrow>
<mi>M</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mn>8</mn>
</mfrac>
</math></span></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> «= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4}\frac{\Gamma }{{M{R^2}}}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mfrac>
<mi mathvariant="normal">Γ</mi>
<mrow>
<mi>M</mi>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{4}\frac{{0.01}}{{0.7 \times {{0.5}^2}}}">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
<mfrac>
<mrow>
<mn>0.01</mn>
</mrow>
<mrow>
<mn>0.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>0.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>«to give <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = 0.04286 rad<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>s<sup>−2</sup>»</p>
<p> </p>
<p><em>Working <strong>OR</strong> answer to at least 3 SF must be shown</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{{\omega _i^2}}{{2\alpha }}">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<msubsup>
<mi>ω</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<mn>2</mn>
<mi>α</mi>
</mrow>
</mfrac>
</math></span> «from <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega _f^2 = \omega _i^2 + 2\alpha \theta ">
<msubsup>
<mi>ω</mi>
<mi>f</mi>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>ω</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<mn>2</mn>
<mi>α</mi>
<mi>θ</mi>
</math></span>»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta ">
<mi>θ</mi>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{{v^2}}}{{32{R^2}\alpha }} = \frac{{{{2.1}^2}}}{{32 \times {{0.5}^2} \times 0.043}}">
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>32</mn>
<mrow>
<msup>
<mi>R</mi>
<mn>2</mn>
</msup>
</mrow>
<mi>α</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>2.1</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>32</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>0.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>0.043</mn>
</mrow>
</mfrac>
</math></span>» = 12.8 <em><strong>OR</strong> </em>12.9 «rad»</p>
<p>number of rotations «= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12.9}}{{2\pi }}">
<mfrac>
<mrow>
<mn>12.9</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
</mfrac>
</math></span>» = 2.0 revolutions</p>
<p><em><strong>[3 marks]</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">a.iv.</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>The <em>P–V</em> diagram of the Carnot cycle for a monatomic ideal gas is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The system consists of 0.150 mol of a gas initially at A. The pressure at A is 512 k Pa and the volume is 1.20 × 10<sup>–3</sup> m<sup>3</sup>.</p>
</div>
<div class="specification">
<p>At C the volume is <em>V</em><sub>C</sub> and the temperature is <em>T</em><sub>C</sub>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an adiabatic process.</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>Identify the two isothermal processes.</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>Determine the temperature of the gas at A.</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 volume at B is 2.30 × 10<sup>–3</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>3</sup>. Determine the pressure at B.</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>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_B}V_B^{\frac{5}{3}} = nR{T_C}V_C^{\frac{2}{3}}">
<mrow>
<msub>
<mi>P</mi>
<mi>B</mi>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mi>B</mi>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
<mo>=</mo>
<mi>n</mi>
<mi>R</mi>
<mrow>
<msub>
<mi>T</mi>
<mi>C</mi>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mi>C</mi>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
</math></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The volume at C is 2.90 × 10<sup>–3</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>3</sup>. Calculate the temperature at C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why a Carnot cycle is of little use for a practical heat engine.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«a process in which there is» no thermal energy transferred between the system and the surroundings</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A to B <em><strong>AND</strong> </em>C to D</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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T = \frac{{PV}}{{nR}}">
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>P</mi>
<mi>V</mi>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T\left( { = \frac{{512 \times {{10}^3} \times 1.20 \times {{10}^{ - 3}}}}{{0.150 \times 8.31}}} \right) \approx 493">
<mi>T</mi>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mn>512</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1.20</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.150</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>≈</mo>
<mn>493</mn>
</math></span> «K»</p>
<p> </p>
<p><em>The first mark is for rearranging.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_B} = \frac{{{P_a}{V_A}}}{{{V_B}}}">
<mrow>
<msub>
<mi>P</mi>
<mi>B</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mi>a</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>A</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>B</mi>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_B} = 267{\text{ KPa}}">
<mrow>
<msub>
<mi>P</mi>
<mi>B</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>267</mn>
<mrow>
<mtext> KPa</mtext>
</mrow>
</math></span></p>
<p> </p>
<p><em>The first mark is for rearranging.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«B to C adiabatic so» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_{\text{B}}}V_{\text{B}}^{\frac{5}{3}} = {P_{\text{C}}}V_{\text{C}}^{\frac{5}{3}}">
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
</math></span> <em><strong>AND</strong></em> <em>P</em><sub>C</sub><em>V</em><sub>C</sub> = <em>nRT</em><sub>C</sub> «combining to get result»</p>
<p> </p>
<p><em>It is essential to see these 2 relations to award the mark.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_{\text{C}}} = \left( {\frac{{{P_{\text{B}}}V_{\text{B}}^{\frac{5}{3}}}}{{nR}}} \right)V_{\text{C}}^{\frac{{ - 2}}{3}}">
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>B</mtext>
</mrow>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mtext>B</mtext>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_{\text{C}}} = ">
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {\frac{{267 \times {{10}^3} \times {{\left( {2.30 \times {{10}^{ - 3}}} \right)}^{\frac{5}{3}}}}}{{0.150 \times 8.31}}} \right){\left( {2.90 \times {{10}^{ - 3}}} \right)^{\frac{{ - 2}}{3}}}">
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>267</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2.30</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.150</mn>
<mo>×</mo>
<mn>8.31</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>2.90</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span>» = 422 «K»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the isothermal processes would have to be conducted very slowly / OWTTE</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">e.</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>
<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>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A bar rotates horizontally about its centre, reaching a maximum angular velocity in six complete rotations from rest. The bar has a constant angular acceleration of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>110</mn><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>. The moment of inertia of the bar about the axis of rotation is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>0216</mn><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the final angular velocity of the bar is about <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>.</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>Draw the variation with time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> of the angular displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> of the bar during the acceleration.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ4AAADRCAYAAAA9rlzrAAAK8UlEQVR4Ae3cPY7cVhqFYQOeJXgiQ6ETQxswlHtgbcDSCkYrsKAFWIAntwJPakUKrVCRFSuwcg/QGxB6Bxx8jbkDqob1wza7znyuh0Ch/sjLU28dvrpkNfTJZEEAAQRWEvhk5fpWRwABBCbiUAIEEFhNgDhWI7MBAggQhw4ggMBqAsSxGpkNEECAOHQAAQRWEyCO1chsgAACxKEDCCCwmgBxrEZmAwQQIA4dQACB1QRuLY7ff//X9PXXf5s+/fQvN7cffvjH6p3bAAEEehK4lTjevXs3ffHFF9NPP/3z5lM/e/bsRh4fPnw4SuH58++nup1jub6+nu7d+/xs+zvHZ7IPBP4fCKwWR8mhpPHq1av/5n/z5s2NOOr+2PLgwVfT27e/Hlttk/eJYxOMBkHgfwisFseTJ09uTlHmI5VE6pTlmDiurq6m+/e/nG96p4/XiKNmJnWzIIDAcQKrxFHXNUoQ89lG7WKcqtT7h5YXL36cnj79bu8qDx9+Mz1+/OjmVgdxSaYO/lrq9GYc3HVf675+/ctHY718+fPNNmPb2l89PuXUaIz90YCeIIDAIoFV4qjZxrgYunv/2Wd/XdzB/MWSQh3c+5aSwfxAH2J48uTvU53i1IxlLDXWXCxDEnVfS627O97YdumeOJaoeA2BZQKrxFFy+PbbRx+NNE5TatZxaKmZw/xAX1p3HOhzQdTjOqiHEMZ2JZV6fcilxFIymS9jHTOOORWPEfjjBE4WR/2SUrOM3Z9dSyT1+rHTlJpp7B7Yu/FLHPuugZR4SgB1q9OdMUMoObx//9uiXGr8Go84dkl7jsAfI3CyOOqn1xJECWQs45pHncIcW+pg35017G6zTxx14JcohgTqeYlozDiIY5ek5wjcLYHV4pjPLGq2UT/NnvL3G3XQz09Blj7Wkjjqp9sSxO6sgTiWCHoNgfMQOFkcu6cq9Vejdc1jPgPZF7kO/roGcWxZEse46DmuZYwxxixkvF7j1/bzZZ905uuMx+PUZzx3jwAC+wmcLI4aoq5vjF9TarZxykyjtquDfHfGsBRpSRzjNGR+fWTIpA728SvNmIGM0yG/qiwR9hoC2xBYJY7b7rJmA6f8teiSOGqfJYU61RmzgpLIkMdcSLVe7WusV+uM6yLHso9tjq3nfQQQmPwv56MExDFIuEfgOIGzzDiOx8ivQRz570CCPgSI4z/fFXH0Ka2keQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHMSRb6EE7QgQB3G0K63AeQLEQRz5FkrQjgBxEEe70gqcJ0AcxJFvoQTtCBAHcbQrrcB5AsRBHPkWStCOAHEQR7vSCpwnQBzEkW+hBO0IEAdxtCutwHkCxEEc+RZK0I4AcRBHu9IKnCdAHDviuHfv88kNgz9LB+5KMcRBHET5J/7HgjjuioBxEUBgNQEzjtXIbIAAAsShAwggsJoAcaxGZgMEECAOHUAAgdUEiGM1MhsggABx6AACCKwmQByrkdkAAQSIQwcQQGA1AeJYjcwGCCBAHDqAAAKrCRDHamQ2QAAB4tABBBBYTYA4ViOzAQIIEIcOIIDAagLEsRqZDRC4GwIvXvw4vXz588HBnz//fqpbeiGO9Ddg/whM01TSqP917Orq6iCPBw++mt6+/fXgOud4kzjOQdk+EDhC4OnT76b79788uFZJ5dg6BwfY8E3i2BCmoRC4DYGSwfz/ON03o6hZSQnm0FKnMfOxHj9+dHQWc2i8fe8Rxz4yXkfgTATev//t5mAvMRxaSgKHroGUNEpC43Tn+vp6evjwm6lOb7ZeiGNrosZDYCWBkkHNEvbNNGq4kkBJoe73LXcliaX9EccSFa8hcEYCp1zfKLnUjOPQMi6w1rp3/csLcRz6JryHwBkI1EyhboeWksuxU5navtYpwYzrHHWacsp2h/a99B5xLFHxGgJnJFCnIMcues6vXZwabcxSSiKvX/9y6mYnrUccJ2GyEgJ3Q6Cua9SBXQf5vqXWue0FzlMvvO7b977XiWMfGa8jcAYCNRMYM4Lxa8jubut6xSnXLMYpz3ycOm25zWxlN8Puc+LYJeI5AmckMH4yLXnsO1059a9Fa6wao8YatxJHzTq2Xohja6LGQ+ACCBDHBXzJPiICWxMgjq2JGg+BCyBAHBfwJfuICGxNgDi2Jmo8BC6AAHFcwJfsIyKwNQHi2Jqo8RC4AALEcQFfso+IwNYEiGNrosZD4AIIEMcFfMk+IgJbEyCOrYkaD4ELIPBv/toqibc/wJQAAAAASUVORK5CYII="></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>Calculate the torque acting on the bar while it is accelerating.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The torque is removed. The bar comes to rest in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><msub><mi>ω</mi><mi>f</mi></msub><mn>2</mn></msup><mo>=</mo><mn>0</mn><mo>+</mo><mn>2</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>110</mn><mo>×</mo><mn>6</mn><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi></math> ✓</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ω</mi><mi>f</mi></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>88</mn><mo> </mo><mo>«</mo><mtext>rad</mtext><mo> </mo><msup><mtext>s</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Other methods are possible.<br>Answer 3 given so look for correct working<br>At least 2 sig figs for MP2.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">concave up from origin </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> <span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Γ</mi><mo>=</mo><mo>«</mo><mi mathvariant="normal">I</mi><mo> </mo><mi mathvariant="normal">α</mi><mo> </mo><mi>so</mi><mo> </mo><mi mathvariant="normal">Γ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>110</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>0216</mn><mo>=</mo><mo>»</mo><mo> </mo><mn>2</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo> </mo><mi mathvariant="normal">m</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><msup><mn>9</mn><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>30</mn></mrow></mfrac><mo>=</mo></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0</mn><mo>.</mo><mn>022</mn><mo> </mo><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> ✓</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo> </mo><mo>«</mo><mo>=</mo><mfrac><mrow><msub><mi>ω</mi><mi>f</mi></msub><mo>-</mo><msub><mi>ω</mi><mi>i</mi></msub></mrow><mi>α</mi></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mn>9</mn></mrow><mrow><mo>-</mo><mn>0</mn><mo>.</mo><mn>0220</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>130</mn><mo>«</mo><mi mathvariant="normal">s</mi><mo>»</mo></math>✓</p>
<p> </p>
<p><em><span class="fontstyle0">Other methods are possible.</span></em></p>
<p><em><span class="fontstyle0">Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">131</mn><mo> </mo><mi mathvariant="normal">s</mi></math> </span></em><em><span class="fontstyle0">if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">2</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">88</mn></math> used</span></em></p>
<p><em><span class="fontstyle0">Allow <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">126</mn><mo> </mo><mi mathvariant="normal">s</mi></math> </span></em><em><span class="fontstyle0">if <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">3</mn></math> used</span></em></p>
<p><em><span class="fontstyle0">Award </span><strong><span class="fontstyle3">[2] </span></strong><span class="fontstyle0">marks for a bald correct answer</span></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.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylindrical space probe of mass 8.00 x 10<sup>2</sup> kg and diameter 12.0 m is at rest in outer space.</p>
<p style="text-align: center;"><img 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"></p>
<p>Rockets at opposite points on the probe are fired so that the probe rotates about its axis. Each rocket produces a force <em>F</em> = 9.60 x 10<sup>3</sup> N. The moment of inertia of the probe about its axis is 1.44 x 10<sup>4</sup> kg<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>2</sup>.</p>
</div>
<div class="specification">
<p>The diagram shows a satellite approaching the rotating probe with negligibly small speed. The satellite is not rotating initially, but after linking to the probe they both rotate together.</p>
<p style="text-align: center;"><img 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"></p>
<p>The moment of inertia of the satellite about its axis is 4.80 x 10<sup>3</sup> kg<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>2</sup>. The axes of the probe and of the satellite are the same.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the linear acceleration of the centre of mass of the probe.</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>Calculate the resultant torque about the axis of the probe.</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 forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>s<sup>–1</sup>.</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>Determine the final angular speed of the probe–satellite system.</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>Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.</p>
<div class="marks">[3]</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>zero</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>the torque of each force is 9.60 x 10<sup>3</sup> x 6.0 = 5.76 x 10<sup>4</sup> «Nm»</p>
<p>so the net torque is 2 x 5.76 x 10<sup>4</sup> = 1.15 x 10<sup>5</sup> «Nm»</p>
<p> </p>
<p><em>Allow a one-step solution.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the angular acceleration is given by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.15 \times {{10}^5}}}{{1.44 \times {{10}^4}}}">
<mfrac>
<mrow>
<mn>1.15</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.44</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> «= 8.0 s<sup>–2</sup>»</p>
<p><em>ω</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span><em>t</em> = 8.0 x 2.00 =» 16 «s<sup>–1</sup>»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.44 x 10<sup>4</sup> x 16.0 = (1.44 x 10<sup>4</sup> + 4.80 x 10<sup>3</sup>) x <em>ω</em></p>
<p><em>ω</em> = 12.0 «s<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow ECF from (b).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial KE <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 1.44 \times {10^4} \times {16.0^2} = 1.843 \times {10^6}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1.44</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>4</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>16.0</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>1.843</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
</math></span> «J»</p>
<p>final KE <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times \left( {1.44 \times {{10}^4} + 4.80 \times {{10}^3}} \right) \times {12.0^2} = 1.382 \times {10^6}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.44</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>4.80</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>12.0</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
<mn>1.382</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
</math></span> «J»</p>
<p>loss of KE = 4.6 x 10<sup>5</sup> «J»</p>
<p> </p>
<p><em>Allow ECF from part (c)(i).</em></p>
<p><strong><em>[3 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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.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>Two of the brightest objects in the night sky are the planet Jupiter and the star Vega.<br>The light observed from Jupiter has a similar brightness to that received from Vega.</p>
</div>
<div class="specification">
<p>Vega is found in the constellation Lyra. The stellar parallax angle of Vega is about 0.13 arc sec.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the mechanism leading stars to produce the light they emit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.</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>Outline what is meant by a constellation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the stellar parallax angle is measured.</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>Show that the distance to Vega from Earth is about 25 ly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«nuclear» fusion</p>
<p><em>Do not accept “burning’’</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>brightness depends on luminosity and distance/<em>b</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{L}{{4\pi {d^2}}}">
<mfrac>
<mi>L</mi>
<mrow>
<mn>4</mn>
<mi>π</mi>
<mrow>
<msup>
<mi>d</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>Vega is much further away but has a larger luminosity</p>
<p><em>Accept answer in terms of Jupiter for MP2</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>a group of stars forming a pattern on the sky <em><strong>AND</strong> </em>not necessarily close in distance to each other</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the star’s position is observed at two times, six months apart, relative to distant stars</p>
<p>parallax angle is half the angle of shift</p>
<p><img src="data:image/png;base64,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"></p>
<p><em>Answers may be given in diagram form, so allow the marking points if clearly drawn</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{0.13}}">
<mfrac>
<mn>1</mn>
<mrow>
<mn>0.13</mn>
</mrow>
</mfrac>
</math></span> = 7.7 «pc»</p>
<p>so <em>d</em> = 7.7 x 3.26 = 25.1 «ly»</p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.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">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</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>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</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>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</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>the length of an object in its rest frame</p>
<p><em><strong>OR</strong></em></p>
<p>the length of an object measured when at rest relative to the observer</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>world lines for front and back of tunnel parallel to <em>ct</em> axis</p>
<p>world lines for front and back of train</p>
<p>which are parallel to <em>ct′</em> axis</p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>realizes that gamma = 1.25</p>
<p>0.6<em>c</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>indicates the two simultaneous events for <em>t</em> frame</p>
<p>marks on the diagram the different times «for both spacetime points» on the <em>ct′</em> axis «shown as Δ<em>t′</em> on each diagram»</p>
<p><img src="data:image/png;base64,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"></p>
<p><em><strong>ALTERNATIVE 2: (no diagram reference)</strong></em></p>
<p>the two events occur at different points in space</p>
<p>statement that the two events are not simultaneous in the <em>t′</em> frame</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An astronomical reflecting telescope is being used to observe the night sky.</p>
<p>The diagram shows an incomplete reflecting telescope.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the diagram, with a Newtonian mounting, continuing the <strong>two</strong> rays to show how they pass through the eyepiece.</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>When the Earth-Moon distance is 363 300 km, the Moon is observed using the telescope. The mean radius of the Moon is 1737 km. Determine the focal length of the mirror used in this telescope when the diameter of the Moon’s image formed by the main mirror is 1.20 cm.</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 final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Hubble Space reflecting telescope has a Cassegrain mounting. Outline the main optical difference between a Cassegrain mounting and a Newtonian mounting.</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>plane mirror to the left of principal focus tilted anti-clockwise</p>
<p>two rays which would go through the principal focus</p>
<p>two rays cross between mirror and eyepiece <em><strong>AND</strong> </em>passing through the eyepiece</p>
<p><em>eg:</em></p>
<p><em><img src="data:image/png;base64,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"></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2 \times 1737}}{{363300}} = \frac{{0.0120}}{f}">
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>1737</mn>
</mrow>
<mrow>
<mn>363300</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.0120</mn>
</mrow>
<mi>f</mi>
</mfrac>
</math></span></p>
<p><em>f</em> = 1.25 «m»</p>
<p><em>Allow ECF if factor of 2 omitted answer is 2.5m</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>M = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.25}}{{0.05}}">
<mfrac>
<mrow>
<mn>1.25</mn>
</mrow>
<mrow>
<mn>0.05</mn>
</mrow>
</mfrac>
</math></span> = 25</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>parabolic/convex mirror instead of flat mirror</p>
<p>eyepiece/image axis same as mirror</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A heat engine operates on the cycle shown in the pressure–volume diagram. The cycle consists of an isothermal expansion AB, an isovolumetric change BC and an adiabatic compression CA. The volume at B is double the volume at A. The gas is an ideal monatomic gas.</p>
<p style="text-align: center;"><img 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"></p>
<p>At A the pressure of the gas is 4.00 x 10<sup>6</sup> Pa, the temperature is 612 K and the volume is 1.50 x 10<sup>–4</sup><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>3</sup>. The work done by the gas during the isothermal expansion is 416 J.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify why the thermal energy supplied during the expansion AB is 416 J.</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>Show that the temperature of the gas at C is 386 K.</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 thermal energy removed from the gas for the change BC is approximately 330 J.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the efficiency of the heat engine.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain at which point in the cycle ABCA the entropy of the gas is the largest.</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>Δ<em>U</em> = 0 so <em>Q</em> = Δ<em>U</em> + <em>W</em> = 0 + 416 = 416 «J»</p>
<p> </p>
<p><em>Answer given, mark is for the proof.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>use <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p{V^{\frac{5}{3}}} = c">
<mi>p</mi>
<mrow>
<msup>
<mi>V</mi>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mi>c</mi>
</math></span> to get <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T{V^{\frac{2}{3}}} = c">
<mi>T</mi>
<mrow>
<msup>
<mi>V</mi>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mi>c</mi>
</math></span></p>
<p>hence <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_{\text{C}}} = {T_{\text{A}}}{\left( {\frac{{{V_{\text{A}}}}}{{{V_{\text{C}}}}}} \right)^{\frac{2}{3}}} = 612 \times {0.5^{\frac{2}{3}}} = 385.54">
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>612</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>0.5</mn>
<mrow>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>385.54</mn>
</math></span></p>
<p>«<em>T</em><sub>C</sub> ≈ 386K»</p>
<p> <em><strong>ALTERNATIVE 2</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_{\text{C}}}{V_{\text{C}}}^\gamma = {P_{\text{A}}}{V_{\text{A}}}^\gamma ">
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<msup>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mi>γ</mi>
</msup>
<mo>=</mo>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<msup>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mi>γ</mi>
</msup>
</math></span> giving <em>P</em><sub>C</sub> = 1.26 x 10<sup>6</sup> «Pa»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{P_{\text{C}}}{V_{\text{C}}}}}{{{T_{\text{C}}}}} = \frac{{{P_{\text{A}}}{V_{\text{A}}}}}{{{T_{\text{A}}}}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span> giving <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_{\text{C}}} = 1.26 \times \frac{{612}}{2} = 385.54">
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mn>1.26</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>612</mn>
</mrow>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mn>385.54</mn>
</math></span> «K»</p>
<p>«<em>T</em><sub>C</sub> ≈ 386K»</p>
<p> </p>
<p><em>Answer of 386K is given. Look carefully for correct working if answers are to 3 SF.</em></p>
<p><em>There are other methods:</em></p>
<p><em>Allow use of P</em><sub>B</sub><em> = 2 x 10<sup>6</sup> «Pa» and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{P}{T}">
<mfrac>
<mi>P</mi>
<mi>T</mi>
</mfrac>
</math></span> is constant for BC.</em></p>
<p><em>Allow use of n = 0.118 and T</em><sub>C</sub><em> = </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{P_{\text{C}}}{V_{\text{C}}}}}{{nR}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>C</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mi>n</mi>
<mi>R</mi>
</mrow>
</mfrac>
</math></span></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><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = \Delta U + W = \frac{3}{2}\frac{{{P_{\text{A}}}{V_{\text{A}}}}}{{{T_{\text{A}}}}}\Delta T + 0">
<mi>Q</mi>
<mo>=</mo>
<mi mathvariant="normal">Δ</mi>
<mi>U</mi>
<mo>+</mo>
<mi>W</mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mtext>A</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
<mo>+</mo>
<mn>0</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = \frac{3}{2} \times \frac{{4.00 \times {{10}^6} \times 1.50 \times {{10}^{ - 4}}}}{{612}} \times \left( {386 - 612} \right)">
<mi>Q</mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>4.00</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1.50</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>612</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>386</mn>
<mo>−</mo>
<mn>612</mn>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p>«–332 J»</p>
<p> </p>
<p><em>Answer of 330 J given in the question.</em><br><em>Look for correct working or more than 2 SF.</em></p>
<p><strong><em>[2 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="{\text{e}} = \frac{{{Q_{{\text{in}}}} - {Q_{{\text{out}}}}}}{{{Q_{i{\text{n}}}}}} = \frac{{412 - 332}}{{416}}">
<mrow>
<mtext>e</mtext>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mrow>
<mtext>in</mtext>
</mrow>
</mrow>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mrow>
<mtext>out</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>Q</mi>
<mrow>
<mi>i</mi>
<mrow>
<mtext>n</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>412</mn>
<mo>−</mo>
<mn>332</mn>
</mrow>
<mrow>
<mn>416</mn>
</mrow>
</mfrac>
</math></span></p>
<p>e = 0.20</p>
<p> </p>
<p><em>Allow </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{416 - 330}}{{416}}">
<mfrac>
<mrow>
<mn>416</mn>
<mo>−</mo>
<mn>330</mn>
</mrow>
<mrow>
<mn>416</mn>
</mrow>
</mfrac>
</math></span>.</p>
<p><em>Allow e = 0.21.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>entropy is largest at B</p>
<p>entropy increases from A to B because <em>T</em> = constant but volume increases so more disorder <em><strong>or </strong></em>Δ<em>S</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{Q}{T}">
<mfrac>
<mi>Q</mi>
<mi>T</mi>
</mfrac>
</math></span> and <em>Q</em> > 0 so Δ<em>S </em>> 0</p>
<p>entropy is constant along CA because it is adiabatic,<em> Q</em> = 0 and so<em> ΔS = </em>0<em><br><strong>OR</strong><br></em>entropy decreases along BC since energy has been removed, Δ<em>Q</em> < 0<em> so ΔS <</em> 0</p>
<p><em><strong>[3 marks]</strong></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.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">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A solid sphere of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> and mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is released from rest and rolls down a slope, without slipping. The vertical height of the slope is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math>. The moment of inertia <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> of this sphere about an axis through its centre is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>5</mn></mfrac><mi>m</mi><msup><mi>r</mi><mn>2</mn></msup></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc0AAABrCAYAAAAVd9laAAAKSUlEQVR4Ae3dTascVR4HYL/HIEMIgsQIEgSdUQY34WK2EjA7NQxux43ZjSvdTVyZzbg0C90q6NpA9gn5Ale/QPIJaviVc6Bu2S/V3dV9T1U9BU2/VdWtek7rj1N1zj8vNRYCBAgQIEBgkMBLg9ayEgECBAgQINAITT8CAgQIECAwUEBoDoSyGgECBAgQEJp+AwQIECBAYKCA0BwIZTUCBAgQICA0/QYIECBAgMBAAaE5EMpqBAgQIEBglqF5586HTR4PHnzTvPzyX5pbt97X0gQIECBA4GCBWYbm9evXmjzu3fv8YCA7IECAAAECRWB2ofn06ZO2d5mepoUAAQIECIwpMLvQfPjwuzY0Hz36dUwn+yJAgAABAvOrCJRLsrk0ayFAgAABAmMLzK6nWQYBjQ1lfwQIECBAYHahmV5mRs1aCBAgQIDA2AKzCs0yCCj3NS0ECBAgQGBsgVmFZhkEdH5+PraT/REgQIAAgboHAv3++2/NF1/8uzk7u9mOiE2hgjzefvut9vN8byFAgAABAqcSqLanmbBMQH722b+ax48fX/DI+3x/7dqr7fOLFy8ufO8NAQIECBA4hkB1oZkATM8yj209yax79+4n7bqC8xg/D/skQIAAga5AdaGZEMxj6PLs2bPm9ddfa95888bQTaxHgAABAgT2EqgqNH/44fv2fuXQXmMCs1yiTc/022//uxeCjQgQIECAwBCBqkIzA3wSnEOWrJd7nmX93OfM9hYCBAgQIHAsgWpCs/Qah5xoGQSUbbpLQrM/aKj7vdcECBAgQOAQgWpCMz3G27c/2Hgu3YE/qwYJZaTt/fv/2bgPXxIgQIAAgX0FqgnNhN22wMsAoQTrunueQ/axL5TtCBAgQIBAVaGZy66blv7l2P66QrMv4j0BAgQIjClQTWjmXuS2y7PbTjw90TIwaNu6vidAgAABArsKVBOaueSa0bDrLr1uO7Fsl+knq+51btvW9wQIECBAYIjApYVmQq4/0jU9xW33NdedVLY7tKe6bt8+J0CAAAECETh6aKb3uOmRaSIpSpAQTS8x6267d9lvujJdpR/C/fW8J0CAAAEChwgcPTQ3HVwC8pdffm7L5uV1pox8/fX99jLr0ODMegnefXuom47PdwQIECBAoCtw6aFZDia9zFK04L33/tG88srVrWXxMuinlNEr+/FMgAABAgSOJVBNaJYTzGXahOG77/69uXLlr83Vq1eaTz/9Z/tZLr/mu4RrepcqABU1zwQIECBwCoHqQrN70gnJjz/+qL3PeePGG+0/AVYGCw29fNvdn9cECBAgQOAQgapDs5xYep+5Z1l6l+lt5jMLAQIECBA4pcAkQrMLksDM1JLcy8zAIfMyuzpeEyBAgMAxBSYXmgUjYZnQTHgmRBOmFgIECBAgcEyByYZmQSkDh8ql21zGdem26HgmQIAAgTEFJh+aXYwMHMpAoTLnU7GDro7XBAgQIHCowKxCs2Dk0m16nLl0e3Z2s710q/dZdDwTIECAwL4CswzNLkZ34FDmdxo41NXxmgABAgR2EZh9aBaMzOvMwKFcus0l3JTvsxAgQIAAgV0EFhOaBSWXaVMgvgwcKsXiy/eeCRAgQIDAOoHFhWYXohSLL3M+VRnq6nhNgAABAn2BRYdmwch9zlIs3pzPouKZAAECBPoCQrMjUuZ8ZsRtep8ZgWvgUAfISwIECCxcQGiu+QFkjmcZOJRncz7XQPmYAAECCxIQmlsau8z5LAOHFIvfAuZrAgQIzFhAaO7QuN05n+l9unS7A55VCRAgMAMBoblHIyYsE5qlWLw5n3sg2oQAAQITFBCaBzRaf86nYvEHYNqUAAECExAQmiM1kmLxI0HaDQECBCoWEJojN04ZONQtFj/yn7A7AgQIELgkgdFD86effmzru+Z525I6sHNeMnCozPlULH7OLe3cCBBYisDoofngwTdtaJ6fn281nHtoFgDF4ouEZwIECExbYPTQvHPnw+add/42SGUpoVkw+gOHFIsvMp4JECAwDYHRQ/P69WvNvXufN+lxJjwTjLduvd+s6nkuLTS7P4lMU0mdW8XiuypeEyBAoG6BUUMzwZggTHB+9dWX7Zk/f/68Dc/0QPvLkkOzWGTgkGLxRcMzAQIE6hYYNTQfPvyuDc0SmOXU0+MUmkVj9bNi8atdfEqAAIGaBEYNzVyWTe+xeym29D7zXX/R0+yL/PFesfjVLj4lQIDAZQuMGpq5d9kfBPTo0a9tkKYX2l+EZl/k4vsy51Ox+Isu3hEgQOCyBEYNzTIIqHsym6agCM2u1ObXisVv9vEtAQIETiEwWmiu61FumoIiNHdvYsXidzezBQECBMYSGC00S4/y6dMnF44tvc9Vg4CyktC8QLXTm/6cT8Xid+KzMgECBPYSGC00M9AnAdldyiCgBOqqRWiuUtn9s36x+FQgshAgQIDA+AKjheY+hyY091Fbv00ZOKRY/Hoj3xAgQOAQAaF5iF7F2yoWX3HjODQCBCYrIDQn23TDDrxfLD6Xci0ECBAgsJ+A0NzPbXJb9QcOKRY/uSZ0wAQIVCAgNCtohFMfgmLxpxb39wgQmIuA0JxLS+5xHorF74FmEwIEFi0gNBfd/H+cfCkWX8r1Zc5nAtVCgAABAhcFhOZFj8W/Uyx+8T8BAAQIbBAQmhtwlvxVmfNZep+ZwpIeqYUAAQJLFhCaS279gefeLRaffzDbpduBcFYjQGB2AkJzdk16vBMqcz5Tcej27Q+ajMK1ECBAYEkCQnNJrT3SufbnfCoWPxKs3RAgUL2A0Ky+ieo+QMXi624fR0eAwLgCQnNcz8XurTvn8+zsZpP7oBYCBAjMTUBozq1FKzgfxeIraASHQIDAUQSE5lFY7TQCZeBQ/gm4u3c/aRSL97sgQGDqAkJz6i04gePPwKEMFipzPhWLn0CjOUQCBFYKCM2VLD48loBi8ceStV8CBE4hIDRPoexv/EmgO3Aocz4NHPoTkQ8IEKhQQGhW2ChLOiTF4pfU2s6VwPQFhOb023A2Z6BY/Gya0okQmK2A0Jxt0073xBSLn27bOXICcxcQmnNv4Ymfn2LxE29Ah09gZgJCc2YNOtfTKXM+FYufaws7LwLTEBCa02gnR/l/gX6xeHM+/TQIEDilgNA8pba/NaqAYvGjctoZAQIDBITmACSr1C3QnfOZYvG5lGshQIDAMQSOHpqpOzrk0T+5VdsMWSfbdZdV++mvk/VXrdfdz7p1+vtatZ/+OqfY16mP/dR/r2+6zt3nw/7748Rpjr+B/v+Xxnh/9NAc4yDtgwABAgQI1CAgNGtoBcdAgAABApMQEJqTaCYHSYAAAQI1CAjNGlrBMRAgQIDAJASE5iSayUESIECAQA0CQrOGVnAMBAgQIDAJAaE5iWZykAQIECBQg4DQrKEVHAMBAgQITEJAaE6imRwkAQIECNQgIDRraAXHQIAAAQKTEBCak2gmB0mAAAECNQgIzRpawTEQIECAwCQEhOYkmslBEiBAgEANAv8D26JurF4zfQ8AAAAASUVORK5CYII="></p>
<p>Show that the linear velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> of the sphere as it leaves the slope is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>10</mn><mi>g</mi><mi>h</mi></mrow><mn>7</mn></mfrac></msqrt></math>.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><span class="fontstyle0">conservation of rotational and linear energy</span></p>
<p><em><strong>OR<br></strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>g</mi><mi>h</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>I</mi><msup><mi>ω</mi><mn>2</mn></msup></math> ✓</p>
<p> </p>
<p><span class="fontstyle0">using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac><mi>m</mi><msup><mi>r</mi><mn>2</mn></msup></math> <em><strong>AND</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>=</mo><mfrac><mi>v</mi><mi>r</mi></mfrac></math> ✓</span></p>
<p><span class="fontstyle0">with </span><strong><span class="fontstyle2">correct manipulation </span></strong><span class="fontstyle0">to find the requested relationship </span><span class="fontstyle3">✓</span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p>The diagram shows two methods of pedalling a bicycle using a force <em>F</em>.</p>
<p><img 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"></p>
<p>In method 1 the pedal is always horizontal to the ground. A student claims that method 2 is better because the pedal is always parallel to the crank arm. Explain why method 2 is more effective.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>in method 1 the perpendicular distance varies from 0 to a maximum value, in method 2 this distance is constant at the maximum value<br><em><strong>OR<br></strong></em>angle between <em>F</em> and <em>r</em> is 90° in method 2 and less in method 1<br><em><strong>OR<br></strong>Γ</em> = <em>F</em> × perpendicular distance</p>
<p>perpendicular distance/ torque is greater in method 2</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A constant force of 50.0 N is applied tangentially to the outer edge of a merry-go-round. The following diagram shows the view from above.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.31.00.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/06"></p>
<p>The merry-go-round has a moment of inertia of 450 kg m<sup>2</sup> about a vertical axis. The merry-go-round has a diameter of 4.00 m.</p>
</div>
<div class="specification">
<p>A child of mass 30.0 kg is now placed onto the edge of the merry-go-round. No external torque acts on the system.</p>
</div>
<div class="specification">
<p>The child now moves towards the centre.</p>
</div>
<div class="specification">
<p>The merry-go-round starts from rest and the force is applied for one complete revolution.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular acceleration of the merry-go-round is 0.2 rad s<sup>–2</sup>.</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>Calculate, for the merry-go-round after one revolution, the angular speed. </p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the merry-go-round after one revolution, the angular momentum.</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>Calculate the new angular speed of the rotating system.</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>Explain why the angular speed will increase.</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>Calculate the work done by the child in moving from the edge to the centre.</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>Γ<strong> «</strong>= <em>Fr</em> = 50 × 2<strong>»</strong> = 100 <strong>«</strong>Nm<strong>»</strong></p>
<p>α <strong>«</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{\Gamma }{I} = \frac{{100}}{{450}}">
<mo>=</mo>
<mfrac>
<mi mathvariant="normal">Γ</mi>
<mi>I</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>450</mn>
</mrow>
</mfrac>
</math></span> <strong>»</strong> =0.22 <strong>«</strong>rads<sup>–2</sup><strong>»</strong></p>
<p> </p>
<p><em>Final value to at least 2 sig figs, </em><strong><em>OR </em></strong><em>clear working with substitution required for mark.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega _t^2 - \omega _0^2 = 2\alpha \Delta \theta ">
<msubsup>
<mi>ω</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>−</mo>
<msubsup>
<mi>ω</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mn>2</mn>
<mi>α</mi>
<mi mathvariant="normal">Δ</mi>
<mi>θ</mi>
</math></span><strong>»</strong></p>
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega _t^2 - 0 = 2 \times 0.22 \times 2\pi ">
<msubsup>
<mi>ω</mi>
<mi>t</mi>
<mn>2</mn>
</msubsup>
<mo>−</mo>
<mn>0</mn>
<mo>=</mo>
<mn>2</mn>
<mo>×</mo>
<mn>0.22</mn>
<mo>×</mo>
<mn>2</mn>
<mi>π</mi>
</math></span><strong>»</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\omega _t} = 1.7">
<mrow>
<msub>
<mi>ω</mi>
<mi>t</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>1.7</mn>
</math></span> <strong>«</strong>rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Accept BCA, values in the range: 1.57 to 1.70.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><em>L</em> = <em>Iω = </em>450 × 1.66<strong>»</strong></p>
<p>= 750 <strong>«</strong>kgm<sup>2</sup> rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Accept BCA, values in the range: 710 to 780.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><em>I</em> = 450 + <em>mr</em><sup>2</sup><strong>»</strong></p>
<p><em>I</em><strong> «</strong>= 450 + 30 × 2<sup>2</sup><strong>»</strong> = 570 <strong>«</strong>kgm<sup>2</sup><strong>»</strong></p>
<p><strong>«</strong><em>L</em> = 570 × <em>ω</em> = 747<strong>»</strong></p>
<p><em>ω</em> = 1.3 <strong>«</strong>rads<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Watch for ECF from (a) and (b).</em></p>
<p><em>Accept BCA, values in the range: 1.25 to 1.35.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>moment of inertia will decrease</p>
<p>angular momentum will be constant <strong>«</strong>as the system is isolated<strong>»</strong></p>
<p><strong>«</strong>so the angular speed will increase<strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω<sub>t</sub></em> = 1.66 from bi <strong><em>AND</em></strong> <em>W</em> = ΔE<sub><em>k</em></sub></p>
<p><em>W</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> × 450 × 1.66<sup>2</sup> – <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> × 570 × 1.31<sup>2</sup> = 131 <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>ECF from 8bi</em></p>
<p><em>Accept BCA, value depends on the answers in previous questions.</em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">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 hoop of mass <em>m</em>, radius <em>r</em> and moment of inertia <em>mr</em><sup>2</sup> rests on a rough plane inclined at an angle <em>θ</em> to the horizontal. It is released so that the hoop gains linear and angular acceleration by rolling, without slipping, down the plane.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxAAAAEjCAYAAACiiOfXAAAgAElEQVR4Ae3dX4wd130f8KNGb4ZJA34yvBQkQDBs/lHrBLC4S6FFgUrc2GhR29TKShwYJpepA9WBSMJRExShaKh2lYCkYEewlF3TMCr4D7VOixaWd2UYQQJxl1RaJIVIKQ8CJGjXefGLSb/4xd7iN/ZsL1e74s7dmbv3nvMZYHH/zZyZ8/ldCffLOWfmttXV1dVkIUCAAAECBAgQIECAwBYE/tkW1rEKAQIECBAgQIAAAQIEKgEBwheBAAECBAgQIECAAIEtC9xer3n3nXfVTz0SIECAAAECBAgQIEBgQ4HbeudARIh4/c03NlzRmwQIECBAgAABAgQIlCtQZwVDmMr9Dug5AQIECBAgQIAAgcYCAkRjMhsQIECAAAECBAgQKFdAgCi39npOgAABAgQIECBAoLGAANGYzAYECBAgQIAAAQIEyhUQIMqtvZ4TIECAAAECBAgQaCwgQDQmswEBAgQIECBAgACBcgUEiHJrr+cECBAgQIAAAQIEGgsIEI3JbECAAAECBAgQIECgXAEBotza6zkBAgQIECBAgACBxgICRGMyGxAgQIAAAQIECBAoV0CAKLf2ek6AAAECBAgQIECgsYAA0ZjMBgQIECBAgAABAgTKFRAgyq29nhMgQIAAAQIECBBoLCBANCazAQECBAgQIECAAIFyBQSIcmuv5wQIECBAgAABAgQaCwgQjclsQIAAAQIECBAgQKBcAQGi3NrrOQECBAgQIECAAIHGAgJEYzIbECBAgAABAgQIEChXQIAot/Z6ToAAAQIECBAgQKCxgADRmMwGBAgQIECAAAECBMoVECDKrb2eEyBAgAABAgQIEGgsIEA0JrMBAQIECBAgQIAAgXIFBIhya6/nBAgQIECAAAECBBoLCBCNyWxAgAABAgQIECBAoFwBAaLc2us5AQIECBAgQIAAgcYCAkRjMhsQIECAAAECBAgQKFdAgCi39npOgAABAgQIECBAoLGAANGYzAYECBAgQIAAAQIEyhUQIMqtvZ4TIECAAAECBAgQaCwgQDQmswEBAgQIECBAgACBcgUEiHJrr+cECBAgQIAAAQIEGgsIEI3JbECAAAECBAgQIECgXAEBotza6zkBAgQIECBAgACBxgICRGMyGxAgQIAAAQIECBAoV0CAKLf2ek6AAAECBAgQIECgsYAA0ZjMBgQIECBAgAABAgTKFRAgyq29nhMgQIAAAQIECBBoLCBANCazAQECBAgQIECAAIFyBQSIcmuv5wQIECBAgAABAgQaCwgQjclsQIAAAQIECBAgQKBcAQGi3NrrOQECBAgQIECAAIHGAgJEYzIbECBAgAABAgQIEChXQIAot/Z6ToAAAQIECBAgQKCxgADRmMwGBAgQIECAAAECBMoVECDKrb2eEyBAgAABAgQIEGgsIEA0JrMBAQIECBAgQIAAgXIFBIhya6/nBAgQIECAAAECBBoLCBCNyWxAgAABAgQIECBAoFwBAaLc2us5AQIECBAgQIAAgcYCAkRjMhsQIECAAAECBAgQKFdAgCi39npOgAABAgQIECBAoLGAANGYzAYECBAgQIAAAQIEyhUQIMqtvZ4TIECAAAECBAgQaCwgQDQmswEBAgQIECBAgACBcgUEiHJrr+cECBAgQIAAAQIEGgsIEI3JbECAAAECBAgQIECgXAEBotza6zkBAgQIECBAgACBxgICRGMyGxAgQIAAAQIECBAoV0CAKLf2ek6AAAECBAgQIECgsYAA0ZjMBgQIECBAgAABAgTKFRAgyq29nhMgQIAAAQIECBBoLCBANCazAQECBAgQIECAAIFyBQSIcmuv5wQIECBAgAABAgQaC9zeeAsbECBAgEBrAsvLy+natWvp1VevVY/Xr99IKyvLaWVl5W37GBsbS2Nje6r3JybGq+f79u1L8WchQIAAAQKDEhAgBiVtPwQIEEgp3bhxI83Pz6eFhfm0uLhYmezbtz9FIDh8eDLt2fOrgDA+Pv42rwgasX2EjggZFy9eTNeuXa3Wm5iYSLFNbxtva8AbBAgQIECgBYHbVldXV+t27r7zrvT6m2/ULz0SIECAQEsC8WM/QsPCwkI6eHA8TU4eTuPjE62cPYhAEW0vLS2ttT81NZUmJyfTrl27WuqBZggQIECgdIE6KwgQpX8T9J8Agc4E4mzB7OxMdaYgdjI9PZ2mph7q9Ed9fYYj9hvB4vjx42l6+nin++wMUMMECBAgMFQCAsRQlcPBECCQk0AdHGZmZlIMTzp16lQ1vGjQfYwzEhcvfrcaMiVIDFrf/ggQIJCfQB0gXIUpv9rqEQECOygQ8xseeOD+tLi4lC5c+Eaam5vbkfAQBDEn4vz5p9KLL/6wOp577/1IdUZkB3nsmgABAgQyEDCEKYMi6gIBAjsvEGcdTpx4tJoYfebMF1PMQRi2Jc5IxDHGlZzOnz+/NmF72I7T8RAgQIDAcAo4AzGcdXFUBAiMoED8MI9/3Y/lypWXhzI8xLHFGYk4GxGXfY2zJDGx20KAAAECBJoKuIxrUzHrEyBAoEcgJiufPXs2DetZh55DrZ7GVZnOnDlThYk4G7G0tFgNc1q/ntcECBAgQGAzAXMgNpPxPgECBG4hED/AIzzMzX1vaM86bNaFuMRrnI2Ie0scOXKkur/EZut6nwABAgQI9AoIEL0anhMgQGCLAhEe4sd3DFka1TtBx03rIvzcuHE9HTnyyVZCxOcfeST91j//F1tUtBoBAgQIjKKAADGKVXPMBAjsqEAdHuLH96jfqC2Ov54X0VaI2NHi2DkBAgQIdC4gQHRObAcECOQkkFN46K1LXO41zqQIEb0qnhMgQIDARgICxEYq3iNAgMAGAqdPn66GLeVw5mGD7lUTweP906f/dKOPG7337NeeSXG5v/iLIU3xune5+sor6TOf/vTaOv/6X/6rt61z/fr19J//5E/W1om2/vzJJ3ubSTFk6t//239XbVvvL9r6wfdfuGk9LwgQIECgPQEBoj1LLREgkLFAXPI07uoc/1I/6sOWNitT9CvCUVyW9ty5s5utdsv344f/4qWX0v/5v/+QXn/zjfSp33m4+uFf/6hffuut9JlP/17Vzto6D/9qnd6gEetceulS+h//639W7Xz16afTd7717Sp49B5EhJEfvPBC+uu//ZtqvUP3HaqCRWxrIUCAAIH2BQSI9k21SIBAZgIxWTr+VT7uLD2qE6a3WpIIEV//+oU0MzNTBYmtbrd+vSe+9KW0e/fu6u1PPfxw9Xj16ivV45/9+izCV55+em2d//AHn0u//bGPpr985pkUASSCRASDP3rssbT/wIFqu/j89z/3uSpU1GGk+iCl9MSX/kvac8cd1cvYdzz/y2e+Vn/skQABAgRaFBAgWsTUFAECeQrEvIfjx49X907Is4c39ypCUtzX4ujRz/Z1ZaYIDvWP+Wh516+DRL2XxZcupf0H9q+Fh/r9Q4fuq8JDhIMIG9FOhIbe5aO/fn3p0ktrb8e+6pBRvxntX33lav3SIwECBAi0KCBAtIipKQIE8hOoh/KcPHkqv869Q4+mpqbSxMREivDU5hJnF+JvfaiIfdRnLOLz5beWN9xtvV2sUy/1dvXreLzjjjuq/fSu1/u55wQIECDQv4AA0b+dLQkQyFxgeXk5nTt3rtg7Ncd8j8XFxW0NZVr/FYkf+/F3oycA1OvUP/bjx/+eO/bUb9/0WG8X67zT8tZbb1X72ShcvNN2PiNAgACBWwsIELc2sgYBAoUKnDhxIh07Np39vIfNyhvzIU6dOtX6WYiJ+w5Vw4vqwFDvvx6WFMOP9u8/sDacqf48Hl/49dWV9uz5/wEiJmWvbyuGL0U7FgIECBBoX0CAaN9UiwQIZCAQVyK6du1q9QM6g+703YXp6ePVtnEVqraWmBgdyx8+8sjaD/+YNB1zH77w2GPV/ImYVB3zGmLCdUymjiU+j0nWcZWluLJTvUR46G0rLg8boeL3P/cH9SoeCRAgQKBFAQGiRUxNESCQj8DZs2eridO5XrK1SaVi/kc9F6TJdputG5Oev/ncf6s+jntExP0bvvPtb1fhIYJDvcQ6ERbiPg+xTtzzIYLDN597rl6leoxhStFm3Va8GZd+jW0tBAgQINC+wG2rq6urdbPxP+i4ZreFAAECJQvEZVvjjsxXrryc7T0fmtb34MF7UwSJmFw9TEuEiriqU9xPwkKAAAEC3QrUWcEZiG6dtU6AwAgKzM7OpKmph4SHntpFeGhzGFNP054SIECAwIgJCBAjVjCHS4BAtwI3btxIzz//fJqenu52RyPW+uTkZDUnJK5MZSFAgACBsgUEiLLrr/cECKwTmJ+fTwcPjqc9eza+jOi61Yt5GXNBIkTMzs4OVZ+/+vTThi8NVUUcDAECJQgIECVUWR8JENiywMLC/NCN89/ywXe84uHDkyl8LAQIECBQtoAAUXb99Z4AgR6BGL60sLCQxsfHe971tBaIMxBxydSYZG4hQIAAgXIFBIhya6/nBAisE4i7Lu/du9fwpXUuvS8nJibS0tJi71ueEyBAgEBhAgJEYQXXXQIENheIm8eNj09svoJPqrMz4WQhQIAAgXIFBIhya6/nBAisE4ihOYYvrUNZ9zICliFM61C8JECAQGECAkRhBdddAgQ2F7h8eSnt27dv8xV8UvmsrKykmC9iIUCAAIEyBQSIMuuu1wQIrBOofxC7fOs6mA1exjwRZyE2gPEWAQIEChEQIAoptG4SIPDOAvGDOO7/YLm1wK5du5Mbyt3ayRoECBDIVUCAyLWy+kWggcDY2PvT7OyMYSkNzEpedWJiPK2suCN1yd8BfSdAoGwBAaLs+us9gTWB+fmFdO+9H0knTjxa5L8ux6VJzX9Y+zp4QoAAAQIENhUQIDal8QGBsgTm5ubSiy/+sOr0Aw/cn44cOZLm58u66/Du3bvKKrreEiBAgACBPgQEiD7QbEIgV4GYQHz+/FPpypWX0+Tk4fT446fTwYP3Gt6Ua8H1iwABAgQI9CFwex/b2IQAgcwFdu3alaanj1d/cRZidnY2nT17Nk1OTqaTJ0+5U/MA6x/zU4ZxOXny5DAelmMiQIAAgQEICBADQLYLAqMsEKEh/uKqO+fOnU0xvGnfvv1penq6en+U+zYKx76y8uOhO8z4HlgIECBAoFwBQ5jKrb2eE2gkUMLwpuvX3Ryt0ZfCygQIECBQpIAAUWTZdZpA/wL18KbLl6+kxx8/k3K5etPevfvcHK3/r4UtCRAgQKAgAQGioGLrKoG2BWJoUy5Xb9q9e3fbPNm2FzfdGxvbk23/dIwAAQIE3llAgHhnH58SILAFgRyGN42NjaXLl5e20FurxFCvqLmFAAECBMoUECDKrLteE+hEYJSHN9U/iG/cyG8exOnTp9OxY0er+3rEJPj4i7MI/S4RtNx0r1892xEgQGD0BQSI0a+hHhAYSoFRHN508OD4tn5YD2UhUkoLC/NVv6anj6UISPHXbwCI4PHud787RVi0ECBAgECZAgJEmXXXawIDExil4U3xo3ppaXFgNoPYUVx+d2VlpfqLezfE3cZjAny/SwSIuIyvhQABAgTKFRAgyq29nhMYqMAoDG8aHx9Pi4t5zYOohyo9+OCD1U0At3vmIALWxMT4QL87dkaAAAECwyUgQAxXPRwNgSIEhnV408TERDWROqd5EK+++qu5DocPT7by3VpaWkpttdXKAWmEAAECBAYuIEAMnNwOCRCoBYZteFP86/zevXurycb1MY76Y31GJULbdpf6bEa/8ye2u3/bEyBAgMBwCAgQw1EHR0GgaIFhGt40NTVVTTrOpSDXrl1NMTm8jeXixYsphnlZCBAgQKBsAQGi7PrrPYGhE9jp4U0xPGdhYaG6UtHQ4TQ8oJhA/bOf/azvKy6t393Fi99N09PH17/tNQECBAgUJiBAFFZw3SUwKgI7Nbwp9nv48OE0OzszKlSbHmfMV4iljSFHcfYh7tbdRlubHrAPCBAgQGAkBASIkSiTgyRQrsBODG+Kf2WPH8yjvsRwo+efn0ttzH8Ij5MnT406ieMnQIAAgRYEBIgWEDVBgMBgBAY1vKke5z/qISLOpkRftn/p1qUUcynaCCKD+abYCwECBAh0KSBAdKmrbQIEOhEYxPCm+Nf2c+fOZjEXYrtFOHv2bDp+/Pi2g8h2j8P2BAgQIDAcAgLEcNTBURAg0IdAl8Ob4mpMY2N7spgL0Qft2iZxFmZlZdnk6TURTwgQIEBAgPAdIEAgC4EuhjedOnUqzczMpLiaUYlL3FAvzsLE2ZjtDoMq0U+fCRAgkKuAAJFrZfWLQKECbQ5vivkDU1MPpRMnThSpGUOX4ixMnI2xECBAgACBWkCAqCU8EiCQlUBbw5viLEQM4cnhsq5NChyXgI37Ppw/f77JZtYlQIAAgQIEBIgCiqyLBEoX2M7wpggi588/leJf469du1YEZQxdOnr0s+nMmS+mOKNjIUCAAAECvQICRK+G5wQIZC3Q7/CmGMoUVyE6duxoEVdlOnLkk9UlWw1dyvo/B50jQIBA3wICRN90NiRAYFQF+hneFBOJI0jEj+v4F/pclxMnHq26FmcfLAQIECBAYCMBAWIjFe8RIFCMQJPhTfWP6tOn/zRLnwgPMUxrbu57rrqUZYV1igABAu0ICBDtOGqFAIERF9jK8KY4cxE/ruNHdv0v9SPe7bXDj/7Mz89X8z2inxYCBAgQILCZgACxmYz3CRAoUuBWw5t6Q0QucyLq8BDhaN++fUXWXacJECBAYOsCAsTWraxJgEBhApsNb1pcXKzORMQN5kZ5TkTM5YgQFGdUrlx5WXgo7PutuwQIEOhXQIDoV852BAgUI7DR8KYHHri/usHaBz7wgXTvvR9Jcd+EUVoiNET4uX79hjkPo1Q4x0qAAIEhEBAghqAIDoEAgdEQ2Gh4049+9KP0wQ9+MD344JF07tzZkehI3BSvvlTr3NycCdMjUTUHSYAAgeERECCGpxaOhACBERLoHd505513pne9613p2WefTePjB4f2bMSvhlwdSbOzs+nChW+kuDSthQABAgQINBUQIJqKWZ8AAQI9AvXwpr/7u/+dvvCFL6Sf/vSn6aGHptLHPvax9Nprr/WsuXNPY67D6dOnq3ATk6RffPGH1T0tdu6I7JkAAQIERllAgBjl6jl2AgSGRqAe3vTaa/+YvvzlL6d/+qcfp/vv/zfp0KGJ9PLLL+/IcUZwiGFVMUcj5jwsLV1OZ86cMWRpR6phpwQIEMhHQIDIp5Z6QoDAkAj87u9+Ov393/9D+qu/+u/VEX3iEx9P99xzoAoWgzjEmNAdl2bdu/dDVXCI4Uox1yHOllgIECBAgMB2BW5bXV1drRu5+8670utvvlG/9EiAQCECY2PvTysrPy6kt4PvZgxleuKJJ9KlSy+lX/7yl+nAgXvS9PSx9PGPf6K1g4nQEDeCW1iYr9o8fHgyTU9PCw2tCWuIAAECBOqsIED4LhAgkASIwX0JZmZm0rPPPpN+8pOfpF/84hfpwx/+cPrN3/yt6h4McYYg5ijEcKjNlhiWFMORYkL0yspyWlxcSpcvL6WxsbEUoWF8fDzFBG8LAQIECBBoW0CAaFtUewRGWECAGHzxIgA8+eR/TQsLC+m9731vet/73pd+4zdur8JA79Hs3bs3vfrqq71vpYMHx6vXExPjae/efWvh46aVvCBAgAABAi0L1AHi9pbb1RwBAgQIbEEgzjb8xV88neKMwsWL360urRqbnTt3vjqDEGch6rMNtzorsYXdWYUAAQIECLQmYAhTa5QaIjC6As5ADEftYg5D3KPh2rWraWrqIXMYhqMsjoIAAQIEfi1Qn4FwFSZfCQIECAyJQO/N6W7cuJ4eeOD+dOzY0aG9Md2QsDkMAgQIEBiwgAAxYHC7I0CAwK0E6pvTXbnycjUpOi7JevDgvenixYvVsKZbbe9zAgQIECDQpYAA0aWutgkQILANgfrmdJcvX0mPP36mChBxU7i4q3RMwrYQIECAAIGdEBAgdkLdPgkQINBQwPCmhmBWJ0CAAIHOBASIzmg1TIAAgfYFDG9q31SLBAgQINBMQIBo5mVtAgQIDIWA4U1DUQYHQYAAgSIFBIgiy67TBAjkJGB4U07V1BcCBAgMv4AAMfw1coQECBDYkkDv8Ka4+ZyrN22JzUoECBAg0FBAgGgIZnUCBAgMu0AMbzp58lSKqzfFY1z+1dWbhr1qjo8AAQKjIyBAjE6tHCkBAgQaC0xNTaW5ubk0N/e9FDenGx8/6OZ0jRVtQIAAAQK9AgJEr4bnBAgQyFQghjSdP/9UevXV15LhTZkWWbcIECAwIAEBYkDQdkOAAIFhEDC8aRiq4BgIECAw2gICxGjXz9ETIECgbwHDm/qmsyEBAgSKFhAgii6/zhMgQCBVQ5oMb/JNIECAAIGtCggQW5WyHgECBDIXMLwp8wLrHgECBFoSECBagtQMAQIEchIwvCmnauoLAQIE2hUQINr11BoBAgSyEnD1pqzKqTMECBBoRUCAaIVRIwQIEMhbwPCmvOurdwQIEGgiIEA00bIuAQIECCTDm3wJCBAgULaAAFF2/fWeAAECfQsY3tQ3nQ0JECAw0gICxEiXz8ETIEBg5wUMb9r5GjgCAgQIDFJAgBiktn0RIEAgcwHDmzIvsO4RIEAgpSRA+BoQIECAQOsChje1TqpBAgQIDI2AADE0pXAgBAgQyE/A8Kb8aqpHBAgQECB8BwgQIEBgIAKGNw2E2U4IECDQuYAA0TmxHRAgQIBAr4DhTb0anhMgQGD0BASI0auZIyZAgEAWAoY3ZVFGnSBAoEABAaLAousyAQIEhk3A8KZhq4jjIUCAwOYCAsTmNj4hQIAAgQELGN40YHC7I0CAQB8CAkQfaDYhQIAAgW4FDG/q1lfrBAgQ2I6AALEdPdsSIECAQOcChjd1TmwHBAgQaCQgQDTisjIBAgQI7JSA4U07JW+/BAgQuFlAgLjZwysCBAgQGHIBw5uGvEAOjwCB7AUEiOxLrIMECBDIV8Dwpnxrq2cECAyvgAAxvLVxZAQIECCwRQHDm7YIZTUCBAi0ICBAtICoCQIECBAYDgHDm4ajDo6CAIG8BQSIvOurdwQIEChWwPCmYkuv4wQIdCwgQHQMrHkCBAgQ2FkBw5t21t/eCRDIT0CAyK+mekSAAAECGwgY3rQBircIECDQh4AA0QeaTQgQIEBgtAUMbxrt+jl6AgR2VkCA2Fl/eydAgACBHRQwvGkH8e2aAIGRFRAgRrZ0DpwAAQIE2hIwvKktSe0QIFCCgABRQpX1kQABAgS2LGB405aprEiAQKECAkShhddtAgQIEHhnAcOb3tnHpwQIlCsgQJRbez0nQIAAgS0IxPCmw4cnU5yZeM973pMef/x0uueeA+mP//g/peXl5S20YBUCBAjkJSBA5FVPvSFAgACBFgWWlpbSkSNH0pEjn6zCwtGjx9LXv34hfeUrX00///nP0/j4wXTs2NEU61kIECBQisBtq6urq3Vn777zrvT6m2/ULz0SIFCIwNjY+9PKyo8L6a1uEri1wI0bN9KJE4+mxcXFdObMF6uzDxttFevNzs6kixcvVh+fPHkqTU5OpjhrYSFAgEBuAnVWECByq6z+EOhDQIDoA80m2QpEKIgzDrt27U4XLlzYchiIEBF/165dTVNTD6Xp6em0Z8+ebJ10jACB8gTqAGEIU3m112MCBAgQ2ESgDg8xgXpubm7L4SGac/WmTVC9TYBAdgICRHYl1SECBAgQ6Fcghi3FWYPz55/qt4nk6k1909mQAIERERAgRqRQDpMAAQIEuhWIuQzXrl3bVnjoPUI3p+vV8JwAgZwEBIicqqkvBAgQINCXQAxdOnv2bBUeupgAbXhTX2WxEQECQyogQAxpYRwWAQIECAxOIM4+7Nu3P42Pj3e6U8ObOuXVOAECAxIQIAYEbTcECBAgMLwCMzMz6dSpU60e4PXr19PnH3kkxVVL4u873/r2WvuGN61ReEKAwAgKCBAjWDSHTIAAAQLtCcSlV2PidJtnHyI8fObTv5d2795d3V/pC489lv78ySdTvL9+2Wh4U0zmdnO69VJeEyAwLAICxLBUwnEQIECAwI4ILCzMb3qjuH4P6A8feaTa9Ikvfal6/NTvPFyFh8WXLm3aZO/wpgg0ESIeeOD+tZvUbbqhDwgQIDBgAQFiwOB2R4AAAQLDJRB3mz58eLK1g/rB919Il166lOKsQ73c2ODMQ/3Z+sfe4U3T08erAPGhD30wnTt3Ni0vL69f3WsCBAgMXECAGDi5HRIgQIDAsAjEZVtjmFGbd4z+zre/lfbccUc6dN+htW6+9davfvjv2r177b2tPOkd3hThYXz8YHVmwvCmrehZhwCBrgQEiK5ktUuAAAECQy8QASKGDrW1LL/1VnX24VMPP3xTkz944fvV6zvu2HPT+1t9YXjTVqWsR4DAIAQEiEEo2wcBAgQIDKXAyspyqwEihi7FEhOm66sv1VdgirMS8bedxfCm7ejZlgCBtgQEiLYktUOAAAECIycQZyDGxvo7K7BRZ69efaV6+6//9m+qqy+9/uYb1WMMk1p/VmKj7Zu8Z3hTEy3rEiDQpoAA0aamtggQIEBgpASuX7/R6vyHq69creY+9J5pePZrz1RXYOqdE9EmkuFNbWpqiwCBrQgIEFtRsg4BAgQIENiiwMSh+25a8wcvvJB++2MfTfsPHLjp/bZfGN7Utqj2CBDYTECA2EzG+wQIECBAYJsCcUnXmFj9Rz2XdN1mk1va3PCmLTFZiQCBPgUEiD7hbEaAAAECBNYL7D+wPy1eeql6++orr6Q/e/LJ6n4QvUOa1m/T5et6eNPS0uVqqNbRo591c7ouwbVNoBABAaKQQusmAQIECLxdIH5gLy0tvv2DPt+pbx4XV176/CP/sTrzEHeh3sgn4LIAAAZwSURBVOkl7nNx8uSp9Npr/5ji5nSzszPJzel2uir2T2B0BW4f3UN35AQIECBAYHsCu3fvSjGRuq0lrrb0zeeea6u5TtqJ4U3xFzeju3jxu9XN6R588ME0NfVQGh8f72SfGiVAIC8BZyDyqqfeECBAgEADgfHxiRSXci1xibBw/vxTyfCmEquvzwS2JyBAbM/P1gQIECAwwgIxhOny5aUR7sH2D93wpu0baoFAaQICRGkV118CBAgQWBOIS5/u3bs3zc/Pr71X8pMY2vTiiz9MFy58Iy0vL1fDm06ceLQa7lSyi74TIHCzgABxs4dXBAgQIFCYQPxoXlgQIHrLbnhTr4bnBAisF7htdXV1tX4zrhrx+ptv1C89EiBQiMDY2PsL6aluEiCwXYF6zsR227E9AQKjJ1BnBVdhGr3aOWICrQusrPy49TY1SIAAAQIECOQpYAhTnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCAgQnbBqlAABAgQIECBAgECeAgJEnnXVKwIECBAgQIAAAQKdCNy2urq6Gi3ffeddnexAowQIECBAgAABAgQI5COwFiDy6ZKeECBAgAABAgQIECDQlYAhTF3JapcAAQIECBAgQIBAhgICRIZF1SUCBAgQIECAAAECXQkIEF3JapcAAQIECBAgQIBAhgL/D446lc0L/M03AAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the forces acting on the hoop.</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>Show that the linear acceleration <em>a</em> of the hoop is given by the equation shown.</p>
<p><em>a</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{g \times \sin q}}{2}">
<mfrac>
<mrow>
<mi>g</mi>
<mo>×</mo>
<mi>sin</mi>
<mo></mo>
<mi>q</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></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>Calculate the acceleration of the hoop when <em>θ</em> = 20°. Assume that the hoop continues to roll without slipping.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the relationship between the force of friction and the angle of the incline.</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>The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.</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>weight, normal reaction and friction in correct direction</p>
<p>correct points of application for at least two correct forces</p>
<p><em>Labelled on diagram.</em></p>
<p><img 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"></p>
<p><em>Allow different wording and symbols</em></p>
<p><em>Ignore relative lengths</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE</strong> <strong>1</strong></em></p>
<p><em>ma</em> = <em>mg</em> sin <em>θ</em> – <em>F</em><sub>f</sub></p>
<p><em>I</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = <em>F</em><sub>f</sub> x <em>r</em></p>
<p><em><strong>OR</strong></em></p>
<p><em>mr </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = <em>F</em><sub>f</sub></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{a}{r}">
<mfrac>
<mi>a</mi>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><em>ma</em> = <em>mg</em> sin <em>θ – mr <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{a}{r}">
<mfrac>
<mi>a</mi>
<mi>r</mi>
</mfrac>
</math></span> → </em>2<em>a</em> = <em>g</em> sin <em>θ</em></p>
<p><em>Can be in any order</em></p>
<p><em>No mark for re-writing given answer<br></em></p>
<p><em>Accept answers using the parallel axis theorem (with I = 2mr<sup>2</sup>) only if clear and explicit mention that the only torque is from the weight<br></em></p>
<p><em>Answer given look for correct working</em></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><em>mgh = </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>Iω</em><sup>2</sup> + <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></p>
<p>substituting <em>ω =</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{r}">
<mfrac>
<mi>v</mi>
<mi>r</mi>
</mfrac>
</math></span> «giving <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {gh} ">
<msqrt>
<mi>g</mi>
<mi>h</mi>
</msqrt>
</math></span>»</p>
<p>correct use of a kinematic equation</p>
<p>use of trigonometry to relate displacement and height «<em>s</em> = <em>h</em> sin <em>θ</em>»</p>
<p><em>For alternative 2, MP3 and MP4 can only be awarded if the previous marking points are present</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.68 «ms<sup>–2</sup>»</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><em>N</em> = <em>mg</em> cos <em>θ</em></p>
<p><em>F</em><sub>f</sub> ≤ <em>μmg</em> cos<em> θ</em></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em>F</em><sub>f</sub> = <em>ma</em> «from 7(b)»</p>
<p>so <em>F</em><sub>f</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg\sin \theta }}{2}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>F</em><sub>f</sub> = <em>μmg</em> cos <em>θ</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg\sin \theta }}{2}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> = <em>mg</em> sin <em>θ </em>– <em>μmg</em> cos <em>θ</em></p>
<p><em><strong>OR</strong></em></p>
<p><em>mg</em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\sin \theta }}{2}">
<mfrac>
<mrow>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mn>2</mn>
</mfrac>
</math></span> = <em>μmg</em> cos <em>θ</em></p>
<p>algebraic manipulation to reach tan <em>θ</em> = 2<em>μ</em></p>
<div class="question_part_label">e.</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>
<br><hr><br><div class="specification">
<p>A monatomic ideal gas is confined to a cylinder with volume 2.0 x 10<sup>–3</sup> m<sup>3</sup>. The initial pressure of the gas is 100 kPa. The gas undergoes a three-step cycle. First, the gas pressure increases by a factor of five under constant volume. Then, the gas expands adiabatically to its initial pressure. Finally it is compressed at constant pressure to its initial volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10<sup>–3</sup> m<sup>3</sup>.</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>Using the axes, sketch the three-step cycle.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.</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>Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="500\,000 \times {\left( {2 \times {{10}^{ - 3}}} \right)^{\frac{5}{3}}} = 100\,000 \times {V^{\frac{5}{3}}}">
<mn>500</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mn>100</mn>
<mspace width="thinmathspace"></mspace>
<mn>000</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>V</mi>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><em>V</em> = 5.3 x 10<sup>–3</sup> «m<sup>3</sup>»</p>
<p><em>Look carefully for correct use of pV<sup>γ</sup> = constant</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct vertical and horizontal lines</p>
<p>curve between B and C</p>
<p> </p>
<p><em>Allow tolerance ±1 square for A, B and C</em></p>
<p><em>Allow ECF for MP2</em></p>
<p><em>Points do not need to be labelled for marking points to be awarded</em></p>
<p><img 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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>PV</em> = <em>nRT</em> <em><strong>OR</strong></em> use of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{P}{T}">
<mfrac>
<mi>P</mi>
<mi>T</mi>
</mfrac>
</math></span> = constant</p>
<p><em>T</em> = «5 x 290 =» 1450 «K»</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>area enclosed</p>
<p>work is done by the gas during expansion</p>
<p><em><strong>OR</strong></em></p>
<p>work is done on the gas during compression</p>
<p>the area under the expansion is greater than the area under the compression</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The first diagram shows a person standing on a turntable which can rotate freely. The person is stationary and holding a bicycle wheel. The wheel rotates anticlockwise when seen from above.</p>
<p style="text-align: center;"><img 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PiuS7cOeVMmAD+pDtOu82tOg/7CvqEr+QoI7vn6NPItbgeDup0F92yp8ckD6mkAdL/H2sXKB/j47rHuXeCbW8eN08R7ygDYGWDqpM8U06Hff8lufV2to4DgXke9inEF9+LCcTMRSNeBI3HNreMDH1eZ+fFDWfjkxa+GEGCn7KT1zjs/KS6aQkoB7S3TTR8Q3IvrziyaupbvpIFhEvCruHRIC9cLAwW/EjiH8v8zILGqWIcUKKOALPcyagUKK7gXF5LtD3BvTAJ06OuTgI+FD/R5AVtedmOX7wA6Z1w+oaBudWPQ0OP3ivcZhbysgODeQU8Q3IuLDjQBroGuqzMDDC9Aa3A3333Tgw/ps1GcDilQRgHBvYxagcIK7sWEZLsG4N4V0GPJV9Mhi/UXhbpaAcH9aj1a+SS4F5P59OlTyc03f3n0cGeQYZDTIQXKKCC4l1ErUFjBvZiQPLWKqYyxWNBdlkNwL9ZnFOqKAoL7FS0KvQPM/otNsZinbq/nnptLFyqxWMl/2aP2+Gd1X2w9wHdPPvnEgjiWhqVvZ78cfB7KYhf232FHRPzbXUI1lrzpK1l7EhXqtAo0SgVGC3f+UQyOwPmVV76fQpWtAYAsMx/cfV8MxCwFX7t2dbJ8+dKr4Gzfd3WmTLyWLFl0VbnY04a6sI8N9WKgYCsEBgirP6tAYztok61bb0hnn8QC2C7Lcdtt+9L2iq2dVJ54FRgs3AEW8GKbXSzpw4cPpQ+ntk2ogDAw7ArGseTLYOUOCDYQ8AuCAY8VoujY9nH8+LHkxhu3tToNskt4T8tbcG+7B/Y/v97DHYgDIADu7rIIsFxoFYUpcSZZ5oCPF75grHp2eGSwYOAw1wnlMLdJ1pmyMuD45SG+DUZZ8biGxW35cLZfGVjktqUw5XMHMMtnUp3s+7wzAwDfky57sQN+6tAk9LdsuT7dNqDpaYbToBrL94J7/2Hbdg16BXf8yfxcP3HieApYgFPEPQKwDVDEwVUBoH03hVmpQKuoq4Ly2LNQAXARnzfp+zAlbp2D8gJcykLanPnMdcpEnvbiurmhGJhsYLAyoVcRXS0MepLOW2/9uLBueXWlzKtWXZfWIxa4dl0OwT2vx+i7LAWihjt+cYD7yCMPp0DOs8QBjX0PuIENVrRZmICtyYP0saYBJOe8wYGwBlI7l4W7aUNeWOsAlvfoVffGmw0Gdi+CXwhY7ORBed2B0spvZ37N8P7gwf0p7IsMdn67vPPOO8k9X/1qmk7XUI0lf8Hd7yX6PE2BKOEOoIADkFi8+Nr0bPDgbAAB4oDHAF4XatPEKvI9MLMnKWE9A0j/qAp33zrnlweDQt5A4ucd4jP50UbmCsNdYwOr20685/rWrVtS0BdtnwcffDB54vHHkz17dmumzM8uP2hbcA/Rc8eVRlRwBxgbNqxbAAoDvFmDTVvhIboAIAPs5qdnADK4lYE7mtiDPsw6J11LK0RZQ6TBoEa5GGwpp7WZC3sG5Wef/ebUshPnzPPPl97qNxYru4lyCO4heum40ogG7rheFi26ZoGVDtABXJ8Pym9+eVwnv/rVvy+op7llgCQDAY/aA3JY58C9beu8rt6UF5BnWfVcm1QftLrppp3pTpBszNUEKPuYpuBet0eOL34UcOcGqWvp8VOeZ4xW8dfG3ITU5+mnjy8AOxDfsWN7wgwRrF7AjhU8hPrzC4PByW1f6gvgs359nD59Onnk4YeTbzz1lBYw/d0lw2AkuMf8nx1n2aKAO//seo1PAwYw/9iyZXPy2rlzyVNPPim4O3Dn/yNrMPT102cpYApEAfd169ZcBXcsd6y9IR342XFTXHvtl66qqzuo8d2pU88NqdppXai73QS3+uKC891tuGqYAvnLX/wi2bv31lrPHe2j6yWvzOimQwqUUSAKuH/44YcLfrbzMx4XBXOn++ieoMxYprhYqAc3VhmwqCtzzA1ydsa3zn0HPk+bSlmmgbsMC7yplz+ThrZlbr1/PP/8Pydfu+++FO48N1QLmC7PlAH6grvfW/R5mgJRwJ1CAoKsm28GP2AQapHMNFGqfo/lyY1RgEa5ATs3R/3BKW+2DGEZBBgQuAnrW7dVy9ZGPNwGDGgMUnltyT2WrAOXzIvf+57g7rhjzJoX3LN6jK7lKRAN3CkkcMCqBWy+tWeQ5+c94AD2QBD4+fDMq3DI7wxmWNpmndtCorx88uBu8SztrKmUFqbLM+WjHgy4Nv2RNprUbnxHuElt5bpkcMsQPoYnMBlcuzzz4O7Nm2e7bG7l3UMFooK7qx/QNgvQ99ca6O1sy+ABoa1MxYIEPpNg4uZV5r1vnbvL/IumUwTublpoYVMpGdBC18nNy31vACd/Bl32lGGlKoMr2pvu1g7u2SBfdAHTiRNPp7NkALvBvUugxpS3HrPn9kq9L6pAtHB3KwAMgRpgASDTYG+QcbckAEj+fjK2spX0gXbWAeCAGxa5WdFmnfNdlaMs3C0PoE7e1A+XD+lUOUiHuLwYBHElkS4DIxq7Wx2vWLEszc80nXQ2mGNh4nZBs6L6EI4tDX7yk/+Tgl1wv+JrZ5AB7ocO3V2lqRVnxAr0Au5++wBioIQlCbABjgvySQCadB2w+FYogMPVQhwAt2vXzekvCSCIFQsQeQExA2Xe2a0D4fyykJZ7ALxJ6f3ud/+ZwpiHWQBTQE98tgOgfOiC35+XDUhufoA4a+93N0zeewM++jAgMPBS1qIwd+vJ+9deO5vcfddd82AH8tQtJuu5y7LwwJK5uTlfNn2WArkK9BLuWTUyaxTw4tv13QdmWeZBK8R3QNN/+QNHkXwMwCHSKpKfH8bdHCzL3ZXVBlWu0W7k9b9/9KN5uDPPXfvKXLHegfu5c2eryKs4I1ZgMHDPa0MsfSxL3DBYmcDf3+YWuGVZ8D70+v7Zt9j5hcJAiAWO1c8vAPvFUNUSz2sL/7uHHnrwKl87LhnB/QrY+cXAc2TpuzqkQBkFRgH3ooIY1GwgAHQAj5e5OXADYcm6fuks4PsWt/s5KzzXGFzccO77POuf+wnmfmHQoqwMYJSbwYx6uO4jrOUYDm6iso/Mz3/+r/NWu8F99+5b5Jb5+5RI5vzTJ3VIgTIKCO5l1CoYNs9fbgOHD3hA7A4u/vtJN3wLFimqYOjDL4UssAN35roL7les99nZmYk3/KNqWBUmKgWigDvWJT87hwSwvFYG3D7csa7HcPzmN79Jf6GwEtW32AE7r2Pf+Ib2lXEWMtFXdEiBsgpEAXdcBu4yfazYGGFvs3TKiuyHHyPc0Y7pfLOzm+ZXoRrM/bPgfsVq1wIm/79Hn4sqEAXc3cICAcAO7PEjY7WwgAfr3hYmueHbfI91TXmYAvjuuz+vnPWY4E5djx8/lk5tBNqTrHUX8Nru9wrcmeN+110HKvc1RRyvAtHB3W8K818DVoDPzUIAC/iBPtcZDIBI024dgzv5s6thVcgPHe60Gc9BxW/OLo9FoW6A13a/V+CuOe4+EfS5qALRw31SRQA57hyAixvHlue74LfFPYRxZ4tMSnPadRfu5FMV8kOGO3XjoSM8XMI2ATNoFz0L7lfg/vUHHkhef/21aV1T30uBBQr0Fu4LauJcAPxAxpbWA2Xgz8ssf4Mzn+07zjZ1kDjui/QYRCyef2Yv9tWri7lrhgh3rHW27MVSP33q1FVTG4tC3cIJ7lfgrmmQzj+23pZSYJBwL6MAoHVfLtDtPcAH/HYPwAe7+5k554Au7xgS3Jkzz/YBZq27+8MYrMueDx48kD5Dtcsl/7HkvXLl8tY2isvrs/qufwqMHu5lmgzYuyB337OZGYPANLCTX9/hTh1/+ctfJHfffTDVg2mNrCotC/FJ4XkKkx7UcSHd8pg+pkMKVFFAcC+hWhbcy0AddxFpZLl3uB7zQdm5SWpAZ6Mv3C9FZr9Mgvik64L7ZbcMA9yBA5opE/P/RcxlE9xLtI4L9zJQJwvi4tbhJi9bA7hWP+9x5wB9IBrDQTm4Z8E0Rlwu+NKx0JsCugt6wf0y3Jkpc+zYN2LoDipDDxUQ3Es0GoAuC3WSxy/NtMkjRw6nTypi3jJb2rJfjLtnDBDlM/79pvd/IX2718BMojfeeD19OLdZ5pQP6/ybJ09etWOjC+Gm3gvul+H+lSNH0mm+JbqogkqBeQUE93kpir0p4lP3UwKizMrBcmdGTRa4SZdwPEAb3z2DAdCtc2B9kwY3PNl98a67LvvI+aUAvO+44/Zk37696Yu56LzwnYe4KVoH/IL7Zbjv2LE97RN1+oDijlcBwb2FtgfmZvED2yIDBOEAPG6cIuEZGFjMderUc/N+cQAOvIE27hTA3YSPvA7Is+Iy/U83VC+krrsWuqeyGKgCgntLDcs8+D/96f+Vyg2oA3cgj//bh/z777+XXH/9TAoBdljEjWLWdx8gngV2rgnulx+txz77OqRAVQUE96rKlYiHFb5+/dr0pirR+IylbQfQzruRSlibY48/nhuvthgLH33dRUOTINvVdcH9QnL82DHdTLV/EJ0rKSC4V5KtXCSs729969n0Rikxf/jDN9PZMYAa6OMDB9bTDgYAXC+2lw7hmW/OTBb3MXVdQTlUvoL7hUQ3U6f9N+j7aQoI7tMUCvA94L7vvnvSGSmAGTfLmTP/nN7UNJdLnWyY6eI+YDoUZLtKR3C/kG6N7P66q9M/FHecCgjuLbT7448/lixefG1qoW/duiV1yTCtklkx+NKLWO15xQQCmzfPBlsh2hXULd+xw/38+bd1MzWvw+u7QgoI7oVkqhfoL3/5S8INVSDOM075jN+d2Sy33LIr/Ud+660f18oE147Bse/nscOdeyjaw73Wv4MiJ0kiuLfQDbCseWYoN0Lxs+OKAcY333xTatGzORSfAX6VgxuygvvlueGxbPhVpxxs8/vd756u0hUURwrMKyC4z0vR3BvmuQN0/zDXDNc3bFiXPls0b9aMH98+M3iwIKmvFjs3g9n7nWmc3Dtgpe6Y57nzy6XqQG99QmcpILi31AdwyWC5uwf/wIBs7949qeXNo/uq3GDFb9+XG6qsfsXtwD41zM3nFwca8HzVs2dfTWcC3XrruHeFRBN/TYPbb/ReChRRQHAvolKAMPyzMu0RHzuuGWDPPzE3Wu1mK9lghftWG/DOO9gPJua57ljljzz8cDoDZNWqlcmDDz6YzhyirlkQ27//ztFa7vxi0eKlvN6u74oqILgXVSpAOPzuTIEE3oCNmTPMmHnlle/Pz4HPyibPkmMb3tnZTVG5ZNjmABcLj9qj7DxLlac0Uecix5jhzk6QbCGhQwrUVUBwr6tgifjAjZWmtnEYFjm+dgDIa9KBpe9b84TFP088YNqVv51tDrJgfvr06bTMWZb5pHradVw0Y/W542+f9kvNdNJZCuQpILjnqdPAd7bjowF9yZJFheHO4MBNWFa83nnnHQmzbNp2x3Dzkzxxs5jPHMu8Dsx9mccMd/pFlQHR11CfpYDg3lEfMLi7Z+DtvrDWgTlz4wmHn57Bge0L2gA7Nz9tFgsuFubl+z7zJuQbK9zlb2+iN403TcG9o7Z3oW7vcb/4L1vFaq4civuP//hQCll3K19cI1V2giSevXgwBxa5C3Ju1jKLhYHGLUOTso0V7vK3N9mrxpe24N5RmxvQ3XPRovCzHdi6D+FgRaObVtH3t9xyc7oaEqDySD32qWkT5Fl1HivcNb89qzfoWlUFBPeqytWMlwXfmkkOJvoY4W77ycjfPphu3HlFBPfOm0AF8BUYI9y5Sc0aCB1SIJQCgnsoJZVOMAXGCHf2kzl37mwwDZWQFBDc1QeiU2CMcN+0aUPhRV7RNZgKFKUCgnuUzTLuQj300NGEmTt1dlbsU1ymtjLFVIcUCKmA4B5STaUVRIGXX34pYVpgnwBdp6wMZEePfj2IdkpECpgCgrsp0dKZlaVZM2XWrVuTMGNCR5KMDe48L/Wdd36ippcCQRUQ3IPKOT0x4A7I/eP9999Loc8mYmM/xgR3ZsmsWLEs+f3vf21Xy1oAACAASURBVD/2Zlf9AysguAcWdFpyk+BOvPvv/1om+KelObTvmTWCNVvH1RF7XKDOnjxLly5Ot5Joa/Xv0PqK6jNZAcF9sjaNfDMN7nw/9gPQcYORFZv43u0FEM+++mq00GdvmEkvqwNAX758abJixfJ0rx5z0Wnx0th7ffj6C+7hNc1NcRLc8bfv2LE9+fTTP+fGH8uXwI6tb3HR2IspkmxexjbJx48dSzdQ68JCB+DkT1tu3jw7fw9l06aNib3Wrl2TlpXyWpk5G8zdM7BnwzgdUiCkAoJ7SDULpAUQ3H9s9z1w/+ijXxdIZbxBTC/gyfutW29ILXusegbI0LAnTdJmkRErSMlz9errEsvfylP3zAZxOqRASAUE95BqFkhrkuUO1IE7N1s///zzAimNMwjPmPVB6sIWKxgI47PHFYKFba4S5pPnwR+XD2GJRzvxWETyMivczzfkZ57SpUMKhFRAcA+pZoG0JsGdqFiJAIOZMzqyFbBnzxYBK1AG/Lxwl/hxbrxx21UWODc3ieM+HcuP09TnmZlN2RXWVSlQUQHBvaJwVaMVgTuQ15GtwMmTzyyAdFPAbTvd7BrrqhSopoDgXk23yrHy4D43950UXH/84x8qpz/0iH2GO24ee3GvYOfOHelrx44bk0WLrkmfiTv09lP92lNAcG9P6zSnSXDH546/nbnuOiYrEAPccfMYpHH3GKQ579u3N7njjtvT1+FDh5L77r230GvXri8ns7NyzUxueX1TVgHBvaxiNcMD96yf+4Bdq1Oni8szZbP0q3KNh5MbpDm71vSePbvnIQ2si0K6Tjiei8v0Tx1SIIQCgnsIFZVGawrw0O4skLvWNHPPXWvaLGnOX/3KV1oBdRXIM6Ds3Xtra1oqo2ErILgPu30HVTsWNjGjBSv74MED0UK6CtiJw8DDwKWtCAbVbTurjODemfTKuKwCt9++L52mCNyrAjT2ePzq0Gypsj1D4bMUENyzVNG16BRgM7G1a1enfvAhw50bsixm0yEF6ioguNdVUPEbVwA3Be6KAwf2p3Bft264lru5ZrSRWOPdavAZCO6Db+L+V3D//jvSmSyuXzp290qd8l1//YxmzfS/23ZeA8G98yZQAfIUYLfEZcuWXDXLBSu+Djxjj8uc90cffSRPFn0nBaYqILhPlUgBulSAqYGs4HSBzF7vbc09d/Nt6z3uJ/a30SEF6igguNdRT3EbVeDSpUsLrHYAy6pQ5oS3Bdsu8uHXiqZENtq9Bp+44D74Ju5vBZ944vF5X7sLWCx5VpO614b2nhlBH3/82/42nkreuQKCe+dNoAJkKcBsEfZmz9qfBZfMkKdDMlAxgJ0583yWNLomBQopILgXkkmB2laAPVaY155lkQP8od9UZb47i7Z0SIGqCgjuVZVTvEYVOHLkcMKskSy4c41Nv7Ks+knh+3ZdN1Ub7V6jSFxwH0Uz96+SK1Ysy4U3bhms275Bu0x5+XWiQwpUVUBwr6qc4jWmAHPb2f42D4T4pP0pknnh+/idZsw01sVGkbDgPopm7lclX3rpxamzYZgKyZTIPkK7aJlvuGFLwkCnQwpUUUBwr6Ka4jSqAAuXprlcmDHDYqaioOxjOMG90W42+MQF98E3cf8qOM3fDqhtg60+QrtomQX3/vXdmEosuMfUGipLuioTX3MRAHLDMeYnKxWpQ14YwV3/EHUUENzrqKe4wRXAx7xhw/pCcGfGzJD3mBHcg3evUSUouI+queOvLA/lKLq1gOAef3uqhN0pILh3p71yzlDgxImnC09xZBAY8nRIWe4ZHUSXCisguBeWSgHbUIAl90VdLUOf6849BT2RqY1eN8w8BPdhtmtva7Vr182F4T70ue5aodrbbhxFwQX3KJpBhTAFysyAGfrukIK79QqdqygguFdRTXEaUwCg5U0PdL8b+kImwb2xbjaKhAX3UTRzfypZBu6Avmx4d3CI/b3g3p9+G2NJBfcYW2WkZeKxckUXMBmYBfeRdhZVe6oCgvtUiRSgLQVYwMT0PwN3kfOQH5Yty72tnjfMfAT3YbZrL2sF3Ddvni0F9yHv6y6497IbR1NowT2aplBBgDuwLmKxW5ghL2QS3PU/UUcBwb2OeoobVIEqcOdRfGWtfRsYYj7zCEF2x9QhBaoqILhXVU7xgivw8ce/LW25D3WuO/ViQZcOKVBVAcG9qnKKF1yBN9/8Qem9Yoa6r7vgHrx7jS5BwX10TR5vhavAHdfKkiWLkgMH9pfy1cfskqFsgnu8/bQvJRPc+9JSIyhnVbjzLFX2mYkd2GXKJ7iPoMM3XEXBvWGBlXxxBarCnd0hi+4BXwawXYYF7jxLVocUqKqA4F5VOcULrkBVuAPCoT0smzrt339HcI2V4HgUENzH09bR17Qq3LGwh7YNgeAefXeNvoCCe/RNNJ4C1oH70LYhENzH0++bqqng3pSySre0AnXgzkKmIT1yT3Av3X0UwVNAcPcE0cfuFKgD96E9lUlw764fDiVnwX0oLTmAetSBO/Pcme/e5QyXkHkL7gPo0B1XQXDvuAGU/RUF6sAdsAJ39mQJCdmu0hLcr/QLvaumgOBeTTfFakCBunAf0va/gnsDHWxkSQruI2vwmKtbF+5DWswkuMfcU/tRNsG9H+00ilLWhTtALLsffFdul2n5Cu6j6PKNVlJwb1ReJV5GAeBeZxuBIe0QKbiX6TkKm6WA4J6liq51okCVh3X4FvDy5UvTHRX96337LLh30gUHlangPqjm7HdlQsCdxUw8nalvMPfLK7j3uy/HUHrBPYZWUBlSBULAHbCzBbAPy759Ftz1T1FXAcG9roKKH0wB4D4zUw/MLGbCNdM3mPvlFdyDdavRJiS4j7bp46s4cL/hhi21wcwOkdxc9YHZp8+Ce3z9s28lEtz71mIDLi9w37hxQ20oD2Exk+A+4I7eUtUE95aEVjbFFAixLzuLmfq+Q6TgXqy/KNRkBQT3ydromw4UCAH3ffv29n4xk+DeQecbWJaC+8AatO/VCQF3Ng8LkU6XPnoGKD1mr++9udvyC+7d6q/cPQVCQZkZM8yc6RLQdfLGrXTq1Jynjj5KgeIKCO7FtVLIFhTYunVLkBWmzHXv82Im4H7mzPMtKK4shqqA4D7Ulu1pvXbtujkI3AE7q1XrWM9dxqXs7LWjQwpUVUBwr6qc4jWiAH5mbibWBStp9HkxE9M5mRqqQwpUVUBwr6qc4jWiwL33fjXheah14U58/Pd9Xcy0Zs2q5NKlS41orETHoYDgPo527k0tuYkYao461m+IXwEhBpqyaTAw6ZACdRQQ3Ouop7jBFTh37mwwuLM3fKiBoiyc64RnQOLGsg4pUEcBwb2OeoobXIELF34a7EZoXxczcTP40UcfCa6tEhyXAoL7uNo7+tpyEzHUo/JYzLRkyaIg/vs6lnjZuMyUOX/+7ejbSgWMWwHBPe72GV3pgHvIKYx9XMy0atVK3UwdXc8PX2HBPbymSrGGAp999rdk2bIlwaxtFjOFmn1T1gKvEp5fGytWLKuhoKJKgcsKCO7qCdEpEGoLAuDKDdWQvwSqALtMHPztR44cjq5NVKD+KSC496/NBl/ikHBn5glujjKA7TIsvzQuXvxg8G2sCjavgODevMbKoaQCofaXMUj3ZTETC64oK64pHVKgrgKCe10FFT+4Anv33hp08RGWex8WM3FvYMeO7cH1VILjVEBwH2e7R11rtiAIuaNjXxYz4ZLRFMiou2avCie496q5xlFYtroNubIUizjU3Hlz9YQ+yyUzjr7dZi0F9zbVVl6FFGCrW6ztUADtw2ImBiDcUTqkQCgFBPdQSiqdYAqEXKVqAwQrVWN+MtPatas1SyZYD1JCKCC4qx9Ep0DoVaoAHrdMrIuZ+GXBStovvvgiurZQgfqrgODe37YbbMmBXMi57sAdH35IV4/9IghxplxPPPH4YNtTFetGAcG9G92V6xQFQsOdqZCx3lRdunSx9pKZ0h/0dXkFBPfymilGCwps2LAuqI/cZqOEsLRDpqG57S10ppFmIbiPtOFjr3bohUwAOcYdIjdsWJ+8996/xd4cKl8PFRDce9hoYygyD6sIuZAJuLNIKHSadax43UgdQ0/uro6Ce3faK+ccBV566cWgC5mAMGCPaYdI3UjN6QD6qrYCgnttCZVAEwrwuD0s7TqWsR83th0i161bk3z88W+bkE9pSgHNc1cfiFMB5rrjj/YBXfdzLDtE2g3eONVXqYaggCz3IbTiAOtw6dKloE9kskEhlh0i+RWxe/euAbacqhSLAoJ7LC2hcixQIPRcdwCPnzvkpmQ2aJQ979u3N9m//44FddYFKRBKAcE9lJJKJ7gCPEs09H4wQDWGxUwMMKdOzQXXTAlKAVNAcDcldI5OgSbmujP9sIlfBGUtdxYvsW+9DinQlAKCe1PKKt3aCjQx1x0Is5ip6yczkb/cMrW7iBLIUUBwzxFHX3WrQBNz3YE7c9279rvrhmq3fWsMuQvuY2jlntbx4sUPgs91B+64RLr2uwN3HgSuQwo0pYDg3pSySre2Asx1n5kJu5AJuNscc9539bIy1BZJCUiBCQoI7hOE0eXuFfjss781MtcdoDPfnZkzXcGdfLmxq0MKNKWA4N6Usko3iAJNzWxhvjsvwT1IMymRCBUQ3CNsFBXpigL4pZuY2YLVjvXeJdw3btyQ4HrSIQWaUEBwb0JVpRlMgdtv39cI3M3n3SXcuZ8guAfrKkrIU0Bw9wTRx7gUOHHi6camLXa9zwwzdgT3uPrbkEojuA+pNQdYl3PnzjbmG2e+e5cP78Dn/+abPxhgq6lKMSgguMfQCirDRAWwbJuak971wztYSMVCLR1SoAkFBPcmVFWawRQA7tx4bMI3zo3aLm+qavOwYN1ECWUoILhniKJLcSnQ1HRIBowm0542ILFSVvvLxNXXhlQawX1IrTnQurD1L7s5ToNlle/ZRCz0tsJFy8EvB2YD6ZACTSgguDehqtIMqgBPLGpirjsQxp/f1UpV6rRr181BtVJiUsAUENxNCZ2jVaCprX+Be5dPZuLXCL9KdEiBJhQQ3JtQVWkGVeD8+bfTbXqLujvKhOOmZpfbEGh/maBdRYk5Cgjujhh6G6cCzJhZt25NIz53XCNNTbUsMsgI7nH2uSGUSnAfQiuOoA5AkC0DigCzTBjg3uV0yDVrViWXLl0aQQuqim0rILi3rbjyq6TAjh3bG7vx2eV0SFbJaguCSl1CkaYoILhPEUhfx6HA3Ny3G/ONdwl37S8TR/8aYikE9yG26gDrhHW7cuXy4G4ZXDhLlizqbK77pk0bkwsXfjrAFlOVulZAcO+6BZR/YQWaWsyE9dzUPPpp/n9m62jzsMJdQAFLKCC4lxBLQbtV4MiRw43s4tg13E+dmutWWOU+SAUE90E26zArdfHiBwlujGnWcNnvgXtXq1TZmZJFWjqkQGgFBPfQiiq9xhTggdlN3PzENcKr7KAQIjzuIG0e1liXGXXCgvuom79/ld++fVtwK7truGt/mf71wz6UWHDvQyupjPMK8HAL5oaHsJotjS7hzo6UGzasm6+f3kiBUAoI7qGUVDqtKMBqztArSruEOwMMriYdUiC0AoJ7aEWVXuMKMCUy5B7swF2bhzXebMqgZQUE95YFV3b1FQi9BXAMm4dxs1iHFAipgOAeUk2l1YoCH3/822Tt2tXB/O5dw/2GG7Zof5lWes64MhHcx9Xeg6jtF198kfqpQ+0S2TXcN2xYL7gPomfGVQnBPa72UGkKKrB3760JD5i2GS91zl3DnUVU/BrRIQVCKiC4h1RTabWmQMinM3UNd27oan+Z1rrOaDIS3EfT1MOqKDcgly5dPAjLHbifOfP8sBpItelcAcG98yZQAaoqsGnThiC7OcZguZ848XRVGRRPCmQqILhnyqKLfVDg5MlngsxP7xru5K/9ZfrQ4/pVRsG9X+2l0joKcBMyxIOzY4D77t27nJrprRSor4DgXl9DpdChAsuXL00OHzpUy/ceA9y3bt3SoYrKeogKCO5DbNUR1SnEAzyAe+j9aspMzWS+vvaXGVGnbamqgntLQiubZhQI9QCPJvaJLwN4wb2Z/jHmVAX3Mbf+AOoe6gEegvsAOoOqcJUCgvtVcuhDHxUI8QCPruG+ceMGbUHQx84XcZkF94gbR0UrpsDc3LdrT4nsGu4zMxsF92LNrVAFFRDcCwqlYPEq8MknnyQrVy6vNWOma7izvwz10CEFQikguIdSUul0qgBwrjMlkimVIR8AUuZmKmF5WIj2l+m0Cw0uc8F9cE06zgrdfvu+WrtEYjkzJbIslEOF1/4y4+y3TdZacG9SXaXdmgLnzp2t9eDsruG+a9eXE54wpUMKhFJAcA+lpNLpVAH81XUWIgH3ffv2dma586uBXx86pEAoBQT3UEoqnc4VwO9e9elMuEV4hXKzlE0HuO/adXPnGqoAw1FAcB9OW46+JjydqarfvGu4awuC0Xff4AII7sElVYJdKcAWwFWtb3zemzfPdma5Y+nzy0OHFAilgOAeSkml07kCdfaZweLH717WnRIy/Jo1q5JLly51rqMKMAwFBPdhtKNqkSTpIqCNG9dXAnQMcNcqVXXjkAoI7iHVVFqdK1B1pan5vENa4mXT2rRpY8KvDx1SIIQCgnsIFZVGNArUWaladWAoC/FJ4blfwHx9HVIghAKCewgVlUY0CjCdsOqMGebJV407CdhlrgP3U6fmotFSBem3AoJ7v9tPpfcU4EHTVQHd9SpVFlHpQdleg+pjZQUE98rSKWKMCtx771cr7zHD5l1Vp1KWsdAnhWVQ0oOyY+xV/SyT4N7PdlOpJyiAW6MqoIkH4CfBt+nrwF0Pyp7QsLpcWgHBvbRkihCzAnXgDly7nuuuhUwx965+lU1w71d7qbRTFKgDd/ZzZ1/3pi30vPQF9ykNrK8LKyC4F5ZKAfugwIkTT1d2ywBd4Fp187E8aBf9TnDvQy/rRxkF9360k0pZUIE6s2UAcNfTIbUFQcGGVrCpCgjuUyVSgD4pwGyTqlMhgTubh1W9IVvUOs8Ld8MNW/Qs1T51uIjLKrhH3DgqWnkFVqxYVutZqHv27E7YBiAPwE1+x+CiB2WXb3fFWKiA4L5QE13pqQJffPFF6jOvA9+ub6oyW0dw72kHjKzYgntkDaLiVFcAKK5bt6a21b1kyaLk8KFDtdOpMsgI7tXbXzGvVkBwv1oPfeqxAnX2c3dBDGC7ep6q4N7jDhhZ0QX3yBpExamuQJ057i7cuaHa1U1V4K5tf6v3AcW8ooDgfkULveu5AufPnw9yM5SbqkDWBX5b7xlUXnrpxZ63hIofgwKCewytoDIEU2DZsiW1/eVMpWS+e1tAd/PhWa5sfqZDCtRVQHCvq6DiR6MAN1TXrl2TLFp0TbJ69XXpJmDAssq8d1aKutBt6z1l1c6Q0XSpXhdEcO9186nwpsCLL34vWbp0cbJhw7rUXz4zsyl1rQD7FSuWp1MkeUYpsC+yvUBXcLfH/Vm9dJYCVRUQ3Ksqp3hRKHDp0qVkx47tCYuXtmy5PgW73RB1z9u2bU398Vj0gJvFQnkWfVdw5xcCrqXPPvtbFPqqEP1VQHDvb9uNvuRvv/1Waq1jnbsgn/aePdux8HHfEDcL8l3CXatUR9+1gwgguAeRUYm0qUBRa30a5LHmDfIA1XXXdLmBmOa6t9mbhpuX4D7cth1czdhe4FvfejZ1q5S11vNAD+RJj5WpQJ6wuEa0kGlwXWhUFRLcR9Xc/a3s6dOnUhfMddetSGfB5MG66ne4azZuXD/vmwf0bc2ScfOR5d7ffhpTyQX3mFpDZUmwzpnSeO7c2eTIkcPJ2rWrU984T0gyq7oqvMvEA/RY8q6rxgVwk+9xCeF6KnL89a9/Te6//2vJp5/+uUjwIGGq5vnUU0+me//kFYJ6cL/j/Pm384LpuwIKCO4FRFKQ5hQA5iy3f+KJx5Pt27el/9jAjemL3PBsG+oMADazhrwpS5ubiHFzl5k/RQ8gCAzbhHvVPAX3oq0aJpzgHkZHpVJCAaxSltgzhREw4Yaween4upmvzhOJsJ7LWNt1w5rv/dprv5QOKuzrbjdcAT3l9H89AGP3VcfSZxDhl0oZq7UqaEs014KgVfMU3BdI2egFwb1ReZW4KYCFDhRmZzel8Ma3DThtgRFnbmrmzVWvC++8+JTFoO4DnHhc40U4ymng5x4ALyx8XgxW7gvXDgMVLwYHXsT1y8I14pXZV+aVV75/VV7Ak4Ntj+296f/RR79Ow3LmuPPOO1J3Di4d8iXO559/nr4n3bm578ynTViLNylP0vS/c+PxvcHdDeeHyXLL4AYirumKUfD++++l9cj748cjL/cXjv896aMH1+0gDi/6LhqZVnyO/RDcY2+hnpePxTi4XPinAGA8Rg7r3KCXBVIffE1+Jn/KQpmaKAu/PkjXfaEDA4SBnoGOzzt33li6tbOs6KJwp00ALQfwNri717kG8Az+hM3KE/gCXReMfjwDNNdJl8MGkT/+8Q/pZx/uhCNdAGtpW/55gLd4bpn88vAd1+wgfYO5XeMzemSV2QY8CxvbWXCPrUUGUh6g/uijj8xD8+DBA6mF2xREyw4AQBeLG2sda7xs/NDhLw8s20u3voHOtUjLwN2AScYAEZABPfcAolw3mPl5kgbfc909CO/GM7i7ZSW8C1kf7gZ/P44NJm5+7nsrozsAMIBYOa1Ofrr2q8IGH4O7q5PV1wZGN9+Y3gvuMbXGQMrCP5bdCDUftLkuQkOxbHquXx03Cp/LptFEeODODWR2hMSFVfQwiLmQKgp3wrmHwR1wuocP6aw8CU98gMfLoOzD3R84iEdYK4sPd8JnxbEymMXvlpf3WNrk7ULZD8Nn8rMyWxziuXC3sll800lwN0V0HrwCQGn//jvSm4I8i9SmC7IYCNdHE1AskybuEMrBwNOVb39SeYE7+95wZrZM0amQBrmu4Q7ogCIgNFiadWwWP4MGlrB/WFyg6cOd9Eh30svS9tM0i9sg7X/PZ4M5YSkDWrplIQzfCe5Z6unaaBQA7FhYwMmsdYP7jTduS28oTgJbk9fNUjeoU74m86uaNrOFuOmKZjwshAGoCOBjgLu5OwCjexSF+zTLPWtAcPPJem/gnmS5m27+4GC/OGxQENyz1NW1USmAOwFwGtDdM7DC8mrTWsZKZwYOPnVcQrFC3QYDbqgyEJluBvhpu0MapHzLHbi5h4UzmOVBq6xbxk/b8jUr2PIkXaxgA6eFwyiwPH3L3cDvxyHtrLQsTSuT63M3XznakB990k8XXdzreTr5g5nlHctZPvdYWqLH5fj4498mK1cuX2CxG6g4283LkIC3mSg2+4Q8mCOP7xqodzFX3mBd9oz/n73mXc1Ig5vSeYdrHZuVahA14ANXc28YaPOgZaC1fIkD8Cyun6cB2R1QDK7EM8AaUAlnUOU9ZbOyW1rE5+A63xPOwlj+FsbK6Z5Jn0GDelo8y59fGlY+F9D2PWW2OHk6uXHdvGN5L7jH0hI9Lsfdd9+VuhJcMPnvcdUwDZJ/HGbMADOsVSzqSVY1lizfufDGGgfglg5+ar6fnZ1Jr+N+4XMsN0qLQh43jL/1MJqhVd4NViAG+NADEHFwzQUV3xvMDNB50CKue/hwz8oT4NoAQlncPA2CpEu+fCaMhbNBiDx9uHMN0Lr1IZ88sFvZ/XjkbfUnjFsOysKvhDI6Wb0sv9jOgntsLdLD8vCP4fvZfbjbZ8IBMaAHuLGubSGT/cO7Z75jqiJ+e1wVxHW3AyA9vsdaB+pFYRpbuCy4o9mGDevTvXZ62C1U5I4VENw7boAhZF8G7gb5EGfAjiuGV98sdX9wAe4MXr4uLHRiIzUdUqCsAoJ7WcUUfoECe/femgkmH1QhPxvYce/4oOzjZ9wv7vRRtKKOXJ92U3VBg+iCFEiSRHBXN6itwHvv/Vs6tz0kvKelhQsGi72PIPfLzI1h7iP4dSYcA6cOKVBFAcG9imqKs0CB22/fl/rQfUA18RmLFldQH10xdpOYm8nu/Qauu1phxWO1F5nrvqAxdEEKyHJXHwilgLuIyYVUE++ZMtgHq91mAgFy3EfAmkHJVqJimXODmMHK1YkVvVjy/CLSIQWqKiDLvapyirdAAQM8e5K7M1pccIV4DzQBpu/e6OKzzbU3gDO7h5k7QJz3WOeUlwHJn+qYpQV14Obqr3717wv01QUpUEYBwb2MWgpbSIG5uW+nViqg8q3SLKCVvXbTTTtTcLYFc3Ol4OcH4vxqsOmbgNzm2jNd05+qWbRuxGMh2E037ZArplAvU6BpCgju0xTS95UUwFeMHx5XRGjIM2AYYLGKQ0DedaEAcKxnAzhWOG4VrHBAb/PtQwxcuGCYy85mYTG4YWwhT9lGrxovKx/SQnNeRRYrZaVR5hoLpFgYNbRDcB9ai0ZWH+ZoG+QBqD/dr6hl64cDrFjKWM4MIACZ9HGTZMHerG/CEBZQA3B3tau5UEgX6Gb5w/1yVPmMywo3DZY6C7AAWN4q1LaaNGt1aJG8q8bLSts2IWsD6pa/4G5K6CwFKijAXG3cNVioQA0IhwI9IGbPGtwj5u82y889uz5wc6GEKsM0yBvQsdIp05EjhxP25InpqArpqvGy6u5vdZAVJvQ1wT20okpvtAoANR69h9WK5Yw1jaujLdBOA3GI7/llwaDDIGZ7rgD0ixc/aNRKZ78T8nNdG7afCvu/sL+KDXjs/2LfGVTtO9dNgRXNJlzud2ZZ58XjO9v3hri8ZyCYdLj7xxCeMlj67j4wtqeLv3cMZbRNytw83Lika2W3MC7cbbMx+87OxCGubShm12M+yy0Tc+uMoGz45vnHAXxY9bhYWHKPawU4NjnrJgTESQOQ48LB1cJAxTNRAQELkPi10qaFbiADpBzAkcN2UgT6dhh40ti4FwAABuNJREFU7WlGWRa4Qc3SIa5/LSueuVesHMTjPcDOA6TB3PKzz0CXePbK2vXRyuUC3vJ007PBz3Rw4W5p+IMQgyKvPh2Ce59aawRlBfZYtydPPpPCEeADypmZjfMbg9kNzTYtfQYZAM6Aw8CDRY6Lxeaub9++Ld2eFzh0uReMwd0FHN1mkkXqXs+CNN8DP/cArLSJWdCT4hHXP7LSc8MYzF0Yk5c7KBHefpn4EKaslq8NaLSJe/gAd+FO3Xz4M6BQBj8dN80Y3wvuMbaKynSVAtxsBJhA/8yZ59PnjO7evSt16/BPx8tuTmL1m+WfdWN12jWmOxKfm6vMkLH08eVzA9ae6LR165a0TLHt+2Jwd6GXBV8T2CAJwPLCATbS5gX80GUS3A2GPpDJ0wWplcE9T4K7D1YAbhB34xu4+eXg1s0N49fTL5N9BvQcpEmd7bObVszvBfeYW0dlm6oA0Ae4BmH/zEM7gHLeKy++n559BvYffvjh1PK1HSAL7gZMH5CUzQ3vQ4/vLS71BpaEN5fLJLhbOqZV1nkSKC0/zm7+ftltgMlKm2vEB9KTvue6ld9gnmaYJPP1szwZRFz3koWL/Sy4x95CKl+uAvi48/6Bm/wOl0wMUxhdgVxY23WDrcHKrnM26xbYZoUDor6v2Sxzg6Mfz//ezW/a+6JwB7h+ufy03br537mffbjzHWmTh9XNd3O58WN9L7jH2jIq11QFTpw4nmu1Nwl2S/u22/ZOLWebAbLgTv6TYMh1XhwGMhsE7LNB3OphALbrFs7i5eUHNPOgbGlz5rDPbtpcB9xZrhLKZNfN525ppQk6adr1LLiTH21sN2Qtbp/OgnufWktlnVfg3Xd/nixefG1nVrvBnTK88MKZ+XJ1/WYS3A10QNEOwEU9bLaMa3HznsPgb58BIteIZ2llxbP8AKcdZklbfnbdPRvMDbz22Yc7eQJx6mBlszzdsGaBW3oMRJTfdbNkwZ0ykb5bT7ecfXgvuPehlVTGqxRgRo2tLDXIdnkG8Aw2MRyT4E7ZgB+wM60AnEHPym4AJoy5atw4vAeeAJL3dvjxuE7aNoCQHuH9/Cy+nfmesBbOPrvAtrBAHTBbfYBxVjjTxMLZoGTpTIK7xbOyWPi+nAX3vrSUypkqEBvYDRgMNpRNx3AUYBBgEOvrIbj3teVGWO5YwS7AD68zmtsn65dAX2oruPelpUZeztjBboBnBo0s+H531r772k19wd2U0DlaBfoCdgM8q2oF+Gi702gKJriPpqn7WVFuVBo0+3SWBd/P/jakUgvuQ2rNgdWFKYYxTHesOqjoJuvAOmTPqiO496zBxlBcVn0ePnyo12C3AQHAt7kr5Bj6h+pYTAHBvZhOCtWSAviqu9xSwKAc8hzTPPiWmlHZRKCA4B5BI6gIlxXAv15lE6+QIG4qLTYae+SRh6Pbi0Z9b7gKCO7Dbdve1Aw3DODrs3+9yKDAwMVWwbFtE9ybjqKCllJAcC8llwKHVgDQAbyhWuxZ0McPH+N2waHbVul1q4Dg3q3+o84dwAG6LAAO/Rq/Up599pujbn9VvlkFBPdm9VXqExRgu96hu2GmDVDUn8fzyU0zoZPoci0FBPda8ilyWQUAGUAbO9hd8LPgqcvnrpZtQ4XvhwKCez/aaRClBGCAzAWb3l9+BiyDXUz7wg+iw428EoL7yDtAW9V/660ft2Ktuzdmt23bmuzZc0u6IOrkyWcSXs89N5e8+eYPFrwAq4U5evSBhCcs7dx54/xgxH4xTQ9EAJ7FW7E9uq+tPqJ8wioguIfVU6llKMA0R+Z5NwFHgzkQB9D8OmjCh026DFCAf82aVY3O7mH2kACf0ZF0qZQCgnspuRS4rAJNzV9nFSuzTbryVbOSFtgfPLg/HbRC30MQ4Mv2NIX3FRDcfUX0OZgCwM8s6zpWu4Hz9ttvS4HahGVep9JY2ewfg1XPPYUQdUYvfo3okAJVFRDcqyqneLkKAOA6QGf+O6AEmBcvftArNwW/JvhVUXePHAY1nuOpQwpUUUBwr6Ka4kxVAKsduBexYpcvX5qGBea4OYg7lIddMMgxODFIzcxsSutZ9OYs2qGHDilQRQHBvYpqilNIAdwVWLFYn8xEAXDMQuFlM1cuXPhpGmZMNxDRBOCbLsyQQRPO6MKNYdw8QxngCnUWBQqugOAeXFIlKAWkgBToXgHBvfs2UAmkgBSQAsEVENyDS6oEpYAUkALdKyC4d98GKoEUkAJSILgCgntwSZWgFJACUqB7BQT37ttAJZACUkAKBFdAcA8uqRKUAlJACnSvgODefRuoBFJACkiB4AoI7sElVYJSQApIge4VENy7bwOVQApIASkQXIH/D/ueEg9FUyzKAAAAAElFTkSuQmCC"></p>
<p style="text-align: center;">© International Baccalaureate Organization 2020.</p>
<p>The wheel is flipped, as shown in the second diagram, so that it rotates clockwise when seen from above.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: center;">© International Baccalaureate Organization 2020.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the direction in which the person-turntable system starts to rotate.</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>Explain the changes to the rotational kinetic energy in the person-turntable system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«person rotates» anticlockwise </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">the person gains angular momentum «in the opposite direction to the new wheel motion</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">so that the total angular momentum is conserved </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle4">OWTTE</span></em></p>
<p><em><span class="fontstyle4">Award </span><strong><span class="fontstyle5">[1 max] </span></strong><span class="fontstyle4">for a bald statement of conservation of angular momentum</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the rotational kinetic energy has increased </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">energy is provided by the person doing work </span><span class="fontstyle3">«</span><span class="fontstyle0">flipping the wheel</span><span class="fontstyle3">» </span><span class="fontstyle2">✓ </span></p>
<p> </p>
<p><em><span class="fontstyle4">OWTTE</span></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>The <em>pV</em> diagram of a heat engine using an ideal gas consists of an isothermal expansion A → B, an isobaric compression B → C and an adiabatic compression C → A.</p>
<p style="text-align: center;"><img 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3gPAQhAwDIBggYsowpuwXQyD0T3WjeD6v6crVu3iooQFwQgAIFkCDDCSYZWQMuqODzxxBNJHVsQr6vmes7YsWPj/cx3EIAABOokgODUiSc8PxYUFBjHFqSbmFPXc/Rif054ng16AgG3CCA4bpH2uB09aC0/P1/27NmTliU6WpoxY4YhXukEIqRlBDdDAAKBJIDgBNJtqRk9YMAAWbx4cWo3R92l+3PmzZsnGoygR1RzQQACELBCAMGxQikkZXQNZt++fbZEmmmuNj20jaOpQ/Jw0A0IuEAAwXEBsp+aUJHYvHmzLSYNHDhQcnJyZNasWbbURyUQgEC4CRAWHW7/1uhduvnVYivUIIQHHnjAyEagAsQFAQhAoDYCjHBqIxPS73X9xY4QaROPBhHMnj3b2BRKEIFJhVcIQCAeAQQnHpWQf2dXiLSJSSPgSktLCSIwgfAKAQjEJYDgxMUS7i/tCpGOpqQBCQQRRBPhPQQgEEsAwYklkiGfNURaRyV2XmYQAZml7aRKXRAIDwEEJzy+TKonOiLRy+51l3HjxhmZpefMmZOUPRSGAATCTwDBCb+Pa+2hJuJcsWJFrb+n8oOZiWDp0qWiyT65IAABCJgEEByTRAa+3nTTTcZpoHYfOaCRcKtWrTKOp7a77gx0E12GQGgIIDihcWXyHdHRiJ0bQaMt0MCE9evXS3FxMelvosHwHgIZTICNnxnsfO263RtBY3GWlZUZR1wvX76cM3Ri4fAZAhlGgBFOhjk8trvmRlC713LMdjRyrU+fPqJn6KR7NIJZJ68QgEAwCSA4wfSbrVYPHjzYGIU4JQijR4827F24cKGtdlMZBCAQLAIITrD85Yi1OsrR7AMbN250pH6t9Mknn5S9e/cK4dKOIaZiCPieAILjexe5Y+A999xj5ENzapRDuLQ7fqQVCPiZAILjZ++4aFteXp5xIqiToxwzXFr3/7BHx0Xn0hQEfEIAwfGJI/xgxvDhw421HCdt0XDpJUuWGHt0OC3USdLUDQH/EUBw/OcTzyzSUU5ubq7jow9tR/foFBYWskfHM2/TMATcJ4DguM/c1y06kdQzXoc1l5smD0V04tHhOwiEkwCCE06/ptwrM6mnG2ss2taoUaNk2rRp7NFJ2WPcCIHgEEBwguMr1yzVRX27jy6ozXhNfdOpUyc2htYGiO8hECICCE6InGlXV9wc5ajNujEU0bHLe9QDAf8SQHD86xtPLXNzlKMdVdFp1qwZIx1PvU7jEHCWAILjLN/A1u72KEdBmSeFkgInsI8NhkOgTgIITp14MvtHt0c5mo2AFDiZ/czR+3ATQHDC7d+0eufFKAfRSctl3AwBXxNAcHztHu+Nc3uUoz1GdLz3OxZAwAkCCI4TVENUpxejHMWH6IToIaIrEPgbAQSHRyEhAS9GOWoUopPQNRSAQKAIIDiBcpc3xuoop0WLFo7nWIvXOyui88Ybb8S7le8gAAGfEUBwfOYQv5ozYcIEI/uAU+fl1NXvRKKjqXEQnboI8hsE/EEAwfGHH3xvhZlJ2snzcuqCUJfoFBUVeTL6qstefoMABGoSqBeJRCI1v7b3myZNmsjp06ftrZTaXCdQUVEhmvts69atxvqK6waIGEk+x44da6TC0ewEep08eVJycnLk+PHjntnlBQvahEDQCDDCCZrHPLRXRznt27eXSZMmeZbdOd5IR08SHTlypOzZs8dDOjQNAQgkIoDgJCLE7xcR0ACCZcuWyaBBgzw7PC1adKZPn26In57js3jx4ots5QMEIOAvAgiOv/zhe2tat24tt99+uzGF1aFDBykrK/PEZlN0jhw5YiT81JHXvn37jOk1TwyiUQhAICEBBCchIgpEE2jTpo1cffXVsmTJEmOhfsOGDTJx4kRX/tDraKZ79+4yZ86c6qg0zb2mRxvoNN99990n27ZtizaX9xCAgI8IIDg+ckZQTGnYsKEsWrRIli5dKvPnzxcd6fTv39/xSLHJkyfLqlWrJDc3V+bOnSstW7aUWbNmGZ/1u507dxp2BYUjdkIg0wggOJnmcZv6269fP2M0YUau6YhHMxKYayo2NVOjmuzsbOnbt68hdBqV1rNnT9m9e7e88MILcvjwYXnllVdkx44dNe7jCwhAwHsCCI73PgikBbqGohsuFyxYYNivEWwaLp2VlSUHDx50pU9qgwYx6Mhn165d8uyzz8rDDz8s48aN8yygwZWO0wgEAkoAwQmo4/xgto40Dh06VD2VpgKge2M6d+7siXna7owZM2T27NlSWFgoOvriggAE/EMAwfGPLwJpyZQpUzxLeVMbMB31lJaWSrdu3arFsLayfA8BCLhHAMFxj3UoW9JRhS7Ye5XypjaoKjr79+831pU2bdpUWzG+hwAEXCSA4LgIOwxNadZo3YsTfT3yyCNSUlLiSmh0dLuJ3muAgUa16ShMQ6m5IAABbwmQS81b/qFp3fyDbuY381PHNMO15l/TfGsaUKBrTVwQgID7BBjhuM88lC0OGzbM2Jfjx4V6FRjdIKqXCo8XRyyE0ul0CgJJEkBwkgRG8fgE9I+6hknPnDkzfgGPv1X7NHxasxL06tWLsGmP/UHzmUkAwclMvzvSaw2TPnHihPh5kV6n/DSCTcOmy8vLHeFApRCAQHwCrOHE58K3KRIwMw94eWaOFdP1hFA90kDzwA0cONDKLZSBAATSJMAIJ02A3H4xAc04UFBQIAsXLrz4B5990nBujWDTfHAa8MC6js8chDmhJMAIJ5Ru9bZTegKnJvPU/GoqQH6+zAg2tVEDC4hg87O3sC3oBBjhBN2DPrRfT+D0cwBBNDIVGM14TTBBNBXeQ8AZAgiOM1wzvlYNINDLzwEE0U4ygwn0qAWCCaLJ8B4C9hFgSs0+ltQUQ8AMIFi/fr3oqCcI1/vvv29EsBUVFRmJSINgMzZCICgEGOEExVMBtFPXb0aNGiVPP/10YKzXdDgaYbd3714ZMWKE79L1BAYkhkIgDgEEJw4UvrKPwKBBg2Tt2rXVR0LbV7NzNZnrOrfccosR/ODH7AnO9Z6aIeAcAQTHObbULGJEfc2bN8/Y8xK00OPi4mJjk6i+lpWV4U8IQCBNAghOmgC5PTEB3fOie3NWrlyZuLDPSugxB7pfZ8OGDcYm0aCJps9wYk6GE0BwMvwBcKv7Dz30kMydOzeQp3Dquo7u0dFjGTQPG1Nsbj01tBM2AghO2Dzq0/6Ye3MmTZoUyF39uq5jhk4zxebThwyzfE8AwfG9i8JjoO7N0dNBgzi1ZnqBKTaTBK8QSJ4AgpM8M+5Ig4Amywzq1JrZbabYTBK8QiA5Amz8TI4XpW0goNkHNHJt+fLlgc9dZmad1v1GOtXGBQEI1E6AEU7tbPjFIQJhmFoz0WgEnmZS2Llzp7FRVDMVcEEAAvEJIDjxufCtwwTCMLVmItKACE0AescddxhpcYKSP860n1cIuEWAKTW3SNNODQJhmlozO6cjnDFjxhjBEVOnTg38lKHZL14hYAcBRjh2UKSOlAjo1Fq3bt18f1hbMp3TgAJdm9Ks07pnR9d4uCAAgb8SYITDk+ApAd25r3+YNYhA10PCdJkBBZplYdy4cYx2wuRc+pISAUY4KWHjJrsI6IbKoOZaS8RABVQzT+vFaCcRLX7PBAKMcDLBywHoox5HvX//fikpKQmAtcmbyGgneWbcET4CjHDC59NA9kiPMaisrAzMCaHJQma0kywxyoeRACOcMHo1oH3SCC9dbNeRji6+h/VitBNWz9KvRAQY4SQixO+uEVCR0TxrGlYc5mMAzNHOtddea6ztsG/HtUeMhjwmwAjHYwfQfE0C06dPN76cPHlyzR9D9o0edaAZtDWpqW6G1U2kXBAIKwFGOGH1bID7pSHEeix1eXl5gHthzfS8vDxj30737t0lJyeHk0WtYaNUQAkgOAF1XJjN1lBpjVobP368ZEJuMu3vwIEDjbWrXbt2yd13380hb2F+wDO4b0ypZbDz/d71MKa+scJcR3YqtrphVE9KZZrNCjXKBIEAI5wgeClDbTRT38yaNSujCOghb7phNCsrS/r37880W0Z5P9ydZYQTbv8GvncarfbAAw/IyJEjRQUo0y4NKpg5c6acOHFCZsyYIbrmwwWBoBJAcILquQyyW9dxCgsLjXWdTP2Dq9OLU6ZMYZotg577MHaVKbUwejVkfdL9OaWlpcaJmidPngxZ76x1R0d3Os2me3fMaLYw71WyRoVSQSOA4ATNYxlqr65rFBUVGXtWMvUPrUaz6THWmolBo9l0qjETQscz9JEPZbeZUgulW8PbqREjRkinTp1k9OjR4e2kxZ5pipxp06ZJixYtZMKECazvWORGMe8IMMLxjj0tp0DgySeflJdffjm0ST6TQaIpclavXm2sb+nIRzM0ZOqUYzLcKOsdAQTHO/a0nAIBnVaaPXu2sYCuEVxcYkTv6fpOu3btjPWdOXPmhDoXHT4PLgEEJ7i+y1jLo4MIMiETgRVHm9kKjhw5YhTXA9/KysoQHivwKOMaAdZwXENNQ3YT0D+oGzZsEJ1m0z+4XN8SUCF+6qmnZNu2bcY6TybuYfqWBu/8QgDB8YsnsCMlAjp9tHfvXpk/f35K94f9Jp12XLBggRw6dMhIl6PRflwQ8IoAguMVedq1jQCRa4lRmhFtWlLztCE8iZlRwn4CCI79TKnRZQK6L2fs2LFyyy23GPtUXG4+UM3pvh3dRKsXwhMo14XCWAQnFG6kE2b6G/1jyn/viZ8HhCcxI0rYTwDBsZ8pNXpEwBSdefPmie5R4UpMAOFJzIgS9hFAcOxjSU0+IKB/QHWqaNWqVaLh01zWCCA81jhRKj0CCE56/LjbhwQQndSdgvCkzo47ExNAcBIzokQACZjp/HUHPnt0knegCs/ixYuNc3h0xHjTTTfBMXmM3BFDAMGJAcLH8BAw9+iwMTR1n5r7eHQD6cSJE6Vfv34IT+o4M/5OBCfjH4FwA0B07PGvCs8LL7wga9euNY6JGDx4sDRv3tyeyqklYwiQSy1jXJ2ZHdVjDPQ4A92nk6nn6NjheT1pdfLkybJ+/XqjOj0ETsWcBKp20M2cOhjhZI6vM7qnmrpfE1syvWbPY6DHIOg0W0lJieTn58uAAQPY/2QP2lDXguCE2r10ziRgZiPQz4iOSSX9V+W6Z8+e6uwFI0eOlFtvvZV1nvTRhrIGBCeUbqVT8QhEiw7JPuMRSu87zde2YsUKY+Sjx4GzzpMezzDejeCE0av0qVYCpujoGsS4ceP4T7xWUqn/oNNtKjxLly41pttUeMj8kDrPMN2J4ITJm/TFEgFTdLQw02uWkKVUSDnv2LFDNNWQXky3pYQxVDcRpRYqd9IZKwR0I6gKjV5Er1khlloZ5awHv61evdo4Enz37t3SsmVLI7qNk1pTYxr0uxjhBN2D2J8yAUY6KaNL+Uadblu3bp3MnTtXOnbsKEOGDCGLQco0g3cjghM8n2GxzQTYHGozUIvVafqcF198sTrIoKCggISrFtkFtRiCE1TPYbetBBAdW3EmVVnsqKewsJDQ6qQIBqcwazjB8RWWOkggOiMB6wsOgo5TtabIKS4ull27dhlTbNFrPWQyiAMswF8xwgmw8zDdfgI60tFwXs7TsZ9tMjWamQzUF3rpvh7NaED+tmQo+q8sguM/n2CRxwQ4T8djB8Q0r6OczZs3y6OPPmqEVmsaHY5LiIEUkI8ITkAchZnuElDR6d+/v5GsskePHu42TmtxCWhUoabR0XN69u3bZ4x61DdsKo2Ly5dfIji+dAtG+YGA/metawvTpk0z9pP4wSZs+CuB2Cm3u+66S3r37k2Um88fEATH5w7CPG8JaACBRk3pGoIGFnD5j4D6SM/p0fUe3duj/uratSvrPf5zlSA4PnQKJvmLgLlBtFmzZjJ16lTyr/nLPRdZowlEdTpU13vuvfdeNpZeRMf7DwiO9z7AggAQUNGZNWuWcabOjBkz+O/Z5z4z13u2b98u6q9JkyZJz549CdwWCwcAAAz0SURBVDbw2G8IjscOoPlgEViyZImRloWw6eD4zRQfzWqgiUQRH+98h+B4x56WA0qACLaAOk5ENNjg9ddfN/ZZPffcc4iPy65EcFwGTnPhIEAwQfD9iPi470MEx33mtBgSAvoHS6dn9OJcnWA7FfFxx38IjjucaSWkBHR9YOHChaTDCZF/ER/nnIngOMeWmjOIwKZNm2TQoEFkJgiZz82AAzPaTUOt2eeTupMRnNTZcScELiIQva4zbNgw9utcRCf4H6LFRzea6ibTO+64Q7p160aGA4vuRXAsgqIYBKwQ0D9Kujm0srLSOFY5Ozvbym2UCSABc5OpZjho1aqVaHqd7t27S15eXgB7447JCI47nGklwwiUlZVJSUmJlJaWCsk/w+98zbun5/msWbNGPvzww+rEom3btmWkG+V+BCcKBm8hYCcBM/mn5mFjis1Osv6uS6dW33rrrRp7fdq3b5/xGSoQHH8/u1gXcAJMsQXcgWmarxFvBw4ckOigg0xe90Fw0nyguB0CVgjoFNvQoUNl5cqVHHVgBVgIy+g/HwcPHjSSi5rrPn369DGmXDPlTB8EJ4QPNl3yJwGdahkzZowR1TRu3Djm9lN0k/7h3rFjh7Rp0ybQC/T6PGzZskV27twp0Wl2wjz1dkmKPuc2CEAgSQIasbZ8+XLjrl69eomu8XBZJ6BCoyNFZffyyy9LixYtrN/sw5L6POgBf/PnzzeykHfp0sWYesvJyZERI0YYfVVRCtPFCCdM3qQvgSGgCUDHjx8vo0aNMv7oBMZwDwxVodm4caMR9Zefny/Dhw8P9MgmEcIwT70hOIm8z+8QcIiALihr6DR7duIDzjShiU9BREc5f/zjH2XDhg2Bn3pDcGrzMt9DwCUCZkDB+vXr2bPzN+bmPqZMGNEk85jVFvXWr1+/QKwJIjjJeJuyEHCIgP4X26FDB4dqp9pMIHD69Gnfd7O+7y3EQAiEikBEzn1xXN49fEw+PxcRqddYvpeXK9dlZ0sQ/mC46Qpd59JMDXrpehcZG6zQvyBfnzohlVXnYwp/R664qrlcXr9ezPfufmSE4y5vWstkAuc+lF1Ln5InZjwj246f/ZZEyz4y6vHH5F8KO8jl3v49+NYmH71DeJJxxlEpG3qbDC07XvMmHzxnCE5Nt/ANBOwncO592fL4SPmn378lnYZNkH8ecJO0zqovZ08fki3//lsp+a9L5J45S2Xuz9pLQ/tbD0WNCI8VN/5NcLbeLL8pLZDrL9V7zkjl0Xfkzf9eIQu3NZaiP7wgT915nXjyv03EhSsrK8uFVmgCAn4lcCbywerRkauzbogUzN4d+fzCxXZe+Hx3ZHbBDZGsq0dHVn9w5uIf+VSDwM6dOyMDBw6M6CtXLIH3IquH5EWy8n4bef3sxb9d+PSlyC9aZ0WyBi6NvBvzDF5c0rlPrOFY+aeBMhBIh8D5Cnlx1iqpajpERj3Qqca0Wb3LO8p9Y8fLp72/K02/OSMiDdJpLfT36loO6znJu7le1pXSSofPVWfkbETEiyEOgpO837gDAkkRiHz4Z9n+RpU0uL+n/Ki5MccRc399uarXSJnaK+ZrPkIgVQIXPpdPjx+TY+bjdu4z+d9tK2TV8bZS9LvbJdejHDMITqoO5T4IWCRw/uOjsltErry+pTSzeA/FIJAWgY9nyaAOs2KqaCDX/uwZ+dU/ZnsxuDFsQXBiXMJHCEAAAoElEPlGvvzsrEijfBk2vqdcWx0Z8I188sf/lAXLxsuw7zWTFVP+Qa6q/s293iI47rGmpQwlUL91e+ndQGTl4eNSKSJXxeEQ+eIDeedEI7nu75pLQw/+EMQxia+CSOD8aTm+/1ORJj3lZ7+YIF2i/8KfGyp9fj1YBv3ut7L4Jz+SCV2auN5Dj2byXO8nDULAOwJX3iDdujWVs+u3y59Oxm7IU7POySfbZsqtnbrK/cvfEV3P5YKA7QTqXy0//LFms3hH/vzeZ7ZXb6VCBMcKJcpAIB0Cl3xf+o34qTQ6tVrmLt8rX8QoSuSLffLcM+ukqlF/Ker9d57Nr6fTRe4NAIHIaXln79siki1511zhicHRAy5PDKBRCISfQANp9ZOx8uSgXTLi14VS8PYYGXFPd7mhySXy1fE/yX89/ZT827Ymcs+c0XJHK0Kiw/88uNDDr/8sW9eUyXtGlFpEzlS+L4ff3CKLF+6RBn1mSaEH02naazINuOB7moCAEoh88Y5sXvj/ZMq05+RAVGYbadlXflHymEwoaFdjjw7kIJAUgXO7ZWaH3vJYnMw20qC99Bs9Vn71z3dLl6suS6pauwojOHaRpB4IWCJwQb6uPCrvHjkhVTq1Vj9LWl2fI9dczmSDJXwUSkDgnHxx4oR8buzsjC56qTRq1kKaNvR2FQXBifYJ7yEAAQhAwDEC3sqdY92iYghAAAIQ8BsBBMdvHsEeCEAAAiElgOCE1LF0CwIQgIDfCCA4fvMI9kAAAhAIKQEEJ6SOpVsQgAAE/EYAwfGbR7AHAhCAQEgJIDghdSzdggAEIOA3AgiO3zyCPRCAAARCSgDBCalj6RYEIAABvxFAcPzmEeyBAAQgEFICCE5IHUu3IAABCPiNAILjN49gDwQgAIGQEkBwQupYugUBCEDAbwQQHL95BHsgAAEIhJQAghNSx9ItCEAAAn4jgOD4zSPYAwEIQCCkBBCckDqWbkEAAhDwGwEEx28ewR4IQAACISWA4ITUsXQLAhCAgN8IIDh+8wj2QAACEAgpAQQnpI6lWxCAAAT8RgDB8ZtHsAcCEIBASAkgOCF1LN2CAAQg4DcCCI7fPII9EIAABEJKAMEJqWPpFgQgAAG/EUBw/OYR7IEABCAQUgIITkgdS7cgAAEI+I0AguM3j2APBCAAgZASQHBC6li6BQEIQMBvBBAcv3kEeyAAAQiElACCE1LH0i0IQAACfiOA4PjNI9gDAQhAIKQEEJyQOpZuQQACEPAbAQTHbx7BHghAAAIhJYDghNSxdAsCEICA3wggOH7zCPZAAAIQCCkBBCekjqVbEIAABOwgUF5eLhUVFXZUJQiOLRipBAIQgEA4CXz55ZdSXFwsEydOTFt46kUikYjTmJo0aSKnT592uhnqhwAEIAABBwhUVVXJxo0bpaSkRPLz82X48OGSl5eXdEsITtLIuAECEIBAZhJIV3gQnMx8bug1BCAAgZQJxArPI488ItnZ2Qnrq5+whE0FdFqNCwIQgAAEwkXgwIED0rp1axk9enTCjrkywkloBQUgAAEIQCAwBDRyrbS0VHJzc5Naz0FwAuNiDIUABCDgLYFUhca0GsExSfAKAQhAAAJxCaQrNGalCI5JglcIQAACEKhBQPff6JVqKHR0hQhONA3eQwACEAgrgXNfyIlPvpL6zVpI04bx9/xHvj4lH1WekYZ1lEkHT/xW06mReyEAAQhAwHcEzlcsk3vadZSCRQfkfFzrTsuef31A2rZ7UP59/+dxS6T7JYKTLkHuhwAEIBAAApdmt5Wbm1bJ/r1/kZM17I3I2XfXye9m/o9c9/NHpPgmZ7axIDg1wPMFBCAAgRASuOI6+UGXK+XslgPy3rmY/kU+kZ3PPC3rzvWTXz7UU75XL+Z3mz4iODaBpBoIQAACviZQ7yq5oet1IsfflneOnY0yNSJf7XteSp6pkB9OGif35TWO+s3etwiOvTypDQIQgIBPCTSWa6/PFZG35a2/RK3RnDsi//nkPHm15YMypbizOCc3wvEEPn0yMAsCEICAzQQaSKt2HSVXjsprhz6RC0bt5+XkjkXy2AvfSJ9fFkuv7zmb7YwRjs0upToIQAACfiVwaavrpVuDU/KnN/9XTqmRX++X559cIUd/+LD8y33tpIHDhiM4DgOmeghAAAK+IdC8jXTq0Eiq9rwrx8+flQ83zJepW5tJ0eRBclNjhyIFojqP4ETB4C0EIACBUBO49Gppe3Nrkf0H5PA7O2R+ySo51+dhGdM3W5yXGxFnJ+xC7Tk6BwEIQCBoBC6Xa/NyRM6Wy9Ip+2XLgR/J+FkFktvADblBcIL2tGAvBCAAgTQIXCbX5t4oV8pGeWljA7m26FkZ+uPmroxu1Gim1NJwHbdCAAIQCBaBetK4TTvprkY36CcTxvSRa9wZ3BiYSN4ZrKcFayEAAQikRyDytZz6qFKq6l8hV7W43NV1FQQnPddxNwQgAAEIWCTAlJpFUBSDAAQgAIH0CCA46fHjbghAAAIQsEgAwbEIimIQgAAEIJAeAQQnPX7cDQEIQAACFgkgOBZBUQwCEIAABNIjgOCkx4+7IQABCEDAIgEExyIoikEAAhCAQHoEEJz0+HE3BCAAAQhYJIDgWARFMQhAAAIQSI8AgpMeP+6GAAQgAAGLBBAci6AoBgEIQAAC6RFAcNLjx90QgAAEIGCRAIJjERTFIAABCEAgPQL/B9z/YCbk1+p3AAAAAElFTkSuQmCC"></p>
<p>The following data are available:</p>
<p style="padding-left: 180px;">Temperature at A = 385 K</p>
<p style="padding-left: 180px;">Pressure at A = 2.80 × 10<sup>6 </sup>Pa</p>
<p style="padding-left: 180px;">Volume at A = 1.00 × 10<sup>–4 </sup>m<sup>3</sup></p>
<p style="padding-left: 180px;">Volume at B = 2.80 × 10<sup>–4 </sup>m<sup>3</sup></p>
<p style="padding-left: 180px;">Volume at C = 1.85 × 10<sup>–4 </sup>m<sup>3</sup></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that at C the pressure is 1.00 × 10<sup>6 </sup>Pa.</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>Show that at C the temperature is 254 K.</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 thermal energy transferred from the gas during the change B → C is 238 J.</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 work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.</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>State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.</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><strong>ALTERNATIVE 1:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_c} = {P_B} = \frac{{{P_A}{V_A}}}{{{V_B}}}">
<mrow>
<msub>
<mi>P</mi>
<mi>c</mi>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>P</mi>
<mi>B</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>P</mi>
<mi>A</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>A</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>B</mi>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.8 \times {{10}^6} \times 1 \times {{10}^{ - 4}}}}{{2.8 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mn>2.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> «= 1.00 × 10<sup>6 </sup>Pa» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2.8 \times {10^6} \times {1.00^{\frac{5}{3}}} = {P_c} \times {1.85^{\frac{5}{3}}}">
<mn>2.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>1.00</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>P</mi>
<mi>c</mi>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>1.85</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span> ✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{P_c} = 2.8 \times {10^6} \times \frac{{{{1.00}^{\frac{5}{3}}}}}{{{{1.85}^{\frac{5}{3}}}}}">
<mrow>
<msub>
<mi>P</mi>
<mi>c</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>2.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>6</mn>
</msup>
</mrow>
<mo>×</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.00</mn>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>1.85</mn>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> «= 1.00 × 10<sup>6 </sup>Pa» ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>Since <em>T<sub>B</sub></em> = <em>T<sub>A</sub></em> then <em>T<sub>c</sub></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{V_c}{T_B}}}{{{V_B}}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>c</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>T</mi>
<mi>B</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mi>B</mi>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.85 \times 385}}{{2.8}}">
<mfrac>
<mrow>
<mn>1.85</mn>
<mo>×</mo>
<mn>385</mn>
</mrow>
<mrow>
<mn>2.8</mn>
</mrow>
</mfrac>
</math></span> «= 254.4<sup> </sup>K» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.80 \times 1.00}}{{385}} = \frac{{1.00 \times 1.85}}{{{T_c}}}">
<mfrac>
<mrow>
<mn>2.80</mn>
<mo>×</mo>
<mn>1.00</mn>
</mrow>
<mrow>
<mn>385</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.00</mn>
<mo>×</mo>
<mn>1.85</mn>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mi>c</mi>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span> «K»✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{T_c} = 385 \times \frac{{1.00 \times 1.85}}{{2.80}}">
<mrow>
<msub>
<mi>T</mi>
<mi>c</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>385</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>1.00</mn>
<mo>×</mo>
<mn>1.85</mn>
</mrow>
<mrow>
<mn>2.80</mn>
</mrow>
</mfrac>
</math></span> «= 254.4<sup> </sup>K» ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>work done = «<em>p</em>Δ<em>V</em> = 1.00 × 10<sup>6</sup> × (1.85 × 10<sup>−4</sup> − 2.80 × 10<sup>−4</sup> =» −95 «J» ✔</p>
<p>change in internal energy = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>p</em>Δ<em>V</em> = −<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span> × 95 =» −142.5 «J» ✔</p>
<p><em>Q</em> = −95 − 142.5 ✔</p>
<p>«−238 J»</p>
<p> </p>
<p><em>Allow positive values.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>net work is 288 −238 = 50 «J» ✔</p>
<p>efficiency = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{288 - 238}}{{288}}">
<mfrac>
<mrow>
<mn>288</mn>
<mo>−</mo>
<mn>238</mn>
</mrow>
<mrow>
<mn>288</mn>
</mrow>
</mfrac>
</math></span> =» 0.17 ✔</p>
<p> </p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>along B→C ✔</p>
<p> </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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A uniform rod of weight 36.0 N and length 5.00 m rests horizontally. The rod is pivoted at its left-hand end and is supported at a distance of 4.00 m from the frictionless pivot.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The support is suddenly removed and the rod begins to rotate clockwise about the pivot point. The moment of inertia of the rod about the pivot point is 30.6 kg m<sup>2</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the force the support exerts on the rod.</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>Calculate, in rad s<sup>–2</sup>, the initial angular acceleration <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> of the rod.</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>After time <em>t</em> the rod makes an angle <em>θ</em> with the horizontal. Outline why the equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\theta = \frac{1}{2}\alpha {t^2}">
<mi>θ</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>α</mi>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> <strong>cannot</strong> be used to find the time it takes <em>θ</em> to become <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{2}">
<mfrac>
<mi>π</mi>
<mn>2</mn>
</mfrac>
</math></span> (that is for the rod to become vertical for the first time).</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>At the instant the rod becomes vertical show that the angular speed is <em>ω</em> = 2.43 rad s<sup>–1</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At the instant the rod becomes vertical calculate the angular momentum of the rod.</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>taking torques about the pivot <em>R</em> × 4.00 = 36.0 × 2.5 ✔</p>
<p><em>R </em>= 22.5 «N» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>36.0 × 2.50 = 30.6 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> ✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\alpha ">
<mi>α</mi>
</math></span> = 2.94 «rad s<sup>–2</sup>» ✔</p>
<p> </p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the equation can be applied only when the angular acceleration is constant ✔</p>
<p>any reasonable argument that explains torque is not constant, giving non constant acceleration ✔</p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«from conservation of energy» Change in GPE = Change in rotational KE ✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W\frac{L}{2} = \frac{1}{2}I{\omega ^2}">
<mi>W</mi>
<mfrac>
<mi>L</mi>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>I</mi>
<mrow>
<msup>
<mi>ω</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> ✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\omega = \sqrt {\frac{{36.0 \times 5.00}}{{30.6}}} ">
<mi>ω</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>36.0</mn>
<mo>×</mo>
<mn>5.00</mn>
</mrow>
<mrow>
<mn>30.6</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</p>
<p>«<em>ω</em> = 2.4254 rad s<sup>–1</sup>»</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>L</em> = 30.6 × 2.43 = 74.4 «J s» ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.44.54.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.47.09.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.a"></p>
</div>
<div class="specification">
<p>The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force <em>F </em>exists on the edge of the wheel as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.49.45.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.b"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The moment of inertia of the wheel is 1.3 × 10<sup>–4</sup> kg m<sup>2</sup>. Outline what is meant by the moment of inertia.</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>In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s<sup>–1</sup> after its displacement.</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>Determine the angular velocity of the wheel at B.</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>Describe the effect of <em>F </em>on the linear speed of the wheel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the effect of <em>F </em>on the angular speed of the wheel.</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>an object’s resistance to change in rotational motion</p>
<p><strong><em>OR</em></strong></p>
<p>equivalent of mass in rotational equations</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ΔKE + Δrotational KE = ΔGPE</p>
<p><strong><em>OR</em></strong></p>
<p><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> + <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>I</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{{{r^2}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = <em>mgh</em></p>
<p> </p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 0.250 × <em>v</em><sup>2</sup> + <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> × 1.3 × 10<sup>–4</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{{1.44 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.44</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = 0.250 × 9.81 × 0.36</p>
<p><em>v</em> = 1.2 <strong>«</strong>m s<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>ω</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.2}}{{0.012}}">
<mfrac>
<mrow>
<mn>1.2</mn>
</mrow>
<mrow>
<mn>0.012</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> = 100 <strong>«</strong>rad s<sup>–1</sup><strong>»</strong></p>
<p><strong><em>[1 mark]</em><br></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force in direction of motion</p>
<p>so linear speed increases</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force gives rise to anticlockwise/opposing torque on</p>
<p>wheel ✓ so angular speed decreases ✓</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></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>A cylinder is fitted with a piston. A fixed mass of an ideal gas fills the space above the piston.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.52.30.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/07._01"></p>
<p>The gas expands isobarically. The following data are available.</p>
<p style="text-align: center;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{Amount of gas}}}&{ = 243{\text{ mol}}} \\ {{\text{Initial volume of gas}}}&{ = 47.1{\text{ }}{{\text{m}}^3}} \\ {{\text{Initial temperature of gas}}}&{ = -12.0{\text{ °C}}} \\ {{\text{Final temperature of gas}}}&{ = + 19.0{\text{ °C}}} \\ {{\text{Initial pressure of gas}}}&{ = 11.2{\text{ kPa}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Amount of gas</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>243</mn>
<mrow>
<mtext> mol</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Initial volume of gas</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>47.1</mn>
<mrow>
<mtext> </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Initial temperature of gas</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mo>−<!-- − --></mo>
<mn>12.0</mn>
<mrow>
<mtext> °C</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Final temperature of gas</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mo>+</mo>
<mn>19.0</mn>
<mrow>
<mtext> °C</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>Initial pressure of gas</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>11.2</mn>
<mrow>
<mtext> kPa</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="specification">
<p>The gas returns to its original state by an adiabatic compression followed by cooling at constant volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the final volume of the gas is about 53 m<sup>3</sup>.</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>Calculate, in J, the work done by the gas during this expansion.</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>Determine the thermal energy which enters the gas during this expansion.</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>Sketch, on the <em>pV </em>diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.</p>
<p><img src="data:image/png;base64,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"></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>Outline the change in entropy of the gas during the cooling at constant volume.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><strong>«</strong>Using <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{V_1}}}{{{T_1}}} = \frac{{{V_2}}}{{{T_2}}}">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>V</mi>
<mn>2</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong></p>
<p><em>V</em><sub>2</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{47.1 \times (273 + 19)}}{{(273 - 12)}}">
<mfrac>
<mrow>
<mn>47.1</mn>
<mo>×</mo>
<mo stretchy="false">(</mo>
<mn>273</mn>
<mo>+</mo>
<mn>19</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>273</mn>
<mo>−</mo>
<mn>12</mn>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
</math></span></p>
<p><em>V</em><sub>2</sub> = 52.7 <strong>«</strong>m<sup>3</sup><strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><strong>«</strong>Using <em>PV</em> = <em>nRT</em><strong>»</strong></p>
<p><em>V</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{243 \times 8.31 \times (273 + 19)}}{{11.2 \times {{10}^3}}}">
<mfrac>
<mrow>
<mn>243</mn>
<mo>×</mo>
<mn>8.31</mn>
<mo>×</mo>
<mo stretchy="false">(</mo>
<mn>273</mn>
<mo>+</mo>
<mn>19</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>11.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><em>V</em> = 52.6 <strong>«</strong>m<sup>3</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>W</em> <strong>«</strong>= <em>P</em>Δ<em>V</em><strong>»</strong> = 11.2 × 10<sup>3</sup> × (52.7 – 47.1)</p>
<p><em>W</em> = 62.7 × 10<sup>3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Accept 66.1 × 10<sup>3</sup> J if 53 used</em></p>
<p><em>Accept 61.6 × 10<sup>3</sup> J if 52.6 used</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>U</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>nR</em>Δ<em>T</em><strong>»</strong> = 1.5 × 243 × 8.31 × (19 – (–12)) = 9.39 × 10<sup>4</sup></p>
<p><em>Q</em> <strong>«</strong>= Δ<em>U</em> + <em>W</em><strong>»</strong> = 9.39 × 10<sup>4</sup> + 6.27 × 10<sup>4</sup></p>
<p><em>Q</em> = 1.57 × 10<sup>5</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Accept 1.60 × 10<sup>5</sup> if 66.1 × 10<sup>3</sup> J used</em></p>
<p><em>Accept 1.55 × 10<sup>5</sup> if 61.6 × 10<sup>3</sup> J used</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>concave curve from RHS of present line to point above LHS of present line</p>
<p>vertical line from previous curve to the beginning</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-13_om_08.30.16.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/07.d.i/M"></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>energy is removed from the gas and so entropy decreases</p>
<p><strong><em>OR</em></strong></p>
<p>temperature decreases <strong>«</strong>at constant volume (less disorder)<strong>» </strong>so entropy decreases</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>different paradigms/ways of thinking/modelling/views</p>
<p>allows testing in different ways</p>
<p>laws can be applied different situations</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A heat pump is modelled by the cycle A→B→C→A.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The heat pump transfers thermal energy to the interior of a building during processes C→A and A→B and absorbs thermal energy from the environment during process B→C. The working substance is an ideal gas.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the work done on the gas for the isothermal process C→A is approximately 440 J.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the change in internal energy of the gas for the process A→B.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the temperature at A if the temperature at B is <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−</span>40°C.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine, using the first law of thermodynamics, the total thermal energy transferred to the building during the processes C→A and A→B.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Suggest why this cycle is not a suitable model for a working heat pump.</span></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 style="text-align:left;"><span style="background-color:#ffffff;">evidence of work done equals area between AC and the Volume axis ✓<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">reasonable method to estimate area giving a value 425 to 450 J ✓</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Answer 440 J is given, check for valid working.<br></span></span></em></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Examples of acceptable methods for MP2:<br></span></span></em></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">- estimates 17 to18 small squares x 25 J per square = 425 to 450 J.<br>- 250 J for area below BC plus a triangle of dimensions 5 × 3, 3 × 5, or 4 × 4 small square edges giving 250 J + 187.5 J or 250 J + 200 J.<br></span></span></em></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Accurate integration value is 438 J - if method seen award <strong>[2]</strong>.</span></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;">«use of <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="U = \frac{3}{2}nRT">
<mi>U</mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mi>n</mi>
<mi>R</mi>
<mi>T</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="pV = nRT">
<mi>p</mi>
<mi>V</mi>
<mo>=</mo>
<mi>n</mi>
<mi>R</mi>
<mi>T</mi>
</math></span> to give»</span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta U = \frac{3}{2}\Delta pV">
<mi mathvariant="normal">Δ</mi>
<mi>U</mi>
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mi mathvariant="normal">Δ</mi>
<mi>p</mi>
<mi>V</mi>
</math></span> ✔</p>
<p>«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{3}{2} \times - 2.5 \times {10^5} \times 1 \times {10^{ - 3}}">
<mo>=</mo>
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mo>−</mo>
<mn>2.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</math></span>»</span></p>
<p><span style="background-color:#ffffff;">=«–»375«J» ✔</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;">Another method is possible: eg realisation that ΔU for BC has same magnitude, so ΔU = 3/2 PΔV.</span></em></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;"><em>T</em><sub>A</sub> = 816<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">K</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">»</span> <em><strong>OR </strong> </em>543«<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">°C</span>»</span><em><span style="background-color:#ffffff;">✔</span></em></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">for CA Δ<em>U</em> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:italic;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">=</span> 0 so <em>Q = W</em> = −440 «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">J</span>» ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">for AB <em>W</em> = 0 so <em>Q</em> = <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">Δ</span>U = <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">−</span>375 «J» ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">815 «J» transferred to the building ✔</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Must use the first law of thermodynamics for MP1 and MP2.</span></span></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">the temperature changes in the cycle are too large ✔<br></span></p>
<p><span style="background-color:#ffffff;">the cycle takes too long «because it contains an isothermal stage» ✔<br></span></p>
<p><span style="background-color:#ffffff;">energy/power output would be too small ✔</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>At SL, Correct answers were rare and very few candidates used the fact the work done was area under the curve, and even fewer could estimate this area. At HL, the question was better answered. Candidates used a range of methods to estimate the area including counting the squares, approximating the area using geometrical shapes and on a few occasions using integral calculus.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Not very many candidates seem to know the generalised formula ΔU =1.5(P2V2 -P1V1) however many correct answers were seen.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The temperature at A was found correctly by most candidates.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The main problem here was deciding whether each Q was positive or negative. But the question was quite well answered.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Because the question was about a heat pump rather than a heat engine very few answers were correct. Only a very small number of candidates mentioned the fact that the isothermal change would take an impracticably long time.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">An ideal gas consisting of 0.300 mol undergoes a process ABCD. AB is an adiabatic expansion from the initial volume <em>V</em><sub>A</sub> to the volume 1.5 <em>V</em><sub>A</sub>. BC is an isothermal compression. The pressures at C and D are the same as at A.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img 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wSMiLa141ydOqoT5li73nnVwIAACCDqAThpHxPr3DD3SZ+4cRLQmfBad9rYca5OHfVh6V2cnqZUsRFA1GPzaKE8dW6YhSh8hUBKwMyIb1rY69ZRs3adbngqKAS2E0DUt7OJ4pe6N8woCkshnBPQLVt1cxpfNoGhG965i0kwMgKIemQOLRYHUS8S4fuuBHxa6kY3/K7eI/yhEUDUI/c4oh65g1sqnu7u5st6cbrhW3I62QRJAFEP0m31jUbU67Mi5HYCZqlbEw9/samjdMNv9xW/HDYBRD1y/9vcMCNHQvEsCTQl7DZ1lG54SycSLXoCiHrkLra5YUaOhOLtQaAJYbeto6YbvunZ+XvgIioEWieAqLeOvN0MbW+Y7VpJbiERMJvT6Mx4F6996qja4MtYvwsWpAGBfQkg6vsS9Dz+PjdMz4uGeR0SMMLuYte5feto29vadoidrCFQSQBRr0QUdoB9b5hhlx7rmyTgUtj3sZNHtO5Dj7ixEUDUY/NooTyIegEIX50S8EXYze53OubPCwKHTABRj9z7iHrkDvageL4Iu66l1zcvCBwyAUQ9cu8j6pE72JPi+SDsLHPzpDJgRqcEEPVO8TefOaLePGNyWBGwFXaXdVRt0PT0kxcEDpEAoh65113eMCNHRfEcEDDCrju+1X25rqOPHz/26iE0dTkQDgIuCCDqLih6nIbrG6bHRcU0TwgYYa+7pWwTdZTxdU8qA2a0TgBRbx15uxk2ccNstwTkFiIBXWam68frCHsTdZTx9RBrDTa7IICou6DocRpN3DA9Li6meUSg7payTdVR02Og28nygsChEEDUI/d0UzfMyLFRPEcEjLBrq12P236xfr1t4uTXNQFEvWsPNJw/ot4wYJKvJKBibp7H3oWw6xBAcX94HR6oMzRQWTgCQMAzAoi6Zw5xbQ6i7poo6dkSUBG9e/duJ8vNysb39dro4k+GLT/iQaAOAUS9DqWAwyDqATsvQtN1qdudO3c2hL2NOqrirfnmH0Dz4MEDefbsWYSUKdIhE0DUI/d+GzfMyBFSPMcEzDi3Edi26qhOnNO8zMQ5/YOxy3p6xxhIDgKNEEDUG8HqT6Jt3TD9KTGWhEBAW8jactaNYtqso+YPhY6pqw3aWucFgZgIIOoxebOkLG3eMEuy5xQEthIwS86arKMq3ircKuZm/Fxb5zrGrr81mffWgvMDBBokgKg3CNeHpLlp+eAFbNhGQIVW66gKrxHdbWFtz6uga/raM5AkSSrmZsc5FXfTHW+bPvEg4BMBRN0nbzRgC6LeAFSSdEpAxdwsO9PWe1MvTVvz0Wvi9PRU7t27l75V6HlBIBYCiHosntxSDkR9CxhOe0dAxVVb003PSNdud83ru9/9rrzxxhvy85//3DsWGAQBWwKIui25QOIh6oE4CjNTAmYiW1ut5z//+c/y1ltvNf5HAvdCoC0CiHpbpDvKB1HvCDzZ1iZQrKPaTa6b1Oi4d1Pj7HnjzB+JJrv+8/lxDIEmCSDqTdL1IO3iDdMDkzABAhsEyuqoirlObtOJbG2IrRF27ZrnBYGQCSDqIXuvhu1lN8wa0QgCgdYI3FRH2xpn18KayXpt9A60BpeMDo4Aoh65y2+6YUZedIoXCIGqOmo2qmlj9zeEPZBKg5lbCSDqW9HE8UPVDTOOUlKKkAnUqaPaLa5d8fpuuiWt3f46ns8LAiESQNRD9NoONte5Ye6QHEEh4JzALnX0d7/7XbrOfDAYpGPu2j2vLXmX4+76p0H/PGirnRcEQiOAqIfmsR3t3eWGuWPSBIdAJwR+8pOfyDe+8Q351a9+la4315a1zpbXum7EeF+RR9g7cS2ZOiCAqDuA6HMSiLrP3sE2GwK6ratuHPPTn/40FXEzY12FWH/Th8SYczbpmzianv5ZoMVuiPAZAgFEPQQv7WEjor4HPKJ6S0Bb59r1rpPnis9Jd2m0tvibTN+lraQFASWAqEdeDxD1yB0cQfFs6qi2yFVsTetcj5varAZhj6CSHVAREPXInW1zw4wcCcXzjIBtHTWtdS2OiruKunaXN/HUNYTds0qDOVsJIOpb0cTxg+0NM47SU4oQCNjW0Xxr3ZRTx9O11d7EmnaE3VDm02cCiLrP3nFgm+0N00HWJAGBWgT2qaP51rrJTCfJ6XmdCa9C7PKFsLukSVpNEEDUm6DqUZr73DA9KgamRExgnzqqIrvtiW56XtPe9rstUoTdlhzx2iCAqLdBucM89rlhdmg2WUPACQEVYG2xu261I+xO3EMiDRBA1BuA6lOSiLpP3sCWrgjkW+06qc7FC2F3QZE0XBNA1F0T9Sw9RN0zh2BOZwTMWLvLGfIIe2fuJOMtBBD1LWBiOY2ox+LJeMvRdh3Nz5B30Wo3wt7EjPt4vU7JmiKAqDdF1pN0275helJszAiIQBd1VFvtuq5dl7/pA2H2fRlhZ0vZfUkSf18CiPq+BD2P38UN03MkmOcZgS7rqAq6dsfrErh994vXVr95oIxniDHngAgg6pE7u8sbZuRoKZ4jAl3XURVjVxPpjLDrnwQXXfuOEJPMARFA1CN3dtc3zMjxUjwHBHypo9qFrmKsLfd9uuRVzM3mNwi7gwpCEjsRQNR3whVeYF9umOGRw+K2CPhWR58+feqkS17H112vj2/LJ+QTLgFEPVzf1bLctxtmLaMJBIGOCWgL23TJ66x22xa3eTSs9gLwgkAbBBD1Nih3mAei3iF8sg6eQH6WvC6Fs3lpy19n2esnLwg0TQBRb5pwx+kj6h07gOyjIKBPhNOudB1vtxFn80Q51/vQRwGXQjglgKg7xelfYoi6fz7Bok0CIdXR/Hj7rs9t1y54/VOgY+223fmb5PgGgesEEPXrTKI6E9INMyrwFKY2gRDrqLa4tUt91/XtKuba4tc3wl67ihBwBwKI+g6wQgwa4g0zRM7YbE8g1DqqomzEXVvfu2xeo+H1TwET6OzrDTHLCSDq5VyiORvqDTMaB1CQSgKh11EVdxVpLccu4q5d+RrHZoy+EioBDpYAoh6560O/YUbuHoonkgpbDCC0pb6ruGtLXVvsGo/u+BhqQfdlQNS790GjFiDqjeIlcQhcI7CruKuYmx3odunCv5YxJyCgf5KhEDcBRD1u/1I6fwnsKu5mo5p9tqj1lwaWtUUAUW+LdEf5IOodgSdbCGQEVNyNYOvjXm9aCqeCrt3x++xiB/jDJoCoR+5/RD1yB0dQvEOpo/nZ8trdvq1Fnu+OZ3Z8BBW85SIg6i0Dbzu7Q7lhts2V/NwROLQ6qqJtNrExO9TpueLL7D1vuz1tMT2+HwYBRD1yPx/aDTNyd0ZZvEOuoyru2mo3Xe7FiXLaUteNanbd5CbKikKhahFA1GthCjfQId8ww/XaYVlOHZV0ExqzHK447q6teDMmT6v9sK4Nm9Ii6jbUAorDDTMgZx2oqdTRK8ergGu3u3bL61tF3HTN6wQ7Pbd7q/1SZuNBuh+Asr5635LhOJHZ4tWVARwFTwBRD96FNxeAG+bNfPgVAr4S0Il02mrXa1hb8fo932pX8a/3ykT9aCyz11cxlosncjLoS/9+Ii+WV+c5CpsAoh62/yqtR9QrEREAAl4T0HH2fOtdj58/f75+MMxNS+RWBSsXdZGvZT65J73ee5IscmrvNQ2MqyKAqFcRCvx3RD1wB2I+BHIEVMC11a4T63QC3enpqdy+fXtjm1kNo2/TbS9SIer9E5le0FTPYQ76EFEP2n3VxiPq1YwIAYHQCKhg68x50z3/gx/8QL7zne+Ifuo1/8Ybb8i3v/3t7Mlx5aK+6n5/R06mLwRJD60GbLcXUd/OJopfEPUo3Bh1Iaij+7lXBV4n1H3/+9/PTYJbTYjTWfPrlvrGJDkzYe6WDCfP5XI/E4jtEQFE3SNnNGEKN8wmqJKmSwLUUTc0tctdWebfDx8+vBL1wkQ5uTyXZHQsvd5tGU2/cGMEqXROAFHv3AXNGsANs1m+pL4/Aero/gxNCqb7XZm++eabN3a/p3EupjLq9+RoPBOmyhmKYX8i6mH7r9J6bpiViAjQMQHqqDsHmK54ZXq1O135mHqaayrqfTmenDOu7s4NnaaEqHeKv/nMuWE2z5gc9iNAHd2PX1nsTaZbRH35QqYnx9Lrvy/JCzagKeMY4jlEPUSv7WDz5sW9Q0SCQgACkRDIRL0w3t7r9WUwmsh0fhFJOSmGEkDUI68HiHrkDqZ4EIAABHIEEPUcjBgPEfUYvUqZIAABCJQTQNTLuURzFlGPxpXRFoQ66t61MHXPNJQUEfVQPGVpJxe3JTiitUaAOuoeNUzdMw0lRUQ9FE9Z2snFbQmOaK0RoI66Rw1T90xDSRFRD8VTlnZycVuCI1prBKij7lHD1D3TUFJE1EPxlKWdXNyW4IjWGgHqqHvUMHXPNJQUEfVQPGVpJxe3JTiiQQACEAiQAKIeoNN2MRlR34UWYSEAAQiETQBRD9t/ldYj6pWICAABCEAgGgKIejSuLC8Iol7OhbP+EKCOuvcFTN0zDSVFRD0UT1naycVtCY5orRGgjrpHDVP3TENJEVEPxVOWdnJxW4IjWmsEqKPuUcPUPdNQUkTUQ/GUpZ1c3JbgiNYaAeqoe9Qwdc80lBQR9VA8ZWknF7clOKK1RoA66h41TN0zDSVFRD0UT1naycVtCY5orRGgjrpHDVP3TENJEVEPxVOWdnJxW4IjGgQgAIEACSDqATptF5MR9V1oERYCEIBA2AQQ9bD9V2k9ol6JiAAQgAAEoiGAqEfjyvKCIOrlXDjrDwHqqHtfwNQ901BSRNRD8ZSlnVzcluCI1hoB6qh71DB1zzSUFBH1UDxlaScXtyU4orVGgDrqHjVM3TMNJUVEPRRPWdrJxW0JjmitEaCOukcNU/dMQ0kRUQ/FU5Z2cnFbgiNaawSoo+5Rw9Q901BSRNRD8ZSlnVzcluCIBgEIQCBAAoh6gE7bxWREfRdahIUABCAQNgFEPWz/VVqPqFciIgAEIACBaAgg6tG4srwgiHo5F876Q4A66t4XMHXPNJQUEfVQPGVpJxe3JTiitUaAOuoeNUzdMw0lRUQ9FE9Z2snFbQmOaK0RoI66Rw1T90xDSRFRD8VTlnZycVuCI1prBKij7lHD1D3TUFJE1EPxlKWdXNyW4IjWGgHqqHvUMHXPNJQUEfVQPGVpJxe3JTiitUaAOuoeNUzdMw0lRUQ9FE9Z2snFbQmOaBCAAAQCJICoB+i0XUxG1HehRVgIQAACYRNA1MP2X6X1iHolIgJAAAIQiIYAoh6NK8sLgqiXc+GsPwSoo+59AVP3TENJEVEPxVOWdnJxW4IjWmsEqKPuUcPUPdNQUkTUQ/GUpZ1c3JbgiNYaAeqoe9Qwdc80lBQR9VA8ZWknF7clOKK1RoA66h41TN0zDSVFRD0UT1naycVtCY5orRGgjrpHDVP3TENJEVEPxVOWdnJxW4IjGgQgAIEACSDqATptF5MR9V1oERYCEIBA2AQQ9bD9V2k9ol6JiAAQgAAEoiGAqEfjyvKCIOrlXDjrDwHqqHtfwNQ901BSRNRD8ZSlnVzcluCI1hoB6qh71DB1zzSUFBH1UDxlaScXtyU4orVGgDrqHjVM3TMNJUVEPRRPWdrJxW0JjmitEaCOukcNU/dMQ0kRUQ/FU5Z2cnFbgiNaawSoo+5Rw9Q901BSRNRD8ZSlnVzcluCIBgEIQCBAAoh6gE7bxWREfRdahIUABCAQNgFEPWz/VVqPqFciIgAEIACBaAgg6tG4srwgiHo5F85CAAIQiJEAoh6jV3NlQtRzMDj0kgB11L1bYOqeaSgpIuqheMrSTi5uS3BEa40AddQ9api6ZxpKioh6KJ6ytJOL2xIc0VojQB11jxqm7pmGkiKiHoqnLO3k4rYER7TWCFBH3aOGqXumoaSIqIfiKUs7ubgtwRGtNQLUUfeoYeqeaSgpIuqheMrSTi5uS3BEgwAEIBAgAUQ9QKftYjKivgstwkIAAhAImwCiHrb/Kq1H1CsREfUViCEAAApgSURBVAACEIBANAQQ9WhcWV4QRL2cC2f9IUAdde8LmLpnGkqKiHoonrK0k4vbEhzRWiNAHXWPGqbumYaSIqIeiqcs7eTitgRHtNYIUEfdo4ape6ahpIioh+IpSzu5uC3BEa01AtRR96hh6p5pKCki6qF4ytJOLm5LcERrjQB11D1qmLpnGkqKiHoonrK0k4vbEhzRIAABCARIAFEP0Gm7mIyo70KLsBCAAATCJoCoh+2/SusR9UpEBIAABCAQDQFEPRpXlhcEUS/nwll/CFBH3fsCpu6ZhpIioh6Kpyzt5OK2BEe01ghQR92jhql7pqGkiKiH4ilLO7m4LcERrTUC1FH3qGHqnmkoKSLqoXjK0k4ubktwRGuNAHXUPWqYumcaSoqIeiiesrSTi9sSHNFaI0AddY8apu6ZhpIioh6Kpyzt5OK2BEe01ghQR92jhql7pqGkiKiH4ilLO7m4LcERDQIQgECABBD1AJ22i8mI+i60CAsBCEAgbAKIetj+q7QeUa9ERAAIQAAC0RBA1KNxZXlBEPVyLpz1hwB11L0vYOqeaSgpIuqheMrSTi5uS3BEa40AddQ9api6ZxpKioh6KJ6ytJOL2xIc0VojQB11jxqm7pmGkiKiHoqnLO3k4rYER7TWCFBH3aOGqXumoaSIqIfiKUs7ubgtwRGtNQLUUfeoYeqeaSgpIuqheMrSTi5uS3BEgwAEIBAgAUQ9CKddyPzJqQz7PVGR7vVuyXCcyGzxqtJ6RL0SEQEgAAEI7E3gq6++ksePH4t+dvlC1LukXzPv5Xwixyrkp09lsRRZLp7IyaAv/dFULirSQNQrAPEzBCAAAQcEVMwfPHggd+7ckSRJOhN3RN2BM5tN4muZT+5J72gss9cmp+xc/0SmF0tzsvQTUS/FwkmPCFBH3TsDpu6Z1k1xPp93Ku6Iel1PdRbuC5mObktvmMgiZ8Pr2ViOevdkMv86d/b6IRf3dSac8YsAddS9P2DqnumuKXYl7oj6rp5qPfxnkgyPpFzUBzKeXa4t0guZNwyoA9QB6oC/dWB9w27oAFFvCKy7ZOuLelmeenHzgoDPBKij7r0DU/dMbVN8+vSp3L17N31r673pF3f8pgnvnT6ivjdCEvCaAALk3j0wdc901xTzYq7Hbb0Q9bZIW+dzKbPxQMq73xlTt8ZKRG8IIEDuXQFT90zrptiVmBv7EHVDwtvPspnur2WRvCc9Zr976zUMq08AAarPqm5ImNYl5S7cy5cv193sbbbMiyVA1ItEPPy+Xqc+eS46LY516h46CZOsCSBA1ui2RoTpVjSN/aDr1NsYM68qAKJeRciL3y9knpzIYD27vS+D0cfsKOeFbzBiXwII0L4Er8eH6XUmh3IGUT8UT1NOCEAAAhCIngCiHr2LKSAEIAABCBwKAUT9UDxNOSEAAQhAIHoCiHqULrZ/qluUOChU9wQWiQx7RzJMPiux5ZW8SN6Xfo1tj0siH9yp1UTZ443dJEshvJ7J+Oj6zmpH45msHyNhIuIfQyL4T0Q9eBdeL8B6trzFU92up8YZCDggkAlM6ZMFL6Yy6vdlMD5LV3c4yC3aJJaLp3I6vCW93uYW0aUFToX6toymX5T+vHES/2zgCPkLoh6y90pt3++pbqVJchICexPIdkY8nsh848GCZh+G9yV58WrvXOJNIOt9OxrK+OFIBjVEve5Dn1bM8E8sdQdRj8WT63Ls91S3dTIcQMApgWxnxOKGSbTSa1L+TJL778vk/EIkbYFXtdTNn6XqxzOvDMA/NR3hfTBE3XsX7WrgfnvF75ob4SFQj0C2C+LGuPmXMhu/U2tnxHp5HEioWqKe/bnvvy2Dt/vZ0xuPZfToTBYbPSWGGf4xJK4+y++lV7/7eYSo++mXPawqr4irrriqf/d7ZEtUCFQQWNXBqzHe5YtE7vf7cjw5l1KdqUjvYH+uI+rLc5kc96U3OJXZZUb38rlMhre3zl3AP8UaVX4vLYby7Tui7ptH9ranvCIi6nuDJYF9CaRi1JPV7OuslZ4XnX3TP5T4dUS9lEVFlzz+KVArv5cWAnn3FVH3ziX7GrTfU932zZ34ENhKwLQeh4m8mE/kuHdL7ief0krfCmzLD9aibrrY35NkcW1Rm0hU/lnKxfTk+jLJbA6H6R1aLs7k0eg4G57oSX84lmS2yOpkQdRT7oVlmRvnVuH7w9/Kw3Wat2R4OpXZf/xBhv1seeHgRJL5xdq5y8VMkvFQ+mYb8MFIHq1tWAerfYCo10YVSsCyf+P1n+oWSimxM0QC2Tjv0Xsy+pfbm13DpjjLTyW5f0tKl76ZMIf+WUfUC+K1QpbdG66tQDBAa/hHsj0FihMeTRI+fV5jUBD6yzMZD/rSH/5Bzhav9ElZcnaq4vqOjGdfioidqPd6xzJKzuVSLuR8cn8l1oMPZKp5ZHn2jA/WNjyS83SYxMQxNuwOFFHfnZn3Mdbr1C2e6uZ94TAwYAKZqKQtkqux9XyB0rr79kAGR3VnbedjH8hxHVGX68Mbq01rbt/QO1Ltn1Vr/m0ZDAb11r936pLsT4oRUMl/Lwi8sTPrrVj9qbQU9XV+Iqt7cb51n/WkHo1l9rqODcaw+p+Ien1WAYW0f6pbQIXE1OAImJtYT9YtlY0yqKi8K8eTv8uT0TsBiMaG8e19KRX1TIBSschMWS5k9kjXtGfdvv2hjJ/Mb9jgp8o/mUgdP5SzJydyNJrKVSdye8Wvn5Mpzz2ZzL8W2Wi558U1n2Je+C1FfZjIwiR5zVf5fPN/oq7v/NfLp2PSq/GJqNeARBAIQKAFAmkr6V2ZzP8vHQ/1XzRaYOJVFuZP17ksVSBD6E1Ju7eP5HjyX/Llxhh7XlzzkDMhT1vbLYm646EMRD3vT44hAIHOCKy6KvMtlqyF1ZlFZLxBwEykMy3/XgjLEbPW8PG/yviXt6V/P5EX6Qq/QiveFHTH7vfVqiLTvV74E6Bp3thSNzaUD0UZk3b9RNR3JUZ4CECgAQLa7fl2bs168XsDWZLkDgQyAVqPFxe/75BUy0Gv/iwWxHM9Sa3mRLm0+15nyK8mtV3tw28r6nI1cc5MpJNXsjjTmfL2f5gQ9ZYrGNlBAAIlBNIbZr5lHo5olJQmwlMlf7Ku+czTYpsehpJu7p2WtKngzj6W0SDboU/nKKT78O8h6qKT7jeX1fU03WS2Zee/asaIejUjQkAAAhCAAASCIICoB+EmjIQABCAAAQhUE0DUqxkRAgIQgAAEIBAEAUQ9CDdhJAQgAAEIQKCaAKJezYgQEIAABCAAgSAIIOpBuAkjIQABCEAAAtUEEPVqRoSAAAQgAAEIBEEAUQ/CTRgJAQhAAAIQqCaAqFczIgQEIAABCEAgCAKIehBuwkgIQAACEIBANQFEvZoRISAAAQhAAAJBEEDUg3ATRkIAAhCAAASqCSDq1YwIAQEIQAACEAiCAKIehJswEgIQgAAEIFBNAFGvZkQICEAAAhCAQBAEEPUg3ISREIAABCAAgWoCiHo1I0JAAAIQgAAEgiCAqAfhJoyEAAQgAAEIVBP4f7J5T4rEuY0wAAAAAElFTkSuQmCC"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The following data are available.</span></span></p>
<p style="padding-left: 90px;"><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Pressure at A = 250 kPa<br>Volume at C = 3.50 × 10<sup>–3</sup> m<sup>3</sup><br>Volume at D = 2.00 × 10<sup>–3</sup> m<sup>3</sup></span></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The gas at C is further compressed to D at a constant pressure. During this compression the temperature decreases by 150 K.</span></p>
<p><span style="background-color: #ffffff;">For the compression CD,</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the pressure at B is about 130 kPa.</span></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><span style="background-color: #ffffff;">Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>V</mi><mi mathvariant="normal">A</mi></msub><msub><mi>V</mi><mi mathvariant="normal">C</mi></msub></mfrac></math>.</span></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><span style="background-color: #ffffff;">determine the thermal energy removed from the system.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">explain why the entropy of the gas decreases.</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;">state and explain whether the second law of thermodynamics is violated.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi mathvariant="normal">B</mi></msub><mo>=</mo><mfrac><mrow><mn>250</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><msup><mn>5</mn><mstyle displaystyle="true"><mfrac><mn>5</mn><mn>3</mn></mfrac></mstyle></msup></mrow></mfrac><mo> </mo><mo>«</mo><mi>from</mi><mo> </mo><msub><mi>P</mi><mi mathvariant="normal">B</mi></msub><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><msub><mi>V</mi><mi mathvariant="normal">A</mi></msub></mrow></mfenced><mfrac><mn>5</mn><mn>3</mn></mfrac></msup><mo>=</mo><mn>250</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><msup><msub><mi>V</mi><mi mathvariant="normal">A</mi></msub><mfrac><mn>5</mn><mn>3</mn></mfrac></msup><mo>»</mo></math> <span style="background-color: #ffffff;">✔</span></p>
<p>= 127 kPa <span style="background-color: #ffffff;">✔</span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mn>127</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><msub><mi>V</mi><mi mathvariant="normal">A</mi></msub><mo>=</mo><mn>250</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><msub><mi>V</mi><mi mathvariant="normal">C</mi></msub><mo>»</mo></math></p>
<p><span style="background-color: #ffffff;">1.31 ✔</span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>work done <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>W</mi><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>250</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>375</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> <span style="background-color: #ffffff;">✔</span></p>
<p>change in internal energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>U</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>300</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>×</mo><mfenced><mrow><mo>-</mo><mn>150</mn></mrow></mfenced><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>561</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math><br><em><strong>OR<br></strong></em><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>U</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>P</mi><mo>∆</mo><mi>V</mi><mo>=</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>×</mo><mn>375</mn><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>563</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> </strong></em><span style="background-color: #ffffff;">✔</span></p>
<p>thermal energy removed <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>Q</mi><mo>=</mo><mn>375</mn><mo>+</mo><mn>561</mn><mo>=</mo><mn>936</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math><br><em><strong>OR<br></strong></em><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>Q</mi><mo>=</mo><mn>375</mn><mo>+</mo><mn>563</mn><mo>=</mo><mn>938</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> </strong></em><span style="background-color: #ffffff;">✔</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>Q</mi><mo>=</mo><mo>«</mo><mi>n</mi><mi>C</mi><mi>p</mi><mo>∆</mo><mi>T</mi><mo>=</mo><mo>»</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>×</mo><mi>n</mi><mi>R</mi><mi>T</mi></math> <span style="background-color: #ffffff;">✔</span></p>
<p>thermal energy removed <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>Q</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>300</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>×</mo><mn>150</mn></math> <span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>935</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math></span><span style="background-color: #ffffff;"> ✔</span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span style="background-color: #ffffff;">«from b(i)» <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>Q</mi></math> is negative <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>S</mi><mo>=</mo><mfrac><mrow><mo>∆</mo><mi>Q</mi></mrow><mi>T</mi></mfrac></math> <em><strong>AND <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>S</mi></math> </strong></em>is negative <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></p>
<p> </p>
<p><strong>ALTERNATIVE 2</strong></p>
<p><em>T</em> and/or <em>V</em> decreases ✔</p>
<p>less disorder/more order «so <em>S</em> decreases» ✔</p>
<p> </p>
<p><strong>ALTERNATIVE 3</strong></p>
<p><em>T</em> decreases ✔</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>S</mi><mo>=</mo><mi>K</mi><mo>×</mo><mi>ln</mi><mfenced><mfrac><mrow><mi>T</mi><mn>2</mn></mrow><mrow><mi>T</mi><mn>1</mn></mrow></mfrac></mfenced><mo><</mo><mn>0</mn></math> ✔</p>
<p><em> </em></p>
<p><em>NOTE: Answer given, look for a valid reason that S decreases.</em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">not violated ✔</span></p>
<p><span style="background-color: #ffffff;">the entropy of the surroundings must have increased<br><em><strong>OR</strong></em><br>the overall entropy of the system and the surroundings is the same or increased ✔</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(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">b(iii).</div>
</div>
<br><hr><br><div class="specification">
<p>The pressure–volume (<em>pV</em>) diagram shows a cycle ABCA of a heat engine. The working substance of the engine is 0.221 mol of ideal monatomic gas.</p>
<p style="text-align: left;"><img 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"></p>
<p>At A the temperature of the gas is 295 K and the pressure of the gas is 1.10 × 10<sup>5</sup> Pa. The process from A to B is adiabatic.</p>
</div>
<div class="specification">
<p>The process from B to C is replaced by an isothermal process in which the initial state is the same and the final volume is 5.00 × 10<sup>–3<sub> </sub></sup>m<sup>3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the pressure at B is about 5 × 10<sup>5</sup> Pa.</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>For the process BC, calculate, in J, the work done by the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the process BC, calculate, in J, the change in the internal energy of the gas.</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>For the process BC, calculate, in J, the thermal energy transferred to the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.</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>Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.</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 why an efficiency calculation is important for an engineer designing a heat engine.</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><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{p_1}V_1^{\frac{5}{3}} = {p_2}V_2^{\frac{5}{3}}">
<mrow>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mn>1</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<msub>
<mi>p</mi>
<mn>2</mn>
</msub>
</mrow>
<msubsup>
<mi>V</mi>
<mn>2</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msubsup>
</math></span><strong>»</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.1 \times {10^5} \times {5^{\frac{5}{3}}} = {p_2} \times {2^{\frac{5}{3}}}">
<mn>1.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>5</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
<mo>=</mo>
<mrow>
<msub>
<mi>p</mi>
<mn>2</mn>
</msub>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>2</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</math></span></p>
<p><em>p</em><sub>2</sub> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.1 \times {{10}^5} \times {5^{\frac{5}{3}}}}}{{{{2.5}^{\frac{5}{3}}}}}">
<mfrac>
<mrow>
<mn>1.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>5</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mn>5</mn>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>2.5</mn>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> = 5.066 × 10<sup>5</sup> <strong>«</strong>Pa<strong>»</strong></p>
<p> </p>
<p><em>Volume may be in litres or m<sup>3</sup>.</em></p>
<p><em>Value to at least 2 sig figs, </em><strong><em>OR </em></strong><em>clear working with substitution required for mark.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>W = <em>p</em>Δ<em>V</em><strong>»</strong></p>
<p><strong>«</strong>= 5.07 × 10<sup>5</sup> × (5 × 10<sup>–3</sup> – 2 × 10<sup>–3</sup>)<strong>» </strong></p>
<p>= 1.52 × 10<sup>3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>if POT mistake.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>U</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span><em>p</em>Δ<em>V</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{2}">
<mfrac>
<mn>3</mn>
<mn>2</mn>
</mfrac>
</math></span>5.07 × 10<sup>5</sup> × 3 × 10<sup>–3</sup> = 2.28 × 10<sup>–3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Accept alternative solution via T</em><sub><em>c</em></sub><em>.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Q</em><strong> «</strong>= (1.5 + 2.28) × 10<sup>3</sup> =<strong>»</strong> 3.80 × 10<sup>3</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Watch for ECF from (b)(i) and (b)(ii).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>for isothermal process, PV = constant / ideal gas laws mentioned</p>
<p>since V<sub>C</sub> > V<sub>B</sub>, P<sub>C</sub> must be smaller than P<sub>B</sub></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the area enclosed in the graph would be smaller</p>
<p>so the net work done would decrease</p>
<p> </p>
<p><em>Award MP2 only if MP1 is awarded.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to reduce energy loss; increase engine performance; improve mpg <em>etc</em></p>
<p> </p>
<p><em>Allow any sensible answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A flywheel is made of a solid disk with a mass <em>M</em> of 5.00 kg mounted on a small radial axle. The mass of the axle is negligible. The radius<em> R</em> of the disk is 6.00 cm and the radius<em> r</em> of the </span><span style="background-color: #ffffff;">axle is 1.20 cm.<br></span></p>
<p><span style="background-color: #ffffff;">A string of negligible thickness is wound around the axle. The string is pulled by an electric motor that exerts a vertical tension force <em>T</em> on the flywheel. The diagram shows the forces acting on the flywheel. <em>W</em> is the weight and<em> N</em> is the normal reaction force from the support of the flywheel.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The moment of inertia of the flywheel about the axis is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>M</mi><msup><mi>R</mi><mn>2</mn></msup></math>.</span></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The flywheel is initially at rest. At time <em>t</em> = 0 the motor is switched on and a time-varying tension force acts on the flywheel. The torque <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Γ</mi></math></em> exerted on the flywheel by the tension force in the string varies with<em> t</em> as shown on the graph.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">At<em> t</em> = 5.00 s the string becomes fully unwound and it disconnects from the flywheel. The flywheel remains spinning around the axle.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">State the torque provided by the force <em>W</em> about the axis of the flywheel.</span></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><span style="background-color: #ffffff;">Identify the physical quantity represented by the area under the graph.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the angular velocity of the flywheel at <em>t</em> = 5.00 s is 200 rad s<sup>–1</sup>.</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;">Calculate the maximum tension in the string.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The flywheel is in translational equilibrium. Distinguish between translational equilibrium and rotational equilibrium.</span></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><span style="background-color: #ffffff;">At <em>t</em> = 5.00 s the flywheel is spinning with angular velocity 200 rad s<sup>–1</sup>. The support bearings exert a constant frictional torque on the axle. The flywheel comes to rest after 8.00 × 10<sup>3</sup> revolutions. Calculate the magnitude of the frictional torque exerted on the flywheel.</span></p>
<div class="marks">[3]</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><span style="background-color: #ffffff;">zero ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">«change in» angular momentum ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow angular impulse.</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">use of <em>L = lω </em>= area under graph = 1.80 «kg m<sup>2 </sup>s<sup>–1</sup>» ✔<br></span></p>
<p><span style="background-color: #ffffff;">rearranges «to give <em>ω=</em> area/I» 1.80 = 0.5 × 5.00 × 0.060<sup>2 </sup></span>×<span style="background-color: #ffffff;"><em> ω</em> ✔<br></span></p>
<p><span style="background-color: #ffffff;">«to get <em>ω </em>= 200 rad s<sup>–1 </sup>»</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>40</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>012</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mn>33</mn><mo>.</mo><mn>3</mn><mo> </mo><mi mathvariant="normal">N</mi></math> <span style="background-color: #ffffff;">✔</span></p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">translational equilibrium is when the sum of all the forces on a body is zero ✔<br></span></p>
<p><span style="background-color: #ffffff;">rotational equilibrium is when the sum of all the torques on a body is zero ✔</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span style="background-color: #ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p><em><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><msup><mn>200</mn><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>×</mo><mi>α</mi><mo>×</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>8000</mn></math> </span></strong></em><span style="background-color: #ffffff;">✔</span></p>
<p><em><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>0</mn><mo>.</mo><mn>398</mn><mo> </mo><mo>«</mo><mi>rad</mi><mo> </mo><msup><mi>s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> </span></strong></em><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;">torque = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mi>I</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>398</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>00</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>060</mn><mn>2</mn></msup></mrow></mfenced><mo>=</mo><mn>3</mn><mo>.</mo><mn>58</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo> </mo><mi mathvariant="normal">m</mi><mo>»</mo></math> ✔</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>change in kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>5</mn><mo>.</mo><mn>00</mn><mo>×</mo><mn>0</mn><mo>.</mo><msup><mn>060</mn><mn>2</mn></msup></mrow></mfenced><mo>×</mo><msup><mn>200</mn><mn>2</mn></msup><mo>=</mo><mo>«</mo><mo>-</mo><mo>»</mo><mn>180</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">J</mi><mo>»</mo></math> ✔</p>
<p>identifies work done = change in KE <span style="background-color: #ffffff;"><span style="text-align: left;color: #000000;text-indent: 0px;letter-spacing: normal;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-variant: normal;text-decoration: none;display: inline !important;white-space: normal;float: none;background-color: #ffffff;"><span style="background-color: #ffffff;">✔</span></span></span></p>
<p>torque = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>W</mi><mi>θ</mi></mfrac><mo>=</mo><mfrac><mn>180</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>8000</mn></mrow></mfrac><mo>=</mo><mn>3</mn><mo>.</mo><mn>58</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo> </mo><mi mathvariant="normal">m</mi><mo>»</mo></math>✔</p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram represents an ideal, monatomic gas that first undergoes a compression, then an increase in pressure.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>An adiabatic process then increases the volume of the gas to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn><mo> </mo></mrow></msup><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the work done during the compression.</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>Calculate the work done during the increase in pressure.</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>Calculate the pressure following this process.</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 how an approximate adiabatic change can be achieved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">–</span><span class="fontstyle0">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math></span><span class="fontstyle1"> </span><span class="fontstyle1">«<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi></math>» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">J</mi></math>» </span><span class="fontstyle2">✓ </span></p>
<p> </p>
<p><em><span class="fontstyle3">OWTTE</span></em></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><msup><mi>V</mi><mfrac><mn>5</mn><mn>3</mn></mfrac></msup></math> is constant «<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>×</mo><msup><mfenced><mrow><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mfrac><mn>5</mn><mn>3</mn></mfrac></msup><mo>=</mo><msub><mi>P</mi><mn>2</mn></msub><mo>×</mo><msup><mfenced><mrow><mn>5</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mfrac><mn>5</mn><mn>3</mn></mfrac></msup></math>» </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>2</mn></msub><mo>=</mo><mn>8</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mn>4</mn><mo> </mo></mrow></msup><mo>«</mo><mi>Pa</mi><mo>»</mo></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>87</mn></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kPa</mi></math>» </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Award </span><strong><span class="fontstyle2">[2] </span></strong><span class="fontstyle0">marks for a bald correct answer</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">adiabatic means no transfer of heat in or out of the system </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">should be fast </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">«can be slow if» the system is insulated </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle3">OWTTE</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(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>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A uniform ladder of weight 50.0 N and length 4.00 m is placed against a frictionless wall making an angle of 60.0° with the ground.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Outline why the normal force acting on the ladder at the point of contact with the wall is equal to the frictional force <em>F</em> between the ladder and the ground.</span></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><span style="background-color:#ffffff;">Calculate <em>F.</em></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The coefficient of friction between the ladder and the ground is 0.400. Determine whether the ladder will slip.</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 style="text-align:left;"><span style="background-color:#ffffff;">«translational equilibrium demands that the» </span><span style="background-color:#ffffff;">resultant force in the horizontal direction must be zero✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">«hence <em>N</em><sub>W</sub> = <em>F»</em></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><span style="background-color:#ffffff;">Equality of forces is given, look for reason why.</span></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">«clockwise moments = anticlockwise moments»<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">50 × 2cos 60 = <em>N</em><sub>W</sub> × 4sin 60 ✔</span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{N_{\text{W}}} = F = \frac{{50 \times 2\cos 60}}{{4\sin 60}}">
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mtext>W</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>50</mn>
<mo>×</mo>
<mn>2</mn>
<mi>cos</mi>
<mo></mo>
<mn>60</mn>
</mrow>
<mrow>
<mn>4</mn>
<mi>sin</mi>
<mo></mo>
<mn>60</mn>
</mrow>
</mfrac>
</math></span>»</span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em>F</em> = <span style="background-color:#ffffff;">14.4«<em>N</em>» ✔</span></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">maximum friction force = «<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">0.4 × 50N</span>» = 20«N» ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">14.4 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><</span> 20 <em><strong>AND</strong> </em>so will not slip ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Many candidates stated that the resultant of all forces must be zero but failed to mention the fact that horizontal forces must balance in this particular question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few candidates could take moments about any point and correct answers were rare both at SL and HL.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The question about the slipping of the ladder was poorly answered. The fact that the normal reaction on the floor was 50N was not known to many.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The moment of inertia of a solid sphere is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="I = \frac{2}{5}m{r^2}">
<mi>I</mi>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> where <em>m</em> is the mass of the sphere and <em>r </em>is the radius.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the total kinetic energy <em>E</em><sub>k</sub> of the sphere when it rolls, without slipping, at speed <em>v</em> is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_{\text{K}}} = \frac{7}{{10}}m{v^2}">
<mrow>
<msub>
<mi>E</mi>
<mrow>
<mtext>K</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>.</span></p>
<p> </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;">A solid sphere of mass 1.5 kg is rolling, without slipping, on a horizontal surface with a speed of 0.50 m s<sup>-1</sup>. The sphere then rolls, without slipping, down a ramp to reach a horizontal surface that is 45 cm lower.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Calculate the speed of the sphere at the bottom of the ramp.</span></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 style="text-align:left;"><span style="background-color:#ffffff;"><em>E</em><sub>k</sub> = <em>E</em><sub>k</sub> linear + <em>E</em><sub>k</sub> rotational</span></p>
<p style="text-align:left;"><em><strong><span style="background-color:#ffffff;">OR</span></strong></em></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_{\text{k}}} = \frac{1}{2}m{v^2} + \frac{1}{2}I{\omega ^2}">
<mrow>
<msub>
<mi>E</mi>
<mrow>
<mtext>k</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>I</mi>
<mrow>
<msup>
<mi>ω</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></span><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"> ✔</span></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{2}m{v^2} + \frac{1}{2} \times \frac{2}{5}m{r^2} \times {\left( {\frac{v}{r}} \right)^2}">
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mn>2</mn>
<mn>5</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mi>v</mi>
<mi>r</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</math></span> <span style="background-color:#ffffff;">✔</span></p>
<p><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{7}{{10}}m{v^2}">
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span>»</span></p>
<p style="text-align:left;"> </p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Answer is given in the question so check working is correct at each stage.</span></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;">Initial <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_K} = \frac{7}{{10}} \times 1.50 \times {0.5^2}">
<mrow>
<msub>
<mi>E</mi>
<mi>K</mi>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mn>7</mn>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>×</mo>
<mn>1.50</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>0.5</mn>
<mn>2</mn>
</msup>
</mrow>
</math></span> «=0.26J» ✔</span></p>
<p style="text-align:left;">Final <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_K} = 0.26 + 1.5 \times 9.81 \times 0.45">
<mrow>
<msub>
<mi>E</mi>
<mi>K</mi>
</msub>
</mrow>
<mo>=</mo>
<mn>0.26</mn>
<mo>+</mo>
<mn>1.5</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>0.45</mn>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«=6.88J» </span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = « \sqrt {\frac{{10}}{7} \times \frac{{6.88}}{{1.5}}} =» 2.56">
<mi>v</mi>
<mo>=</mo>
<mrow>
<mo>«</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>10</mn>
</mrow>
<mn>7</mn>
</mfrac>
<mo>×</mo>
<mfrac>
<mrow>
<mn>6.88</mn>
</mrow>
<mrow>
<mn>1.5</mn>
</mrow>
</mfrac>
</msqrt>
<mo>=</mo>
<mrow>
<mo>»</mo>
</mrow>
<mn>2.56</mn>
</math></span> «m s<sup>–1</sup>» ✔</span></span></span></p>
<p style="text-align:left;"> </p>
<p style="text-align:left;"><span style="background-color:#ffffff;">Other solution methods are possible.</span></p>
<p style="text-align:left;"> </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>The derivation of the formula for the total kinetic energy of a rolling ball was well answered.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Although there were many correct answers, many candidates forgot to include the initial kinetic energy of the ball at the top of the ramp. The process followed to obtain the answer was too often poorly presented, candidates are encouraged to explain what is being calculated rather than just writing numbers.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>