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<h2>HL Paper 2</h2><div class="specification">
<p>The ball is now displaced through a small distance <em>x </em>from the bottom of the bowl and is then released from rest.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.19.20.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d"></p>
<p>The magnitude of the force on the ball towards the equilibrium position is given by</p>
<p style="text-align: left;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{mgx}}{R}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mi>x</mi>
</mrow>
<mi>R</mi>
</mfrac>
</math></span></p>
<p>where <em>R </em>is the radius of the bowl.</p>
</div>
<div class="specification">
<p>A small ball of mass <em>m </em>is moving in a horizontal circle on the inside surface of a frictionless hemispherical bowl.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_12.45.38.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a"></p>
<p>The normal reaction force <em>N </em>makes an angle <em>θ</em> to the horizontal.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the resultant force on the ball.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, construct an arrow of the correct length to represent the weight of the ball.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the magnitude of the net force <em>F </em>on the ball is given by the following equation.</p>
<p> <span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="F = \frac{{mg}}{{\tan \theta }}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The radius of the bowl is 8.0 m and <em>θ</em> = 22°. Determine the speed of the ball.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ball will perform simple harmonic oscillations about the equilibrium position.</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>Show that the period of oscillation of the ball is about 6 s.</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>The amplitude of oscillation is 0.12 m. On the axes, draw a graph to show the variation with time <em>t </em>of the velocity <strong><em>v </em></strong>of the ball during one period.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.</p>
<p> <img src="images/Schermafbeelding_2018-08-12_om_13.41.19.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.d"></p>
<p>The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>towards the centre <strong>«</strong>of the circle<strong>» </strong>/ horizontally to the right</p>
<p> </p>
<p><em>Do not accept towards the centre of the bowl</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>downward vertical arrow of any length</p>
<p>arrow of correct length</p>
<p> </p>
<p><em>Judge the length of the vertical arrow by eye. The construction lines are not required. A label is not required</em></p>
<p><em>eg</em>: <img src="images/Schermafbeelding_2018-08-12_om_13.22.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>F</em> = <em>N</em> cos <em>θ</em></p>
<p><em>mg</em> = <em>N</em> sin <em>θ</em></p>
<p>dividing/substituting to get result</p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>right angle triangle drawn with <em>F</em>, <em>N </em>and <em>W/mg </em>labelled</p>
<p>angle correctly labelled and arrows on forces in correct directions</p>
<p>correct use of trigonometry leading to the required relationship</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-12_om_13.28.39.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/01.a.ii"></p>
<p><em>tan θ</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\text{O}}}{A} = \frac{{mg}}{F}">
<mfrac>
<mrow>
<mtext>O</mtext>
</mrow>
<mi>A</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mi>F</mi>
</mfrac>
</math></span></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{mg}}{{\tan \theta }}">
<mfrac>
<mrow>
<mi>m</mi>
<mi>g</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</math></span> = <em>m</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v^2}}}{r}">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>r</mi>
</mfrac>
</math></span></p>
<p><em>r</em> = <em>R</em> cos <em>θ</em></p>
<p><em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{gR{{\cos }^2}\theta }}{{\sin \theta }}} /\sqrt {\frac{{gR\cos \theta }}{{\tan \theta }}} /\sqrt {\frac{{9.81 \times 8.0\cos 22}}{{\tan 22}}} ">
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mrow>
<msup>
<mrow>
<mi>cos</mi>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mi>θ</mi>
</mrow>
<mrow>
<mi>sin</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mi>g</mi>
<mi>R</mi>
<mi>cos</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mi>θ</mi>
</mrow>
</mfrac>
</msqrt>
<mrow>
<mo>/</mo>
</mrow>
<msqrt>
<mfrac>
<mrow>
<mn>9.81</mn>
<mo>×</mo>
<mn>8.0</mn>
<mi>cos</mi>
<mo></mo>
<mn>22</mn>
</mrow>
<mrow>
<mi>tan</mi>
<mo></mo>
<mn>22</mn>
</mrow>
</mfrac>
</msqrt>
</math></span></p>
<p><em>v</em> = 13.4/13 <strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[4] </em></strong><em>for a bald correct answer </em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for an answer of 13.9/14 </em><strong>«</strong><em>ms <sup>–</sup></em><em><sup>1</sup></em><strong>»</strong><em>. MP2 omitted</em></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>there is no force to balance the weight/N is horizontal</p>
<p>so no / it is not possible</p>
<p> </p>
<p><em>Must see correct justification to award MP2</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the <strong>«</strong>restoring<strong>» </strong>force/acceleration is proportional to displacement</p>
<p> </p>
<p><em>Direction is not required</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><em>ω</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{g}{R}} ">
<msqrt>
<mfrac>
<mi>g</mi>
<mi>R</mi>
</mfrac>
</msqrt>
</math></span><strong>»</strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{9.81}}{{8.0}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>9.81</mn>
</mrow>
<mrow>
<mn>8.0</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> <strong>«</strong>= 1.107 s<sup>–1</sup><strong>»</strong></p>
<p><em>T</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{\omega }">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>ω</mi>
</mfrac>
</math></span> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{1.107}}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>1.107</mn>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 5.7 <strong>«</strong>s<strong>»</strong></p>
<p> </p>
<p><em>Allow use of </em>or <em>g = 9.8 or 10</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for a substitution into T = 2π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{I}{g}} ">
<msqrt>
<mfrac>
<mi>I</mi>
<mi>g</mi>
</mfrac>
</msqrt>
</math></span></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>sine graph</p>
<p>correct amplitude <strong>«</strong>0.13 m s<sup>–1</sup><strong>»</strong></p>
<p>correct period and only 1 period shown</p>
<p> </p>
<p><em>Accept ± sine for shape of the graph. Accept 5.7 s or 6.0 s for the correct period.</em></p>
<p><em>Amplitude should be correct to ±</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>square for MP2</em></p>
<p><em>eg: v /</em>m s<sup>–1 </sup> <img src="images/Schermafbeelding_2018-08-14_om_06.59.06.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/01.d.iii"></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>speed before collision <em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gR} "> <msqrt> <mn>2</mn> <mi>g</mi> <mi>R</mi> </msqrt> </math></span> =<strong>»</strong> 12.5 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p><strong>«</strong>from conservation of momentum<strong>» </strong>common speed after collision is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></span> initial speed <strong>«</strong><em>v<sub>c</sub></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12.5}}{2}"> <mfrac> <mrow> <mn>12.5</mn> </mrow> <mn>2</mn> </mfrac> </math></span> = 6.25 ms<sup>–1</sup><strong>»</strong></p>
<p><em>h = </em><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{v_c}^2}}{{2g}} = \frac{{{{6.25}^2}}}{{2 \times 9.81}}"> <mfrac> <mrow> <msup> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mn>6.25</mn> </mrow> <mn>2</mn> </msup> </mrow> </mrow> <mrow> <mn>2</mn> <mo>×</mo> <mn>9.81</mn> </mrow> </mfrac> </math></span><strong>»</strong> 2.0 <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><em>Allow 12.5 from incorrect use of kinematics equations</em></p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for mg(8) = 2mgh leading to h = 4 m if done in one step.</em></p>
<p><em>Allow ECF from MP1</em></p>
<p><em>Allow ECF from MP2</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">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.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.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">d.iii.</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 vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The centre of the ball, still carrying a charge of 1.2 × 10<sup>−6 </sup>C, is now placed 0.40 m from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.</p>
<p>P is the point on the line joining the charges where the electric field strength is zero. The distance PQ is 0.22 m.</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>The charge per unit area on the surface of the wall is<em> σ</em>. It can be shown that the electric field strength <em>E</em> due to the charge on the wall is given by the equation</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mi>σ</mi><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac></math>.</p>
<p>Demonstrate that the units of the quantities in this equation are consistent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.</p>
<p>Determine the horizontal force that acts on the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge on the ball is 1.2 × 10<sup>−6 </sup>C. Determine <em>σ</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread breaks. Explain the initial subsequent motion of the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the charge on Q. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, without calculation, whether or not the electric potential at P is zero.</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>identifies units of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>C</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>×</mo><mfrac><mrow><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><msup><mi>C</mi><mn>2</mn></msup></mfrac></math> seen and reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>N C</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <strong>✓</strong></p>
<p> </p>
<p><em>Accept any analysis (eg dimensional) that yields answer correctly</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on ball <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>T</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>30</mn></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>cos</mi><mo> </mo><mn>30</mn></mrow></mfrac></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo> </mo><mo>«</mo><mo>=</mo><mi>m</mi><mi>g</mi><mo> </mo><mi>tan</mi><mo> </mo><mn>30</mn><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mo> </mo><mn>9</mn><mo>.</mo><mn>8</mn><mo> </mo><mo>×</mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>»</mo><mo> </mo><mo>=</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>14</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow g = 10 N kg<sup>−1</sup></em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer.</em></p>
<p><em>Award <strong>[1max]</strong> for an answer of zero, interpreting that the horizontal force refers to the horizontal component of the net force.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>»</mo></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>85</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em> <br>Allow <strong>ECF</strong> from the calculated F in (b)(i)</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal/repulsive force and vertical force/pull of gravity act on the ball <strong>✓</strong></p>
<p>so ball has constant acceleration/constant net force <strong>✓</strong></p>
<p>motion is in a straight line <strong>✓</strong></p>
<p>at 30° to vertical away from wall/along original line of thread <strong>✓</strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>Q</mi><mrow><mn>0</mn><mo>.</mo><msup><mn>22</mn><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>18</mn><mn>2</mn></msup></mrow></mfrac></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>+</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><mtext>C</mtext><mo>»</mo></math><strong>✓</strong></p>
<p>2sf<strong> ✓</strong></p>
<p><em><br>Do not award <strong>MP2</strong> if charge is negative </em></p>
<p><em>Any answer given to 2 sig figs scores <strong>MP3</strong></em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>work must be done to move a «positive» charge from infinity to P «as both charges are positive»<br><em><strong>OR</strong></em><br>reference to both potentials positive and added<br><em><strong>OR</strong></em><br>identifies field as gradient of potential and with zero value <strong>✓</strong></p>
<p>therefore, point P is at a positive / non-zero potential<strong> ✓</strong></p>
<p><em><br>Award <strong>[0]</strong> for bald answer that P has non-zero potential</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 pipe is open at both ends. A first-harmonic standing wave is set up in the pipe. The diagram shows the variation of displacement of air molecules in the pipe with distance along the pipe at time <em>t</em> = 0. The frequency of the first harmonic is <em>f</em>.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>A transmitter of electromagnetic waves is next to a long straight vertical wall that acts as a plane mirror to the waves. An observer on a boat detects the waves both directly and as an image from the other side of the wall. The diagram shows one ray from the transmitter reflected at the wall and the position of the image.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the diagram, the variation of displacement of the air molecules with distance along the pipe when <em>t</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{4f}}">
<mfrac>
<mn>3</mn>
<mrow>
<mn>4</mn>
<mi>f</mi>
</mrow>
</mfrac>
</math></span>.</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>An air molecule is situated at point X in the pipe at <em>t</em> = 0. Describe the motion of this air molecule during one complete cycle of the standing wave beginning from <em>t</em> = 0.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The speed of sound <em>c</em> for longitudinal waves in air is given by</p>
<p style="text-align: center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="c = \sqrt {\frac{K}{\rho }} ">
<mi>c</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mi>K</mi>
<mi>ρ</mi>
</mfrac>
</msqrt>
</math></span></p>
<p>where <em>ρ</em> is the density of the air and <em>K</em> is a constant.</p>
<p>A student measures <em>f</em> to be 120 Hz when the length of the pipe is 1.4 m. The density of the air in the pipe is 1.3 kg m<sup>–3</sup>. Determine the value of <em>K</em> for air. State your answer with the appropriate fundamental (SI) unit.</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>Demonstrate, using a second ray, that the image appears to come from the position indicated.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the observer detects a series of increases and decreases in the intensity of the received signal as the boat moves along the line XY.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>horizontal line shown in centre of pipe ✔</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«air molecule» moves to the right and then back to the left ✔</p>
<p>returns to X/original position ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>wavelength = 2 × 1.4 «= 2.8 m» ✔</p>
<p><em>c</em> = «<em>f λ</em> =» 120 × 2.8 «= 340 m s<sup>−1</sup>» ✔</p>
<p><em>K</em> = «<em>ρc</em><sup>2</sup> = 1.3 × 340<sup>2</sup> =» 1.5 × 10<sup>5</sup> ✔</p>
<p>kg m<sup>–1 </sup>s<sup>–2</sup> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>construction showing formation of image ✔</p>
<p><em>Another straight line/ray from image through the wall with line/ray from intersection at wall back to transmitter. Reflected ray must intersect boat.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>interference pattern is observed</p>
<p><em><strong>OR</strong></em></p>
<p>interference/superposition mentioned ✔</p>
<p><br>maximum when two waves occur in phase/path difference is nλ</p>
<p><em><strong>OR</strong></em></p>
<p>minimum when two waves occur 180° out of phase/path difference is (n + ½)λ ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.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 lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The following data are available for the lamps when at their working temperature.</p>
<p> </p>
<p style="padding-left: 90px;">Lamp specifications 24 V, 5.0 W</p>
<p style="padding-left: 90px;">Power supply emf 24 V</p>
<p style="padding-left: 90px;">Power supply maximum current 8.0 A</p>
<p style="padding-left: 90px;">Length of each rod 12.5 m</p>
<p style="padding-left: 90px;">Resistivity of rod metal 7.2 × 10<sup>–7</sup> Ω m</p>
</div>
<div class="specification">
<p>A step-down transformer is used to transfer energy to the two rods. The primary coil of this transformer is connected to an alternating mains supply that has an emf of root mean square (rms) magnitude 240 V. The transformer is 95 % efficient.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline <strong>one</strong> other electrical advantage of this system compared to one in which the lamps are connected in series.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how eddy currents reduce transformer efficiency.</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>Determine the peak current in the primary coil when operating with the maximum number of lamps.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt {\frac{{\rho l}}{{\pi {\text{R}}}}} ">
<mi>r</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>l</mi>
</mrow>
<mrow>
<mi>π</mi>
<mrow>
<mtext>R</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{\pi \times 0.1}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mi>π</mi>
<mo>×</mo>
<mn>0.1</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em>For MP2 accept any SF </em></p>
<p><em>For MP3 accept only 2 SF </em></p>
<p><em>For MP3 accept <strong>ANY</strong> answer given to 2 SF</em></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{0.1}}">
<mi>A</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mn>0.1</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em>For MP2 accept any SF </em></p>
<p><em>For MP3 accept only 2 SF </em></p>
<p><em>For MP3 accept <strong>ANY</strong> answer given to 2 SF</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current in lamp = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{{24}}">
<mfrac>
<mn>5</mn>
<mrow>
<mn>24</mn>
</mrow>
</mfrac>
</math></span> «= 0.21» «A»</p>
<p><em><strong>OR</strong></em></p>
<p><em>n</em> = 24 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{5}}">
<mfrac>
<mn>8</mn>
<mrow>
<mn>5</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>so «38.4 and therefore» 38 lamps ✔</p>
<p> </p>
<p><em>Do not award ECF from MP1</em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>when adding more lamps in parallel the brightness stays the same ✔</p>
<p>when adding more lamps in parallel the pd across each remains the same/at the operating value/24 V ✔</p>
<p>when adding more lamps in parallel the current through each remains the same ✔</p>
<p>lamps can be controlled independently ✔</p>
<p>the pd across each bulb is larger in parallel ✔</p>
<p>the current in each bulb is greater in parallel ✔</p>
<p>lamps will be brighter in parallel than in series ✔</p>
<p>In parallel the pd across the lamps will be the operating value/24 V ✔</p>
<p> </p>
<p><em>Accept converse arguments for adding lamps in series:</em></p>
<p><em>when adding more lamps in series the brightness decreases</em></p>
<p><em>when adding more lamps in series the pd decreases</em></p>
<p><em>when adding more lamps in series the current decreases</em></p>
<p><em>lamps can’t be controlled independently</em></p>
<p><em>the pd across each bulb is smaller in series</em></p>
<p><em>the current in each bulb is smaller in series</em></p>
<p> </p>
<p><em>in series the pd across the lamps will less than the operating value/24 V</em></p>
<p><em>Do not accept statements that only compare the overall resistance of the combination of bulbs.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«as flux linkage change occurs in core, induced emfs appear so» <span style="text-decoration: underline;">current</span> is <span style="text-decoration: underline;">induced</span> ✔</p>
<p>induced currents give rise to resistive forces ✔</p>
<p>eddy currents cause thermal energy losses «in conducting core» ✔</p>
<p>power dissipated by eddy currents is drawn from the primary coil/reduces power delivered to the secondary ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power = 190 <em><strong>OR</strong> </em>192 «W» ✔</p>
<p>required power <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 190 \times \frac{{100}}{{95}}">
<mo>=</mo>
<mn>190</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>100</mn>
</mrow>
<mrow>
<mn>95</mn>
</mrow>
</mfrac>
</math></span> «200 <em><strong>or</strong> </em>202 W» ✔</p>
<p>so <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{200}}{{240}} = 0.83">
<mfrac>
<mrow>
<mn>200</mn>
</mrow>
<mrow>
<mn>240</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.83</mn>
</math></span> <em><strong>OR</strong> </em>0.84 «A rms» ✔</p>
<p>peak current = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.83 \times \sqrt 2 ">
<mn>0.83</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
</msqrt>
</math></span> <em><strong>OR</strong> </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.84 \times \sqrt 2 ">
<mn>0.84</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
</msqrt>
</math></span>» = 1.2/1.3 «A» ✔</p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A fixed horizontal coil is connected to an ideal voltmeter. A bar magnet is released from rest so that it falls vertically through the coil along the central axis of the coil.</p>
<p style="text-align: center;"><img 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"></p>
<p>The variation with time<em> t</em> of the emf induced in the coil is shown.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the maximum magnitude of the rate of change of flux linked with the coil.</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>State the fundamental SI unit for your answer to (a)(i).</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>Explain why the graph becomes negative.</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>Part of the graph is above the <em>t</em>-axis and part is below. Outline why the areas between the <em>t</em>-axis and the curve for these two parts are likely to be the same.</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>Predict the changes to the graph when the magnet is dropped from a lower height above the coil.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«−» 5.0 «mV» <em><strong>OR</strong> </em>5.0 × 10<sup>−3</sup> «V» ✓</p>
<p> </p>
<p><em>Accept 5.1</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>kg m<sup>2 </sup>A<sup>−1 </sup>s<sup>−3</sup> ✓</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>Flux linkage is represented by magnetic field lines through the coil ✓</p>
<p>when magnet has passed through the coil / is moving away ✓</p>
<p>flux «linkage» is decreasing ✓</p>
<p>suitable comment that it is the opposite when above ✓</p>
<p>when the magnet goes through the midpoint the induced emf is zero ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>reference to / states Lenz’s law ✓</p>
<p>when magnet has passed through the coil / is moving away ✓</p>
<p>«coil attracts outgoing S pole so» induced field is downwards ✓</p>
<p>before «coil repels incoming N pole so» induced field is upwards<br><em><strong>OR</strong></em><br>induced field has reversed ✓</p>
<p>when the magnet goes through the midpoint the induced emf is zero ✓</p>
<p> </p>
<p><em><strong>OWTTE</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>area represents the total change in flux «linkage» ✓</p>
<p>the change in flux is the same going in and out ✓</p>
<p>«when magnet is approaching» flux increases to a maximum ✓</p>
<p>«when magnet is receding» flux decreases to zero ✓</p>
<p>«so areas must be the same»</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>magnet moves slower ✓</p>
<p>overall time «for interaction» will be longer ✓</p>
<p>peaks will be smaller ✓</p>
<p>areas will be the same as before ✓</p>
<p> </p>
<p><em>Allow a graphical interpretation for <strong>MP2</strong> as “graph more spread out”</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>ai<br>Well answered, with wrong answers stating 8 for the difference or 3 without realising that the sign does not matter.</p>
<p>aii<br>Very few candidates managed to get the correct fundamental SI unit for V. All kinds of errors were observed, from power errors to the use of C as a fundamental unit instead of A.</p>
<p>bi) Most scored best by marking using an alternative method introduced to the markscheme in standardisation. There were some confused and vague comments. Clear, concise answers were rare.</p>
<p>bii) It was common to see conservation of energy invoked here with suggestions that energy was the area under the graph. Many candidates described the shapes to explain why the areas were the same rather than talking about the physics e.g. one peak is short and fat and the other is tall and thin so they balance out.</p>
<p>c) A surprising number didn't pick up on the fact that the magnet would be moving slower. As a result, they discussed everything happening sooner, i.e. the interaction with the magnet and the coil, and that led onto things happening quicker so peaks being bigger.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The table gives data for Jupiter and three of its moons, including the radius <em>r</em> of each object.</p>
<p style="text-align: center;"><img 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BEfwUb+EzMxgJGaF3/65SPjwZvmcWOM/n0/whzfGWebsM83f4tK3j+NQArE0xBOayC5nZaapxxLXp+CL5ysXwfsrxrh4EUeRLmUP/svQnAtjIj82px8dg0Ekttr8LTXy+R1L2Jt41P8/8Epxf8fLJa9y41kWWpff6ZdN7r7RpY124f7FP9/cE3x/weLZe9yI1mW2hT/RanNml2U2AFhRbmU4j+AjLOXjMg/249c73gEktvjMZ3BYvI6Awtr+BDlUor/GvxWo4jIr07Kh5dAILm9BE27nUxed0OWEwIEolxK8Q8AW6k7In+lGO8aS3K7JvPJ65q8jogqyqUU/xFsnLxmRP7JbuRyHRBIbjuAOoHJ5HUCEhZxIcqlFP9FCK6FEZFfm5PProFAcnsNnvZ6mbzuRSzHRwhEufSF+DMoP4lB5kDmQOZA5kDmwDo5UDoYfCH+pQHZd30EKOJsayKQ3CavayKQUR2FQLRHpPgfhfDEdiLyJ3Y5XWtEILltBOpiw5LXixE2sbtRLqX4T0zaUa5F5B9lP+2MQyC5HYd9z5WT157o3st2lEsp/jfIg4j8G4S+fIjJ7ZoUJ69r8joiqiiXUvxHsHHymhH5J7uRy3VAILntAOoEJpPXCUhYxIUol1L8FyG4FkZEfm1OPrsGAsntNXja62XyuhexHB8hEOVSin+E2EL9EfkLhXjbUJLbNalPXtfkdURUUS6l+I9g4+Q1I/JPdmOJ5X777dfPfwvj+++/e40JfO2HMWe15PZ4pD98+OULPt+8+eb4RTYsJq8bAOXjZgSiXErxb4bwugMj8q8b0TjPv/76q5c///zj5dOnTy+IAv99cLWPHz++vH37rb6eck1u+8L8/v3PL2ce5hRN8iok8vosAlEupfg/i+wF5kfkX8D1qV1E6K3480vA2UKR3PZLEQ55I976iSh57cfr3SxHuXQp8WejJRDeuo5qnOx5m1Pj7c1u6Oq/8jUiv3dMYAm2f//91+ZSiCZj8ZUN9wwRRbz5ide3H3/84fPPvvhUGoMw2Lf8UUIxglv/szg+6AN2LS3CvmXunjHv3v30UvLJx8A430Yc5uTDCF61dl7XQiDKpduLv6eZTYkDwUotIr9njAg/Is7aW+Iv4bfjem+82Mc3L+xwTw7IF4kE4q7GM8bYQyjzvC2N73kdwW0pHmLnoATvWy3Cfmve3udwAj5e/Dnc46sOmPDpD3lwS5/leO/6z4yfhddnYsi5cyAQ5VKKv+Mnxd8B8sBXhEA4kngS0sgUYuDfvNiYe/zkKrsSdS/YrFnrU2xeFIjXHhCiWI/ujwr76HVq9vQLj8fNz9nC3o9/9Dv5Rk4h/vDpxZ9c47ltvo8Dgh9jx/e+n4HX3jGm/XMQiHLp0uKvtzQLoe1jEyBwCltvoVztz/qM54RPYwNnPB/10c+mZvvtJqe3CDYYxmB/toZfZzY2TcQRbFh7S/zBGh5s01wvshoD3pYH9cN1qd8+xx/s4psfiy82P5jHWoqJOfajt0f6Wt565cdRV9Yd3cCH2tlqcFPD3s+Hm5IAg3mpX/OZJ17xC/9sY67PN8b7msffUW0GXkfFnusei0CUS7cQf7uhU+SAIUGy4g/kbBZ2Y+CePm3sEnttLhIpbRSyeyx9z1mLyH/O6vZsYbOFCZux8JNVNnjLk/p1RbzhRTzQjw1vR+P9tST+cMyaXvyVA97GDN9HcavY4baEmZ6XriXsS+Pog08r9OQFvGOjpTHWiz8HdFvj2FGuttptWfuZMaN5fcb3nDsXAlEu3UL8faFT/BIJntkTP5uFHc8zvd2JUgRHb/jaNEb85Ct/tq4R+Vvznn0ubLbEX3jqgMV48MXvrbkIA/NLB4ia/yUBioSMfCAvZmyjuBUW1JFqQX1b1xL2tTnil+se4cdmSfypaVvjjFOupvjXmMhnV0Qg2iNuIf4Utm36GZe+mvhLDADPf3Rg0KaxJVJ2/bPvI/J7+7EHGzZ2YSxB57sOBDVfGbdXnEsClG/+NZTLz0pCWh75T28J+3+elu/ICXjeK84l8eewkuJfxjl710OAuim1FP/Km7/Ev/ZWv0fgSgSc0ReR33vtZ7DhMKADVs1PHRSOePNnHdb0v/T4n55r/pz9bBS3xEldsH6tPkp47BX/o9/8S7kC5y35VoqnR99IXnvEkzbHIRDl0tTi798qvCBwevc/OVLYeguUeDPPNnvyr735s0nhg59vbT0jcNZOz/uI/J5rYrsVG8RVnMmnLcGFG+ZYbpjDp6VFAkRuWJvY0gGjxe7ZY0ZxS5zg9IhgRtiXsPN5cMS/+XubigWeZ2kjeZ0Fg/TjGASiXJpa/Pl5ns2YzYJGcdoCZSMgMESGpu8SEok/G5R+lpfYy6a+vxr4/38jtALCPfO1Bj8N44P+j4haBU72R1wj8nv70oqNxgljrvBee6MEfy/SxANfpX4fayRAzGVt5YtyquaLt33m91HcEiMcqNb2xBxh723Aha13PYcT1Z/6oiv++bH6xQI7NLguHfoim2f0j+T1jPhyjfMQiHJpavFnk6D4cZ4P9xJtQYd42+ds/tqQJP4ScNnQxo4NL/7a7BmrtdiEtAZX7KlJuKxNPZvlis8jWoSN8LSYgTuHLHyFPx0EevkdCZDPOfzB31nbKG7BoySswkm1V8Iuwl5zj7xGPtp9Awz9AeFIHx6xNZLXR/zNOfMiEOXS1OL/LJzagHoLybN+9p4fkd973bTfH4Hktj/GI1ZIXkegvuaaUS6l+K/J9xdRReR/MSi/XBKB5PaStG06nbxuQpQDGhGIcinFvxHAKw+LyL9yTOn7/yGQ3K6ZCcnrmryOiCrKpaXFfwTQM64ZkT+jr+nTPgSS2314XWV08noVpub3M8qlFP/5uXvaw4j8pw2ngeEIJLfDKejiQPLaBdZbGo1yKcX/BukQkX+D0JcPMbldk+LkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXErxjxBbqD8if6EQbxtKcrsm9cnrmryOiCrKpRT/EWycvGZE/slu5HIdEEhuO4A6gcnkdQISFnEhyqUvxJ9B+UkMMgcyBzIHMgcyB9bJgdI55gvxLw3IvusjQBFnWxOB5DZ5XROBjOooBKI9IsX/KIQnthORP7HL6VojAsltI1AXG5a8Xoywid2NcinFf2LSjnItIv8o+2lnHALJ7Tjse66cvPZE9162o1xK8b9BHkTk3yD05UNMbtekOHldk9cRUUW5lOI/go2T14zIP9mNXK4DAsltB1AnMJm8TkDCIi5EuZTivwjBtTAi8mtz8tk1EEhur8HTXi+T172I5fgIgSiXUvwjxBbqj8hfKMTbhpLcrkl98romryOiinIpxX8EGyevGZF/shtLLPfbb79+/lsY33//3WtMpb6zgk1u+yD94cMvrzx//fVXL3///VefRSpWk9cKOJM8evfup9ccefPmmyE50gpDlEsp/q0IXnhcRP6FQxrmOmLw559/vHz69OmFov/99/+8lPrOcjC5PR5pxP7t229fDXMI+PHHH45fZMNi8roB0ODH5Aj1TyNH3r//ebBH8fJRLqX4x5gt8yQif5kABwWCQCD+tpX67POj75PboxH9v82cjR1sdbA7fpW6xeS1js/opx8/fvws/vzyl+I/mhG3PoVLEdkPb2x3a2dvJAgiIsi6cMDJeKtRQOKLjZfvvRs+lnzjTU85E/nP2z/zbSv12ec97s/mthQDP3+2vB2zYfJPJcKWeb1b5Bu8yw+u1heekYPsFfZXgN6+Wvsz8Gr9efae2iAmf1j2doW3uCnVp5/z7PdHcoQ1bS7j96wtyqXl3/xJNoI/I4muRn4Pf9kwEUyKnWZ/Ho/Wk/DbAqKweh4AVLg+LzjBI+ryhefkj+IhBm1Q9iBZ6oviPbI/Kuwj16jZAi98aBF/f9iCg55vTJFv7AnkqPIL7uwhD851GLBveDUcjn42mtcj49EeQEw18QdrywM+wKG4ONIn2Xo0R8gd5bxqXzZnu0a5tLz4QwzB+01+NoJ6+hOR32NNcKaAbaNI2OijxjNf4BSX/k0tmvdIv+xK1H1esGatj2eImBX+Ut8jvj0y50xurX/UlcQbzLQR2jH2XnXIVQ3cfK7o2TPXLd/INZ+Pto+DnnKPez/2Gd9a547itdW/PePADzyJqSb+5INwl30OBMzjemR7NkfwVXsWtvyvgEf6+qytKJduK/468QGMP20+C/Zs8yPye/hZ2tC3xB/84cM2/WJjRdY+xyZr+UZBlvo1jucUK3bBxY/FF79ByX/NYZ4+zNe9rnqj1Jo9r6w5ohG3sGPj6yH+2C8JL/iW+oXDlm/M9fnGHHsQIU/Alj7y5ew2itej49Rhm0MUMfnasuuRQ15EVXPRvFE5gl/4qhyxvwzamGa4j3LpluJPknHCVFGToABEIq3YIvJ7xEpRsGGqGPgO1jVBZDPWKVo+iRNxpH5dVXyWM2x4Oxrvr8z3nOstw280CIXflLy9Ud/P5DaKsUX8mcs4y1eJd78GfFqhJy+wA38treQb+ejFH87BstVuy9rPjJmB12f8Z65+xmcvoI6JydeWXYPciN78bd7YOdzfNUc8DtH3KJduJ/7a4L0YkUA+8SIwr9Yfkd8rDgqVNfVhA641Fb1+2mOjgAvmR+IvewgD81uERHO4lsQ/2qBS/C1y/74vCey/R728HgiVE1w5JLaIrfjlukf48aHkG+um+JcYOrYP7IVzVFt2RT+G3KCuyRW4r7U75kgND/sM/ErtduKvE74XFZIHkFo2oxKQM/dF5PfwGRwRbgk5a1DAWz8LC398laBzb+1E/jKOjWZPK4m/Dob+7STFv45sSWD9DL+x8xxcWw/cEoG99VnyjTUlSvJT+8Je+5p/9PXMmj3ad+zxMmVrssR/aV140MGfq34B9C9rpbl3y5ESBqW+KJdS/P8fLYnPLMVfIvHRvoj8R+3V5lHwFL5tj2ys8MEb2lbTQYGrX7c2tyT+jGdNv9FgF/sztjO5jeIvCawfWxJ6ceAPW34uuSCeWWtPjZZ8K+UKnLfkm/et1/cZeH0mNrAkhtLHH7xq6+jQoH9GjMbeMUciLHx/lEu3E3+93ZU2+Na3EA/u7N8j8nv4zWbri3tL/P1bAn5tCS4CwFoUvRpz+LQ0CY+dzzxywPdJeFrsnj3mTG6j2EoC68eSE4yzTRzUxN/nAXWLndYDQMk3bxOfJB7Wv5H3M/B6ZPwS8RrXOoBZbtVX88XzeZccqWFin0W5tLz4S3jshk6ysMmTkDSSBYDsGAve1e8j8nvEBYZsuMKWNRDP2s/+4kgbA1f4qZ32sVfiC25L/T5WCY8fy/dSbtR88bbP/H4mt1FcJYH1Y8kH/6uKsPZj9Z3n5I5v1Gstn+z4km9wCW7YoeFb6dBn7Zx9PwOvR8YMxsSkGi/ZpibJEb088KK2dfC+c46UMCz1Rbm0tPiXfnrSqZKkARQ+sxV+icBn+iLyn7FZmwu2FnsE2TZhbw8IbMSaw4Zd2ySsrUfvI/Gnnw1HucEVf2dtZ3NbwqEksNrsLXZwylhhC84t/zcdpTVb+0q+MReBkR9cWw8Tres+O24GXp+Nwc5XPti6Vp/NEfqUI+wH9pm1d+T9VXOkFYMol5YW/1ZwVh8Xkb963HeIL7ldk+XkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXErxjxBbqD8if6EQbxtKcrsm9cnrmryOiCrKpRT/EWycvGZE/slu5HIdEEhuO4A6gcnkdQISFnEhyqUU/0UIroURkV+bk8+ugUByew2e9nqZvO5FLMdHCES5lOIfIbZQf0T+QiHeNpTkdk3qk9c1eR0RVZRLKf4j2Dh5zYj8k93I5TogkNx2AHUCk8nrBCQs4kKUSyn+ixBcCyMiv6Fm7ksAABSGSURBVDYnn10DgeT2Gjzt9TJ53YtYjo8QiHIpxT9CbKH+iPyFQrxtKMntmtQnr2vyOiKqKJe+EH8G5ScxyBzIHMgcyBzIHFgnB0qHji/EvzQg+66PAEWcbU0EktvkdU0EMqqjEIj2iBT/oxCe2E5E/sQup2uNCCS3jUBdbFjyejHCJnY3yqUU/4lJO8q1iPyj7KedcQgkt+Ow77ly8toT3XvZjnIpxf8GeRCRf4PQlw8xuV2T4uR1TV5HRBXlUor/CDZOXjMi/2Q3crkOCCS3HUCdwGTyOgEJi7gQ5VKK/yIE18KIyK/NyWfXQCC5vQZPe71MXvciluMjBKJcSvGPEFuoPyJ/oRBvG0pyuyb1yeuavI6IKsqlFP8RbJy8ZkT+yW4ssdxvv/36+W9hfP/9d68x/fnnH5/7Pnz45dQ4k9s+cMMj2H799Vcvf//9V59FKlaT1wo4kzyi/uHpzZtvXj5+/DiJV/92I8qlFP9/Y7VcT0T+coGeEBBigNh/+vTpteh///0/L2/ffvvCoYANAKx5dlZLbo9HGrGHUxqHgB9//OH4RTYsJq8bAA1+TN3bw/+IHGmFIMqlU8VfgOGMPoA24mTdCtyz49hE3r//+VkzT82PyH/KaE5+FQhyWo085nCQ4i9ErnlF8Hmbo2502Ds7kqzZsxHftx458u7dT6+TOPSTJ7O2KJdOE3/9jMZVjU0S8cc53qZWbHcWfxVFy+FOP6GRC/r0Pk3Djc1H5Z9yEj8o6tIY8lVvh8zTPwfobUC2el/xcUSDU8sZWLTwzIYpfpnf+6DEeqU80n4kX7SRgyXPEH98IybL81lYj+L1kfjI/Vbxa6mtK+QIh37llXLpEezOmBPl0iniTwHhAElSahTX2ZtmyY8efcR2xzd/hF9vTy2iwNiSyPbgBJsSLr8mXFkhU2Hbw6kEoSRc2PU2e8WA3aiwe65J3PClzY+12LARgBIm8oXxdg5Y9RRWuAQfuya+sHHjq/Yj+LSHPPjTYUB5rBjOuo7g9ZHYwBJfW8S/pbaukiNgpT2EHKYeZm1RLp0i/hTSniKn4EgCnNYHoLWxKOEoUpKOMdinX6SU1lOBY4c5+CWB4sp8bRg8Z03b2CREuJ7jq23Wb+7xA5tqLTY09qgrvp7Z4EVxszYx1xoYMk781cY++4wNH67xkTW52qZnUZ9iUy4yjrxSjHDubVpbR9+fzS3+gyHrWgyEQxQ7+DDHHqK4p8/X0LMYqcaoO/iEE9uoe1/btg+/mEfj3o+1tnrdj+B1TyxwD65gw7VF/Ldq60o5wl5lc4T8mbVFuXSK+AOSFcAtkBAOW3AATQDaWPSdMdqAuBcZeq4NmfW0YbHRMAd7jNfGw5r0iUTm6rDAfObY7/TZNflOEWBHNvmOTcXeYgM7Rzd8OLOJlxIPJT8eEQGwVT5Ym/BX6tcYnsOtcsCPhWP8to21FBNY2g95Jf/pZ9yZ7Wxua7H5+rBjwVn1aftr98wp4QnmpX7ZYp54pR7hzzbmqibVz3j8VyNPwJY+u4/oee/rTLyWYgUT4QqWFrvSePoYE9UWz+HgSjlCHsGT3fOj2Ef2R7l0ivhDui82Egen7IcNOWrYkDBLVNh01STuskESaTxjIEobRmnjJ/HwRfOZgw35HSUmfrE2gs987m2zsW/ZsPOOvMevEU08bW2e4AJOKib8tdyVfIcnio65aszZmqexpRwQh36DIgdYa8Y2iluPhbi2NWnHCEP4wmc+8K2Dsh1r7+FTdUs/9QUXtk7teH/PWImUntm6Vp/8b7Wreb2us/DaEh/cUr+11lJbmSM1BB9/FuXSKeJfKjYbijYEW3gUOcmgxCIAFXGpUH2f5mGTD8kpoeA79pijxjOfwGwc2KGVDivY4MNcvf15odtjQ74cfcXHEU2ceEy8L2zw5IgVAvAW3368/Y4wgD/XVuFnvnJAOUEffvq8oJ8cgMcZ2yhuPRbgU8MfLqkvOwZc4X2riV+urAN3rY3xPo/wQ3UtO8rVPbY1t8d1Fl5bYgNLv3f6eS21lTniUTvme5RLp4g/BV/bPClqHFThsZGrQEksEofvKuJSofo+nTSxzYf5ss+V9ZijpjH6zhWftUmwtn0DseO4bxX/mg1v86jvEflH2Y/siJMt8S/NF572QFAaRx/x1fKrNE85AO9qyhmbFzwjB/bal83e11Hc2rjI6S182AO80IuD6NcCvwaxqobts9o9fmnf0LjSy4hyda992Tz6OgOvrTG1iH9LbWWOtCK+b1yUS6eIf3TqUwhswCpsjbUbAgW5V/yxTdFT/GxOVnS16dhNfkv8txJcPtZ+9t+yITyOvkbkH72Ot6cN9RHxVx5szYVXuONq3yq9L/67csCKP2PIM88hdm3+eFsjv4/iVjGDCzUGnrUmjvwY8PYc+DGay7VlLTu/JP6lXIFzfJmljeZ1Dw6t+9pWbYlnv3bmiEdk3/col04Rf1yFWJwgUdQ4DSLQ9Gvj1gmR8TQ2FYqVMTrBS1TshlPr80mnjX+P+OMXdqwIKCYJlE6ujKXx3cbcYuN14sH/gw8jmjgRPpEPvImJf41hLnhHDQ7Z2JUnjMOGt1ObDy52PmPxxffBue+L7J7dP4pbOAX/VjHmMO/f/FXr9qDv8YNPW3OIdOua2GKs9g3Z9jbph1+7jsaOuo7i9ZF4W8V/q7YyRx5Bf3tOlEuniT8usqFL7HGID9+tCDNOp3CNoTAZp81DorIl/thiDiJixz4i/thiw2ODkF9sLN53CkHP8Zkx9sDTYoO1jmz4M6KJpy3xh1940qEJX8HO4ub953lJkNnYS/1+vnLAj5Uv8plcBL+aQHnbZ34fwa0OseT2nsZ4izf81mwwtiTIcAL/LQ37fixcght2aHBdEqYW+73GjOD10VjgsXZQl92W2socEVrHXaNcOlX8jwun3VKp+NtnrzEyIr93dJH4swngkwQWP+hjA6GfD997tkj86bcHvDN8eSZO/Du7ccAST/4qoYVbjx3Y8lxzwJm+ni2qfwRLfnCV3z192WMbn67SIvEHU3soaKmtzJHjWY9yaWnx1wnfiszx0M5vMSJ/fs/Twy0EktsthK75PHm9Jm8zeh3l0rLiz4mfoHu/Qc5ItvcpIt+Py+/XQyC5vR5nLR4nry0o5ZgWBKJcWlb8W0C5y5iI/LvEv3Kcye2a7Cava/I6Iqool1L8R7Bx8poR+Se7kct1QCC57QDqBCaT1wlIWMSFKJdS/BchuBZGRH5tTj67BgLJ7TV42utl8roXsRwfIRDlUop/hNhC/RH5C4V421CS2zWpT17X5HVEVFEupfiPYOPkNSPyT3Yjl+uAQHLbAdQJTCavE5CwiAtRLqX4L0JwLYyI/NqcfHYNBJLba/C018vkdS9iOT5CIMqlFP8IsYX6I/IXCvG2oSS3a1KfvK7J64ioolz6QvwZlJ/EIHMgcyBzIHMgc2CdHCgdOr4Q/9KA7Ls+AhRxtjURSG6T1zURyKiOQiDaI1L8j0J4YjsR+RO7nK41IpDcNgJ1sWHJ68UIm9jdKJdS/Ccm7SjXIvKPsp92xiGQ3I7DvufKyWtPdO9lO8qlFP8b5EFE/g1CXz7E5HZNipPXNXkdEVWUSyn+I9g4ec2I/JPdyOU6IJDcdgB1ApPJ6wQkLOJClEsp/osQXAsjIr82J59dA4Hk9ho87fUyed2LWI6PEIhyKcU/Qmyh/oj8hUK8bSjJ7ZrUJ69r8joiqiiXUvxHsHHymhH5J7uRy3VAILntAOoEJpPXCUhYxIUol1L8FyG4FkZEfm1OPisj8Ntvv37+Q1jff//d66A///zjc9+HD7+UJ3bqTW77AAuPYPv111+9/P33X30WqVhNXivgTPKI+oenN2++efn48eMkXv3bjSiXUvz/jdVyPRH5ywV6QkCIAWL/6dOn16L//ff/vLx9++0LhwI2ALDm2VktuT0eacQeTmkcAn788YfjF9mwmLxuADT4MXVvD/8jcqQVgiiXphZ/NtN37376/FZFEHzfu7lSyO/f//yKFaRhBxt8uN/ztrZnbCs5vcdF5PdeF/72vjk9MufROMiLEp8UMpjxwf/SGNZkPvmkhmgwfm9+av4j11HcEqvefPABLPa8IYMp83pjxX5R2pi1Pj7wYZwaz3ibo1+HPT0768raV2kcfMGppYEtY4nP1w/zqX+bV5aXFvuPjHk0R+Sb9qxH1j5jTpRL04q/NlIKVxuEEoPCVF8LeCRZSfxb5tox2MDW1VpEfs844EobaKsoPDLn0Ri0wbAZ2SaO5bNEgrd92/huc0H/HKC3ATu25/0Ibqk9uLWiykbYevCx/0yyp4734giX4GP9xAYHNnyFM5r2GuUCV+0xPLM87/Xh0fEjeH3EV71MtYg/Y4Ura5EHPmfAWjwwhnrS3v2If1tzHs0RYlFeaY/YWmvU8yiXphV/kkAnKwuaNp7SMzvO3mNLCaRkfWTTwcaIjcDG8sh9RP4jtlrmUAzCnLUlpLW5j8yp2YueseGzAalgudqmZ7U+CUIph9isvE1r6+j7s7nFfx10fPxs5Fuxq37BGd+9jSPwgR+JButok5Zt9g5/SLN9xKD9RQdSzT3rOoLXPbHBG7iCI9cW8Wec58LmDLz5/QIuWmzv8Z2xz+YINogdf9nryLNZW5RLU4q/3gy4lprvJ0G0mRAoyaJTPfMlRNxb8SeBGa8NS78s0MeHeYyn6YSoZyQPza+tTeP14ST/g89nNooCbIW1sKr5sHcOm4h4s3bBv9SvMTzHH8+9npM74lx9rIV/NGyTF8xXY45ijPzS2KOvZ3Nb8x8catgzF/zBknH4bnH0thkj3O0zarvUrzHMkx9w5QWHuXoZsHPwn8b+os2c+9pamn/0dSZeS7GR78IVLIVdaaz6GK856rM5g03iVi0xBh5rtkflCHuEzZEZ931hHOXSlOK/RbiC4iqBsQcCitUmTKv4M88WOoRaO/7NHz8BVgcNkpaE8Alu/R1xH5Hf2xdxY4t5a83WOYgGvMKBGny1FmFJ/Dn8gRU+2CbeNYcx+sA9uafvNn+sjV73rDtDE2+2Dr1fYEV9gKNqh/tag0+LKTb84as2vyT++ODFX/7LH9YFW+p/T/7WfNnzbBZeW3xuFX8wFv/YJVfAl7pT8zUN91s1PSpH8A2e8NnGoFhmuUa5dHnxLwGsjUWEQI6K3Ra5NnMJCIlpNxpvWyKgfsb7xGRzAmytrbEjrxH5vX0S1ns2z71z4Av+WjYJG6/nnmf4CVb4YJvn3T4bfT+KWx83NeZrwY6hHtjoha1qVGJrx/p78cuVdVrmyAbj/WEcP7QfaJzybo9tze1xnYXXltjAEkxbmgST+Ph4HuxBmufYbeHkjjnSgjdjolxaQvxJDpKIj00uiU6r+GsDACzs+MTkO7ZorMk4ks62SEDsmLPvI/J7+yE8xUPLeo/MIT7x0rIGY0r8IVDYwgfbLO+2f4b7Udza2KmVLfx5bg8H1A2+t2zsrKW6bh0v/1jXi3/Lm7/mj7rOwGtr7NRHi/jDAzyqUW9woT20tHdimzEt7W450oIJY6JcmlL8dfqLfkIkWZQwGgvxJIqeEbBEhw2AZzSJC5tISQAYgw3GY4Ok1ls8fdrkormlBH5deOD/ROT3dklYi4eW9fbOgXf44mrFZWutiD/45tcb27CL/RnbKG6FBbhQE+AZNdUEvpY+/rDl7Yhfrltr+bmM9+JfyhU4bxEwb7/X99G87omLfXELO9Wbry27p3LvhV7zMkf2MPLl2CiXphR/XKdoo82cBFFB+9Mkc0kiApboYIs+msSFpFJisalEjaTWXK7YUsMP72P+7C90/sFaPPzzJL4TP1tz4A4uLHdw4fmIVoq4h1Nrk/mIhe+L7J7dHxV2bz/gB/z5gOXeBp74vjUXPu3Bi/rasyZjtVfIR2+Tfvyx62jsqOsoXh+Jl32xVfy9iNs91d7LD9Wpn6fnXD2fd8kRi0HtPsqlacWfzYWEonC1QfAGToGyQettHOL5rjEQzzwCloCwAZBYNIkL45VY2tixYzcKjVXiYYMxahJ6rjTW8zY0duQ1Ir+3T8JPPLSs1zoHnsSbtUs+lPrtGO4993rOXDiUz+I4+hVK80ZdR3BL7VFj1NWjDZzxXXVbssOYkiDDia3T0lz1lcRfvxb6um3JG9ntfR3B66MxsS9uiT+24Qw+xTlXak24U3PYES/M4Zndc72Pd84Rj0X0PcqlacWfQNhkSBic14fNXcnDGO5JKD3nnoTgu5KoVfxJPmvLJqb80cFCBwLWYJzW1yEjImJEP76NaJGQix8JrPUtmmPHHHFP3oALvtjm86k0xo4ffT+CW2qQdUsfiTLc1rBTDtha7oFlSfxZhzq1/svvHj48YhPfrtIi8QdTfyiwucMzX3/UP5yJG/Zjvej1wuOqOdKKR5RLU4t/a3A5ro5ARH59Vj69AgLJ7RVY2u9j8rofs5xRRiDKpRT/Ml5L9UbkLxXkTYNJbtckPnldk9cRUUW5lOI/go2T14zIP9mNXK4DAsltB1AnMJm8TkDCIi5EuZTivwjBtTAi8mtz8tk1EEhur8HTXi+T172I5fgIgSiXUvwjxBbqj8hfKMTbhpLcrkl98romryOiinIpxX8EGyevGZF/shu5XAcEktsOoE5gMnmdgIRFXIhyKcV/EYJrYUTk1+bks2sgkNxeg6e9XiavexHL8RECUS6l+EeILdQfkb9QiLcNJbldk/rkdU1eR0QV5VKK/wg2Tl4zIv9kN3K5Dggktx1AncBk8joBCYu4EOVSiv8iBNfCiMivzcln10Agub0GT3u9TF73IpbjIwSiXPpC/BmUn8QgcyBzIHMgcyBzYJ0cKB0MPot/6WH2JQKJQCKQCCQCicB6CKT4r8dpRpQIJAKJQCKQCFQRSPGvwpMPE4FEIBFIBBKB9RBI8V+P04woEUgEEoFEIBGoIpDiX4UnHyYCiUAikAgkAushkOK/HqcZUSKQCCQCiUAiUEUgxb8KTz5MBBKBRCARSATWQ+B/AdhOJMx6FPxkAAAAAElFTkSuQmCC"></p>
</div>
<div class="specification">
<p>A spacecraft is to be sent from <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math> to infinity.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the surface of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>, the gravitational field strength <em>g</em><sub>Io</sub> due to the mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Jupiter</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>orbit</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow><mrow><mo> </mo><mi>gravitational</mi><mo> </mo><mi>potential</mi><mo> </mo><mi>due</mi><mo> </mo><mi>to</mi><mo> </mo><mi>Io</mi><mo> </mo><mi>at</mi><mo> </mo><mi>the</mi><mo> </mo><mi>surface</mi><mo> </mo><mi>of</mi><mo> </mo><mi>Io</mi></mrow></mfrac></math> is about 80.</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, using (b)(i), why it is not correct to use the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>G</mi><mo>×</mo><mtext>mass of Io</mtext></mrow><mtext>radius of Io</mtext></mfrac></msqrt></math> to calculate the speed required for the spacecraft to reach infinity from the surface of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math>.</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>An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation. </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><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mrow><mi>G</mi><mi>M</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn></math><strong> ✓</strong></p>
<p>N kg<sup>−1 </sup><em><strong>OR</strong> </em>m s<sup>−2</sup><strong> ✓</strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math><strong> <em>AND </em> </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math><strong> </strong>seen<strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>27</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>4</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>22</mn></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mn>78</mn></math><strong> ✓</strong></p>
<p><em><br>For <strong>MP1</strong>, potentials can be seen individually or as a ratio.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«this is the escape speed for <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Io</mtext></math> alone but» gravitational potential / field of Jupiter must be taken into account<strong> ✓</strong></p>
<p><em><strong><br>OWTTE</strong></em></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><mi>G</mi><msub><mi>M</mi><mtext>Jupiter</mtext></msub><mfenced><mrow><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>88</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac><mo>-</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>.</mo><mn>06</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></mfrac></mrow></mfenced><mo>=</mo><mo>«</mo><mn>5</mn><mo>.</mo><mn>21</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup><mo> </mo><msup><mtext>J kg</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math><strong> ✓</strong></p>
<p>« multiplies by 3600 kg to get » 1.9 × 10<sup>11 </sup>«J» <strong>✓</strong></p>
<p><em><br>Award <strong>[2]</strong> marks if factor of ½ used, taking into account orbital kinetic energies, leading to a final answer of 9.4 x 10<sup>10 </sup>«J».</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<p><em>Award <strong>[2] marks</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A student strikes a tennis ball that is initially at rest so that it leaves the racquet at a speed of 64 m s<sup>–1</sup>. The ball has a mass of 0.058 kg and the contact between the ball and the racquet lasts for 25 ms.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The student strikes the tennis ball at point P. The tennis ball is initially directed at an angle of 7.00° to the horizontal.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The following data are available.<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Height of P = 2.80 m<br>Distance of student from net = 11.9 m<br>Height of net = 0.910 m<br>Initial speed of tennis ball = 64 m s<sup>-1</sup></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the average force exerted by the racquet on the ball.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the average power delivered to the ball during the impact.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Calculate the time it takes the tennis ball to reach the net.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that the tennis ball passes over the net.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine the speed of the tennis ball as it strikes the ground.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">A student models the bounce of the tennis ball to predict the angle<em> θ</em> at which the ball leaves a surface of clay and a surface of grass.</span></p>
<p><img 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"></p>
<p><span style="background-color:#ffffff;">The model assumes</span></p>
<p><span style="background-color:#ffffff;">• during contact with the surface the ball slides.<br>• the sliding time is the same for both surfaces.<br>• the sliding frictional force is greater for clay than grass.<br>• the normal reaction force is the same for both surfaces.</span></p>
<p><span style="background-color:#ffffff;">Predict for the student’s model, without calculation, whether <em>θ</em> is greater for a clay surface <strong>or</strong> for a grass surface.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F = \frac{{\Delta mv}}{{\Delta t}}/m\frac{{\Delta v}}{{\Delta t}}/\frac{{0.058 \times 64.0}}{{25 \times {{10}^{ - 3}}}}">
<mi>F</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mi>m</mi>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>0.058</mn>
<mo>×</mo>
<mn>64.0</mn>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="F">
<mi>F</mi>
</math></span></span><em><span style="background-color:#ffffff;"> = </span></em><span style="background-color:#ffffff;">148 «N»≈150<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«N</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> </p>
<p> </p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 1</strong></em></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = \frac{{\frac{1}{2}m{v^2}}}{t}/\frac{{\frac{1}{2} \times 0.058 \times {{64.0}^2}}}{{25 \times {{10}^{ - 3}}}}">
<mi>P</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>t</mi>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>64.0</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> ✔</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 4700/4800">
<mi>P</mi>
<mo>=</mo>
<mn>4700</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>4800</mn>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{W}}">
<mrow>
<mtext>W</mtext>
</mrow>
</math></span>»</span></span><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></span></p>
<p> </p>
<p><span style="background-color:#ffffff;"><em><strong>ALTERNATIVE 2</strong></em></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = {\text{average}}Fv{\text{ / 148}} \times \frac{{64.0}}{2}">
<mi>P</mi>
<mo>=</mo>
<mrow>
<mtext>average</mtext>
</mrow>
<mi>F</mi>
<mi>v</mi>
<mrow>
<mtext> / 148</mtext>
</mrow>
<mo>×</mo>
<mfrac>
<mrow>
<mn>64.0</mn>
</mrow>
<mn>2</mn>
</mfrac>
</math></span></span> <em><strong><span style="background-color:#ffffff;"> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></strong></em></span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = 4700/4800">
<mi>P</mi>
<mo>=</mo>
<mn>4700</mn>
<mrow>
<mo>/</mo>
</mrow>
<mn>4800</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;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{W}}">
<mrow>
<mtext>W</mtext>
</mrow>
</math></span></span>»</span><span style="background-color:#ffffff;"> </span><span style="background-color:#ffffff;"><em><strong><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;">✔</span></strong></em></span></p>
<p><span style="background-color:#ffffff;"> </span></p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">horizontal component of velocity is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="64.0 \times \cos 7^\circ = 63.52">
<mn>64.0</mn>
<mo>×</mo>
<mi>cos</mi>
<mo></mo>
<msup>
<mn>7</mn>
<mo>∘</mo>
</msup>
<mo>=</mo>
<mn>63.52</mn>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{m }}{{\text{s}}^{ - 1}}">
<mrow>
<mtext>m </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» ✔ <br></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = ">
<mi>t</mi>
<mo>=</mo>
</math></span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{11.9}}{{63.52}}">
<mfrac>
<mrow>
<mn>11.9</mn>
</mrow>
<mrow>
<mn>63.52</mn>
</mrow>
</mfrac>
</math></span>»<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{0}}{\text{.187/0}}{\text{.19}}">
<mrow>
<mtext>0</mtext>
</mrow>
<mrow>
<mtext>.187/0</mtext>
</mrow>
<mrow>
<mtext>.19</mtext>
</mrow>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{s}}">
<mrow>
<mtext>s</mtext>
</mrow>
</math></span>» ✔</span></span></span></p>
<p> </p>
<div class="question_part_label">bi.</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><span style="background-color:#ffffff;">u<sub>y</sub></span></em>=64sin7/7.80«ms<sup>–1</sup>» <span style="background-color:#ffffff;">✔</span></p>
<p><span style="background-color:#ffffff;">decrease in height = 7.80 × 0.187 + <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 9.81 × 0.187<sup>2 </sup></span>/ 1.63«m» <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></p>
<p>final height = <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«2.80 – 1.63</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">»</span> = 1.1/1.2<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«m</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 style="background-color:#ffffff;"><br></span></p>
<p><span style="background-color:#ffffff;">«higher than net so goes over»</span></p>
<p><span style="background-color:#ffffff;"><br><em><strong>ALTERNATIVE 2</strong></em></span></p>
<p>vertical distance to fall to net <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«=2.80 – 0.91</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;">» = 1.89«m» ✔</span></p>
<p><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">time to fall this distance found using «<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.89 = 7.8t + \frac{1}{2} \times 9.81 \times {t^2}">
<mn>1.89</mn>
<mo>=</mo>
<mn>7.8</mn>
<mi>t</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>t</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span></span>»</span></p>
<p><span style="font-size:14px;"><span style="text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-variant:normal;font-weight:400;text-decoration:none;display:inline;white-space:normal;float:none;background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t">
<mi>t</mi>
</math></span></span> = 0.21<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;">«s</span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">» ✔</span></span></span></p>
<p><span style="font-size:14px;"><span style="text-align:left;color:#000000;text-indent:0px;letter-spacing:normal;font-family:Verdana , Arial , Helvetica , sans-serif;font-variant:normal;font-weight:400;text-decoration:none;display:inline;white-space:normal;float:none;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;">0.21«s» > 0.187«s» ✔</span></span></span><span style="background-color:#ffffff;"><br></span></p>
<p><span style="background-color:#ffffff;">«reaches the net before it has fallen far enough so goes over»</span></p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span style="background-color:#ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p><span style="background-color:#ffffff;">Initial KE + PE = final KE /</span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 0.058 \times {64^2} + 0.058 \times 9.81 \times 2.80 = \frac{1}{2} \times 0.058 \times {v^2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>64</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0.058</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>2.80</mn>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> ✔</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = 64.4">
<mi>v</mi>
<mo>=</mo>
<mn>64.4</mn>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{m }}{{\text{s}}^{ - 1}}">
<mrow>
<mtext>m </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></span><span style="background-color:#ffffff;"><br></span></p>
<p><span style="background-color:#ffffff;"><br><em><strong>ALTERNATIVE 2</strong></em></span></p>
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{v_v} = ">
<mrow>
<msub>
<mi>v</mi>
<mi>v</mi>
</msub>
</mrow>
<mo>=</mo>
</math></span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {{{7.8}^2} + 2 \times 9.81 \times 2.8} ">
<msqrt>
<mrow>
<msup>
<mrow>
<mn>7.8</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>2</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>2.8</mn>
</msqrt>
</math></span>» = 10.8«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{m }}{{\text{s}}^{ - 1}}">
<mrow>
<mtext>m </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» ✔</span></span></p>
<p><span style="background-color:#ffffff;"><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="v = \sqrt {{{63.5}^2} + {{10.8}^2}} ">
<mi>v</mi>
<mo>=</mo>
<msqrt>
<mrow>
<msup>
<mrow>
<mn>63.5</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mrow>
<msup>
<mrow>
<mn>10.8</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</math></span>»</span></span></p>
<p><span style="background-color:#ffffff;"><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style: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 = 64.4">
<mi>v</mi>
<mo>=</mo>
<mn>64.4</mn>
</math></span>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{m }}{{\text{s}}^{ - 1}}">
<mrow>
<mtext>m </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math></span>» ✔</span></span></span></p>
<p><span style="background-color:#ffffff;"> </span></p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">so horizontal velocity component at lift off for clay is smaller ✔<br></span></p>
<p><span style="background-color:#ffffff;">normal force is the same so vertical component of velocity is the same ✔<br></span></p>
<p><span style="background-color:#ffffff;">so bounce angle on clay is greater ✔</span><span style="background-color:#ffffff;"><br></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>At both HL and SL many candidates scored both marks for correctly answering this. A straightforward start to the paper. For those not gaining both marks it was possible to gain some credit for calculating either the change in momentum or the acceleration. At SL some used 64 ms-1 as a value for a and continued to use this value over the next few parts to the question.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was well answered although a significant number of candidates approached it using P = Fv but forgot to divide v by 2 to calculated the average velocity. This scored one mark out of 2.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question scored well at HL but less so at SL. One common mistake was to calculate the direct distance to the top of the net and assume that the ball travelled that distance with constant speed. At SL particularly, another was to consider the motion only when the ball is in contact with the racquet.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>There were a number of approaches students could take to answer this and examiners saw examples of them all. One approach taken was to calculate the time taken to fall the distance to the top of the net and to compare this with the time calculated in bi) for the ball to reach the net. This approach, which is shown in the mark scheme, required solving a quadratic in t which is beyond the mathematical requirements of the syllabus. This mathematical technique was only required if using this approach and not required if, for example, calculating heights.</p>
<p>A common mistake was to forget that the ball has a vertical acceleration. Examiners were able to award credit/ECF for correct parts of an otherwise flawed method.</p>
<div class="question_part_label">bii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This proved difficult for candidates at both HL and SL. Many managed to calculate the final vertical component of the velocity of the ball.</p>
<div class="question_part_label">biii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>As the command term in this question is ‘predict’ a bald answer of clay was acceptable for one mark. This was a testing question that candidates found demanding but there were some very well-reasoned answers. The most common incorrect answer involved suggesting that the greater frictional force on the clay court left the ball with less kinetic energy and so a smaller angle. At SL many gained the answer that the angle on clay would be greater with the argument that frictional force is greater and so the distance the ball slides is less.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In an experiment a beam of electrons with energy 440 MeV are incident on oxygen-16 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>O</mtext><mprescripts></mprescripts><mn>8</mn><mn>16</mn></mmultiscripts></mfenced></math> nuclei. The variation with scattering angle of the relative intensity of the scattered electrons is shown.<br><br></p>
<p style="text-align: center;"><img 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L6YRTwK8d82NCWqjC/lbGP1ucY4LEo8J3ZkUu9hPNbdG79cvYEia+0mQRg+qQcKE9/HsgOm2uni/EOIEzOmtdnN4kFleaP78JcRWPh3LFqWYoq7OB/pcWIGsxpX7s9yv4Fq3LFIOK2mf7F95RIstjo8Ldiwz1Kqfnylx07dXq91W3RHIa7eKLtvM/kaWauxeKXp9yOOzUp1f1mBL2O4ehyrVJwH4+QQBISvRbr2OxKz+dPwZS4Q9HQAWpgeVS3+/v5o1qwZDh06JHuIiEivSpO0V+vB+MuWt9AyeTxC/ESJTiAGbG2GSOP7GOv/gPoAXxiWbcHGSbcwp2db+PqFYGxaZ0Rr2x9Bn2lLMOuRnRgbom7z7YFp6Y9iUkQoGiIL6aeuq6/QEj1Hv4xHE0fjSd+pMOY3K9NuhOC31sAY3RlpY0Pg5/sI/EJm4FjHSBjXvQp/q9F7oVHwZMQb56Nb2pumuP26Y+yxjlhojhtNTfuNbIatAwLV7c9i3mV/DAtsaNpFObbs05INj6/02KnbW4Rg9LiHkDg2CL7hSbgg91zC/Bolv5/7xyZ+MoIb2XAercYQ9pdViGy5C8O135EvAgdsQ8vIzVg3tn3l/zgqMWbMGCQmJsoWERHpJoe9iaqtshKsPn2eURI2bZIt6+x5DZHXVq1jbNbZOzYivfSeLBFVKiJiJlJTU2WLiIj0qKIEi6hiogQrfuMm2Srtzp07mPT6RKyIW4nGjRvL3rpz5coVPPzww7LlXBibPs4eG0uwyC6082kiHaq641jEjBlKYmKibJVnz+FJDttax9iss3dsRHpxuJvspmfPnli/fh1u374te4iIqDqYpMlumjdvjt69n8aRI+Iuc0REVF1M0mRXQ4YMwQcffCBbRERUHUzSZFe9evXSvufm5mrfiYjIdkzSZHevvvoq9u3bJ1tERGQrJmmyu9DQUCxcGI2CggLZQ0REtmCdNOlWWZ10WZ999hm8vb3vD3/bG+t99WFs+rBOmuxGK8Qi0qGqOmnL2tKcnBxlxIgRsmViz7pW1vtax9iss3dsRHpxuJvqhFgdS+DqWEREtmOSpjozY8YMbdibiIhswyRNdaZr165ITf2SE8iIiGzEJE11pkGDBhg58hUkJyfLHiIiqgyTNNWpsLAw7X7eRERUNSZpqlM+Pj4IDOzICWRERDZgnTTpVp06aUvZ2dn4+uuvMX78eNlT+1jvqw9j04d10mQ3WiEWkQ7VqZO2VFRUpPTp84xiTEqSPdbVpK6V9b7WMTbr7B0bkV4c7qY6Z55AlpaWJnuIiMgaJmlyCDGBbPee3bJFRETWMEmTQ4gJZL6+vjh69KjsISKispikyWF69+qN3bt5Nk1EVBEmaXKYJ598EqtWreAdyIiIKsAkTQ5Tv359zJkThczMDNlDRESWWCdNuumtk7Z09uxZfLz1Y0RFRsme2sF6X30Ymz6skya70QqxiHTQWydtZt4u1pkW602XVZO6Vtb7WsfYrLN3bER6cbibHE6UY+3bt0+2iIjIjEmaHG7w4MHYuvVj3L59W/YQEZHAJE0O5+3trS26ceTIEdlDREQCkzQ5hTFjxuCzzz6TLSIiEpikySl07doVmzcnsGaaiMgCkzQ5BbHoBmumiYhKY5006SbqpJcuWSZbNZeXl4edn+7E1ClTZQ+R62CdNNmFVohFpENt1UlbEutMnz9/Xvu5JnWtrPe1jrFZZ+/YiPTicDc5lYkTJyElJUW2iIg8G5M0OZW+ffti/fp1skVE5NmYpMmpiHWmW7ZsxXWmiYhUTNLkdCZNmohDhw7JFhGR52KSJqcTHNxNu03onTt3ZA8RkWdiCRbpVhtLVVZkxcoV6N+vPwIDA2VP9XDJRX0Ymz5cqpLsRpvjTaSDPUqwzPbu/Vx5fdIk2SqvpiUxNYmtJs8VGJt17hwbkV4c7ian1Lv300j+n11cGYuIPBqTNDklcZvQwf/1AlfGIiKPxiRNTuvJJ5/kylhE5NGYpMlptWvXjitjEZFHY5Imp1W/fn1MmTKNK2MRkcdikian9swzz2D79h2yRUTkWVgnTbrZs07a0tt/ehvz581H48aNZU/VWO+rD2PTh3XSZDdaIRaRDvaskxbM21evXq3VTVuqad1qTWKryXMFxmadO8dGpBeHu8np9erVi0PeROSRmKTJ6XXp0gXZ2Sc5y5uIPA6TNLmEkSNf4SxvIvI4TNLkEjjkTUSeiEmaXAKHvInIEzFJk8vgkDcReRrWSZNudVUnbXb27FnsSt6FaVOnyZ6Ksd5XH8amD+ukyW60QiwiHeqqTtqsqKhIe81r167VuG61JrHV5LkCY7POnWMj0ovD3eQyxPKVvJc3EXkSJmlyKbyXNxF5EiZpcildu3bFrl2f4s6dO7KHiMh9MUmTSzEPeZ85c0b2EBG5LyZpcjliyPvEiROyRUTkvpikyeWIIe/k/9mF27dvyx4iIvfEOmnSra7rpC2tWLkC/fv1R2BgoOwpjfW++jA2fVgnTXajFWIR6VDXddKWli5ZoixatEi2ymO9r3WMzTp7x0akF4e7ySX5+/sjOXmXbBERuScmaXJJjRs3RmBgRxw9elT2EBG5HyZpclm9e/fGoUOHZIuIyP0wSZPL6tu3L1JSUmSLiMj9MEmTy/Lx8dG+X7hwQftORORuWIJFuokSrKVLlsmWY+zfvx8PPPCANvRN5EgswSK70OZ4E+ngyBIs87asrCxl8uTJ2s+WWEpkHWOzzt6xEenF4W5yaV26dEF29kkUFBTIHiIi98EkTS5v8OAXuMY0EbklJmlyeWLBjYyMTNkiInIfTNLk8sSCG6tWreCCG0TkdpikyeWJNaZfeGEocnJyZA8RkXtgkia3MHz4MN59jIjcDuukSTdHLlVZ1tWrV7F4yWIsXbJUa3PJRX0Ymz5cqpLsRivEItLBGeqkLY0YMUI5f/689jPrfa1jbNbZOzYivTjcTW5D3Ms7PT1dtoiIXB+TNLmNXr16Yc+ePbJFROT6mKTJbTzxxBPYtetTlmIRkdtgkia3IUqxpkyZhiNHjsgeIiLXxiRNbqVbt2D87//+r2wREbk2JmlyK8HB3ZCcvEu2iIhcG+ukSTdnqpO2FP1eNMKGhqFTp06yx7mwFlkf1kmTR9IKsYh0cLY6abPExERl2tSpsmWdvV5bqGo7a5Gtc+fYiPTicDe5HXEGnXsmV7aIiFwXkzS5nS5duuDkyRMsxSIil8ckTW4ppMdTLMUiIpfHJE1uKSAgAEePHpUtIiLXxCRNbqm1T2ts3fqxbBERuSYmaXJL3g95o2XLVrhw4YLsISJyPayTJt2ctU5aEHWrX3/9Nby9vbWFN5wJa5H1YZ00eSStEItIB2etkxZE3WpqaqoyZ84c2VOaPV/bltgqw9isY500eSIOd5Pb6tq1KzZvTmApFhG5LCZpcltiVawXXhiKnJwc2UNE5FqYpMmt9e7dG8ePH5ctIiLXwiRNbu2pp57Czp07ZYuIyLUwSZNb8/f3x1dfHUJBQYHsISJyHUzS5PamTJmGU6dOyRYRketgnTTp5ux10uaa2szMTFy8eBFDhgzR2o7GWmR9WCdNHkkrxCLSwdnrpM3Onz+v9OnzjGyZ2PO1qxObNYzNOtZJkyficDe5PR8fH+07bxFKRK6GSZo8wsiRr+Cbb7Jli4jINTBJk0fo0qULMjIyZYuIyDUwSZNH6NChA1atWiFbRESugUmaPIJYDatnz17Izc2VPUREzo8lWKSbKMFaumSZbDm/1NRUPPDAA+jWrZvsIao9LMEiu9DmeBPp4ColWGZZWVn3l66052vric0SY7OOJVjkiTjcTR7jiSee4NKVRORSmKTJY3DpSiJyNUzS5FG4dCURuRImafIonTp10iaQERG5AiZp8ijiuvSuXZ/izp07soeIyHkxSZNHEdelR48ei/Pnz8seIiLnxTpp0s1Vlqos69ChQ9oM7/79+8ueusXlIPXhUpXkkbRCLCIdXK1O2iwnJ0cxGH4nW9bV5LVrEptQk/0ztoo5MjYivTjcTR7H398fGRmHWS9NRE6PSZo80rN9nsORI0dki4jIOTFJk0dq3749jh49KltERM6JSZo80qOPPoqUlBTZIiJyTkzS5JF8fHzw1VeHUFBQIHuIiJwPkzR5LFEvferUKdkiInI+rJMm3Vy1TtpM1EuLM+khQ4bInrrBWmR9WCdNHkkrxCLSwVXrpAXxfFEvPWLECNlTWk1euzZiqwxjs86ZYyPSi8Pd5LFEvTSvSxORM2OSJo/G69JE5MyYpMmjhYSEsF6aiJwWkzR5tI4dO7JemoicFpM0eTRelyYiZ8YkTR6P16WJyFmxTpp0c/U6abO6rpdmLbI+rJMmj6QVYhHp4Op10mbW6qVr8tq1GZs1jM06Z46NSC8Od5PH43VpInJWTNJEKl6XJiJnxCRNpGK9NBE5IyZpIpWolz527JhsERE5ByZpIpW4Lr1r16e4ffu27CEicjwmaSJJXJfOycmRLSIix2OdNOnmLnXSZqJeWpxJ9+/fX/bYR0WxXbhwAd9//z1Onz6N7G+y1cf9ILeU6NatO1q2aIl27dqpx98XzZs3l1tqB+uk9WGdNNmNVohFpIO71EmbiXrpyZMnaz/X5LWrE1tRUZGSlJSk1WmLr8TERGX9unXKtWvX5CNKO3/+vLIiLk5ZvXr1/eeI55sfX5uxWVOT/XtybER6cbibSKrr69L79u3FoEGhSEtLQ3R0NLZt24bRo0ejbdu28Pb2lo8qzcfHB4GBgXjjjTe0x8fGxuLSpUt48UUDFi9erJ2NE5H7YJImslAX16VvFd7Skuz27TuwYcPf8N5772kfEPQQSVvsa/fuPWjfvj0+WP4BIiMjkZubKx9BRK6MSZrIgqiXPn78uGzVPnGmGxcXh969e2PNmjW6k3NZDRo0gMFgQPSCaO09hIdP0PbPu6gRuTYmaSILol46NTVVtmqXSNCvvvoKRrw0QhvWtof69etryVqcWTdu3FgbBhfD6kTkmpikiSyYr0vfuXNH9tQOc4JeuHBRrZ09V0acWYsPAh999LE2rC6GwHlWTeR6WIJFuokSrKVLlsmW+/jkk0/w1FNPaSVOtUEk/GXvL9POoOsiQVuTkZGBPZ/vcWgM7o4lWGQX2hxvIh3crQTLTJQ0RcyYIVvlVTduUdYlSqbMHFVKJErM+vXrqyxatEgr/bKGJVjW1TQ2Ir043E1UhrguffRY7Sy2YTQate9iBrajiTPot2e9rf08c+ZMlmsRuQAmaaIyRDLLzc2p8TVckQSnT5+KuXPnyh7HExPLZs+ejdDQUO0aOVf+InJuTNJEVjzb57kary+9atUqxMWt1GqZnY2YAR4Xt0L9EDGNs7+JnBiTNJEVXbp0qdFZprgP+JkzZ7Rk6KzEexSzv9etW6/VVBOR82GSJrJCzOxOSUmRreoRs7k/+OADREVFyR7nJc7yN23apK2lLcq0arv0jIhqhkmayAqxutTly/m6rksfPnxYW6VKnKm6AlFTHRMTg1//+tf46OOPuKY2kRNhnTTp5m5LVZYlFrAQyTY4OFj2VE2ciUbNjcKMt2ZUeC3amZdc3Lp1K65cvYLXJ72uTTJzJlyqkjySVohFpIO71kkLYvvevZ9rNcVlVfZc8ZzRo0bJlnXOXu9rXgZTLItZlqNjq4wzx0akF4e7iSoQHNwNycm7ZMs2YhLWwIEDZcs1iZruvn37aiVarKUmciwmaaIKiDWdW7ZsZXOiMs8Gd8aSq+oSiXrkyFeYqIkcjEmaqBJhYWFIT0+Xrcr9/e9/x6RJE2XL9TFREzkekzRRJTp16oQ9e/bIVsXELPDNmxPQu/fTssc9MFETORaTNFElRBmVWLqyqrKkf/zjH5gzJ0orZ3I35kS9YMEC1lET1TEmaaIqTJkyDUeOHJEt6z766CM8//zzsuV+RKLu3Lkz/rrur6yjJqpDrJMm3dy9TtosMzNTu8Xnyy+/LHtKE8PA8ZviERVp2x3GnL3et7LYPvvsM3x37juH1FGzTpo8klaIRaSDu9dJm127dk3p0+cZ2Sr/XFFXLNagNqvL2MqqyXMFW2KbM2eOtka2NY6OrTKOjI1ILw53E1VBlGIFBna0uuCGGPrduvVj9OnTR/a4v3nz5mnfuSgHkf0xSRPZYPjwYdrKVmWJa9UigYtE7inM9/oWi3IwURPZF5M0kQ3E3cfEGXPZSVPiGu2YMWNky3OIRD137lztmFj78EJEtYNJmsgG4kxZ1EBbzvI210Z37dpV9ngWcWc1sR71nDl/ZqImshMmaSIbDRkyRDtzNnPn2mhbiUS9cOEiLVHzZidEtY9JmshGvXr1Qmrql/eTkbvXRttKHBcxmUzclYw3OyGqXayTJt08pU7akhjWPX36NJ566ins/2I/pk2dJrfYzpXrpCtj7xpq1kmTR9IKsYh08JQ6aUtFRUVKcHBXrW46KytL9pbmqNiEmjxXqGlsBsPvtLpxaxwdW2Xb7R0bkV4c7iaqBnH9efafZmvDu+K+3lSaOItOSUmB0WiUPURUE0zSRNXUvHlzPP/8ANkiS2KYOzY2Vv2K4YxvolrAJE1EtUrM+I6LW8EZ30S1gEmaiGqduBQQETFT/YrgqllENcAkTUR2YTAY0K1bN7z77ruyh4iqi0maiOxm+vTp+PHHHzmRjEgn1kmTbp5YJ10bPC22q1evYvGSxXhj8hto27at7K0+1kmTR9IKsYh08MQ6aaEmzxU8MbbU1FStvlyszV0RR8Um1OS5AuukyV443E1EdiduHToodBCioqI4kYyoGpikiahO9O/fX/seHx+vfSeiqjFJE1GdiY6O5hrURNXAJE1EdUasy80bnRDZjkmaiOqUuNHJxImTsGDBAl6fJqoCS7BIN1GCtXTJMtkiqp74TfFo80ib+9eqXR1LsMgutDneRDqwBMs6xmZd2W2iHMtyyU9niq2smsZGpBeHu4nIIczXp6dPn4aCggLZS0SWmKSJyGHM16dF/TQRlcckTUQONXr0aO07y7KIymOSJiKHmzt3LpKMScjNzZU9RCQwSRORw/n4+OCVka8gPHwCy7KILDBJE5FTCA4OxuDBLyAuLk72EBHrpEk3LlWpD2Or2J07dxA1N0o7qxZJ2xKXqiSPpBViEenAOmnrGJt1tj43JydHq58uu6wl66TJE3G4m4icir+/P8uyiCQmaSJyOuayLKPRqH0n8lRM0kTklERZ1vTpU7laFnk0JmkickqiLOvDDzdytSzyaEzSROS0nn9+AB566CFs375d9hB5FiZpInJqs2bNwvr165Cfny97iDwH66RJN9ZJ68PYqi8zMxP/b+f/Q1RkFOrXry97nQfrpMlutEIsIh1YJ20dY7OuprGNHj1KSUxMlK3yHBkb66TJXjjcTUQuYeCAgdqw99GjR2UPkftjkiYilyCGuePiVmD69Gmc7U0eg0maiFxGly5duAgHeRQmaSJyKdOnT0dy8i4Oe5NHYJImIpfSoEEDDnuTx2CSJiKXw2Fv8hSskybdWCetD2PTp2xs5rWnZ7w1Q7uFqCOxTprsRivEItKBddLWMTbr7BFbVlaWMmLECKWoqMjpYiOqDRzuJiKXJYa9u3Xrxnt7k9tikiYilyZme4ubnHBJS3JHTNJE5NLEbO958+YhflM8Z3uT22GSJiKXJ5a0bP2b1hz2JrfDJE1EbuGll17isDe5HSZpInILjRs31oa9FyxYIHuIXB/rpEk31knrw9j0sTW2jRs3on379ujVq5fssT/WSZPdaIVYRDqwTto6xmZdXcV2/vx57d/mtWvXtLaZI2Mj0ovD3UTkVsTdx+LiVmLZsmWyh8h1MUkTkdsxGAw4c+YM9u3bK3uIXBOTNBG5pejoaLz77rusnSaXxiRNRG7J398fEydO4kpZ5NKYpInIbQ0fPhzJybtw9OhR2UPkWliCRbqJEqylSzg5h5xbXl4edn66E5PUs+r69evL3trHEiyyC22ON5EOLMGyjrFZ58jY5syZo0SqXxWxd2xEenG4m4jc3qxZs7B7z27eMpRcDpM0Ebk9b29vvDLyFd4ylFwOkzQReYTg4GDtO2unyZUwSRORx5g5c6ZWO11QUCB7iJwbkzQReQxz7fT69etlD5FzY5ImIo9irp3Ozc2VPUTOi3XSpBuXqtSHselTm7GdPXsWH2/9GG/PertWaqe5VCXZjVaIRaQD66StY2zWOVtsonY6KSlJ+9nesRHpxeFuIvJIonZ6+vSprJ0mp8YkTUQeSdROi3WnV61aJXuInA+TNBF5LPO609nZ2bKHyLkwSRORRxPrTm+M38h1p8kpMUkTkUcTtdM9uvdAfHy87CFyHkzSROTxxLD31q0fs3aanA7rpEk31knrw9j0sXdsmZmZSD2UimlTp8ke27FOmuxGK8Qi0oF10tYxNutcIbbJkycre/d+rv1sqaaxEenF4W4iIokLcJCzYZImIpLEJLKRI1/hAhzkNJikiYgsjBs3jgtwkNNgkiYistCgQQMsXLgIUVFRsofIcZikiYjK6NWrF9q1awej0Sh7iByDSZqIyIopU6ZoC3BwEhk5EuukSTfWSevD2PRxRGz79+9HXl4exo8fL3usY5002Y1WiEWkA+ukrWNs1rlibEVFRcqIESOU9evWyR7rWCdN9sLhbiKiCohJZGIC2cdbP+YCHOQQTNJERJXo0qULWv+mNbZv3y57iOoOkzQRURVeeuklREb+GRcuXJA9RHWDSZqIqAqNGzdGXNxKrFq1SvYQ1Q0maSIiG4jlLM+cOYNDhw7JHiL7Y5ImIrJRdHQ05sz5MyeRUZ1hnTTpxjppfRibPs4S27Zt2/Dggw9iyJAhsod10mRHWiEWkQ6sk7aOsVnnLrFdu3ZN6dPnGSUnJ0f2sE6a7IfD3URE1eDt7Y158+YhJiZG9hDZD5M0EVE1Pf/8AO17TRbgEOVcvC84VYVJmohIh5kzZyI2NkZ3ok1JScGLLxqwb99e2UNUHpM0EZEO/v7+mDhxEtavXy97qmf06NGIi1uBd999F5GRkbxRClnFJE1EpNPw4cORnLwL+fn5sqd6xC1Hd+/eg8DAQPz2t09x/WoqhyVYpJsowSKi2tWzZy+tzItIo83xJtKhqhIse2731NcWGJt1zhybLZKSkrT9rF69WvYQsQSLiMihcnNz8cYbb+Cjjz7C/v0p2s9EZkzSREQOIG4tunnzZvTv3xehoaHYtGmTNhmNyBKTNBGRA8TFxSE1NRX//OfX2uIdDRo0kFuISjBJk93k5Z2XP1lXk+1VPbcq9nxtxmadJ8dmzcSJE7FmzRr4+PjInrpwB/mZB5CZf0e2geL8TCRn5qNYtqvvLvKNU+HrOxXG/LuyzxX9C8bwzvANN0LfXH2zqzgQFYpw479k28Kt0zBGDdUm3foOWoADFr+HijBJExE5gLi9aF27m7kSgwwLcfCiTA53M7F8UBgiD16sQZKuh1aGleoHmZUwtKon+zzYjRPYu6M5nu5YdjEY9cPMvhWYc20Cvjp3Fl9NvoIZKw7hhtxaESZpIiKiWlGMG5lfYIf/APR+/AHZVzNM0kRETqMYt3L3IjY8xDQkqn4FhMdhf67F+datXOyPnYAAK9vF0LXRYpuvb3sMitqiDW/fzYxBd0MMCnASsYYOCFoUg0XdwxBbABTEhqFtUAwyxWh1cT4yjTEIDzDvYyiiEtORr51qy6HtgN8jfJyMMWwdUrZbDHfnGxHuG4Lw2JWIGtS+ZB/G07gldiGor5EeZ/keFmCpeM8VDjWLYXpjqeNSOi7TUHVA+FJ8aB5O1t67Ebm3SsYIivMPIe7+PtQYly5Q32dn60PT5V6z5FhWrAhnjhyB/7Df4vFy2bUeWj0/DQub/Q09/dqi59qH8cG0Xmgit1ZIlmIREZGj/ZSiRHZ4Qgmdt0+5dE9t3zyhbJzQQ2kzdKOSI9r3vleSXlfbHaYrSRd+KdneYZ6S8mO2snHoE0qHCQnKqZviwb8ol9LWKBM6+CgdIlOUn9Sef2e8r3RpM1CJybiptrQOJaaLj9IlJkP5t9bxo5IRY1D397qy8ZR4xj3l5qkEdR9qTDFpyk31UZeSpiht2sj2vUvKkSN5ynmtb4qSdEndy6UkZUIbH6VN6DwlKUfsQ+6zzavKxpzb5V9D3Ufa8teUDuI5E5KUSyKMMu7lbFSGtumhTNh4Qo1BdJif01uJTLmiduQpSRM6qa8xRIlMOqU+Ro07Y7kSqsY5dOMptaW6mabEhJYcn3uXUpXl4ti16aRMSMor2YcWg/n5Fq9pPtahy5UM7fhace+U+jvoJ2OqHTyTJiJyFkXXcblQ/f5QEzQSf50bdcS4DWnI2zkO/mq7+Nsv8GHyTwia/SbCWtcv2f7NO3iuaQDG7TyNbzaMQXvtyfXRqltfPO3fEIWXr6vneDa4kYXt67LV/UdgbHtxjueFRu1HYPbs7she9ykO3zCflXbHyCGd1BhbISjoN/g/srdEQwSNHIUwf7GPpgga8jsE4Ti+PHml/Guo++gx9U+YHdTQ9FQrvPzHYWdeGjaM64hGWkcrdPuvZ+CPG7h8/bb2GE3QcIwLa68+Ro07KBQjg4CsL7/BD2IY+vCnWJfdXX0vI7Tj49WqF6aqx1F9iBUFOLx9G7KD3sTssfI11WM9Vjw+exu2H7a+qErxt//EjtzeGBBce/MNmKSJiJxFq354+52++D72RQRqQ8ZbYfw0Uw7pqkngZgHy8Cu0aPpgBX+8xRDtbu0e4Ebj3xA1OAzzs0TWt03x5XM4XliIrPn94Xd/WLkd+s8/CBQW4HqROUk/hKaNK5skVjpGr8ZN0UL+fPdMJnYV+qFvZ5+S9+DVDH6dyk60KkMMw38q3pf6FR+Fwf3nIktuuq9FUzS+/6IPommLX8mGGIb+GoXe3dD5sZJrxV4t/dDJ2meD4ms4d1z9QJE1F/39zMfhEfhpr1nmg8F9P+Pb1L3IHdYPwU1qL7XW3p6IiKiGmqD9uLX4JjsFCXGRGIy9mDMlDCGDbSjXKb6IA/OHI8SwCunXRTJtgQHLE/BOJWeo1vlhTEKWVnZW+stxs7eL8/dj/uBnYViVjuuio2kolhv/bwVnwbWn4ZjNOFHuOBzDBkMb+QhLt3Ah9yp693i86uvM1cAkTZUTn14TozBIfpIsN4lF/VSZuz/OYpKJ+PRvrGJyhR3cSkfsoPYIis1ESaWm42ITk3SC5DEr+QpFbKZ56owjj5v62sb593+nvoOikFiqTtYRsZlrbc2vWebr/oQiBx63chO21iLd8nXLbPcNmIBYY8lZcLU08sdzBgOGRfwNJ/cv0IZYN391WT0j9YYvfsEP14vKlUwVf/s5YuJ/VBPsRkSPGwaDYSie+81t5ObafiZtOrM8hx17T6hH2j7qtQvGC+prpBy7UPIezGeuVqlnqLs/RPz3v0fCtncxTj0uBsPT+M2N75ErH1G1B9Gu61NoWJCBY9/9LPvUl9VGDmTDkjyzL9zxBTLvD/FXocLSq5phkqZK3MHFnQsx6r1rGLk3G3nn0rCm9V6MD5sHo6yzLM7dgT+O3wy8sQ1p587jXNpCtN4zG6NsqP+rNcV5MM6agtjs0v+3OS62u7iadxYFDV9Dwok8i0/gexARrF3dcmBs6u/UOA9ha+vjz2lntd9pQsgxRI1aiJ0O/Z2aa20tz1hOwBjRQz2dGYJ33u6HVuqjHHfcriNz/Z8w9fRQ7FdfV8S2peMeDFfPejO12cM/I/e//4Lx69TQth/GOfX3n7bmMeyZPh0r/nHVtAsbFF80YnKA+sEj7pBM7uqHktSv1GTUSfvj7/V4P7w2+NfIWrza9PvSzp7FbOZRSLjeQk2wV5DxxVHTc8WNMxa/j0SL/y3qtW6L7ijE1RsyUdV7GI9198YvV2+Yrlk3CcLwST1QmPg+lh0w1U7fnxEdFo9cG/NVpbTXCFTfQywSTovf2g2cTojF4gqH5eujpd/jaFh4BF9oHybFDPidWLzo7+o7sZUXmnQfikmBh7F48Sc4LX5nt04iQT2O5YbMNd7oPvxlBBb+HYuWpZiO5/0Z6aMQn1uS6E1qv/TKjEmaKlb8HT7/cDcwbCSGaRM8WuO5NydgYGEKPku7rD7AdA0my3sk3nyzF1qp/5q8WvXGmJHqn4HqfAKtEfFB4n3MSb4o22aOjO1nXPxO/Yzv3xY+2gSeshwY241DWDVnN/xHjkCfVvVNv9NZf8QYONPvVFD/EGcmIDL2AgYvjJSTmBwY292zOLgpG/49A7TXFZOhOj/7DLyzd+Fgjpreir9H6o7D8J40BW/2aKX+Ya2PVn1GYGTQlWqdlXq1Hoy/bHkLLZPHI0S7FhqIAVubIdL4Psb6q3/8vXxhWLYFGyfdwpyebeHrF4KxaZ0RLbb3eB7TEiLwyCd/MD03cBbS/UciYmBrIDUTp8TxaRGC0eMeQuLYIDk60RI9R7+MRxNH40mthKoRgt9aA2N0Z6SNDdGuS/uFzMCxjpEwrntVm7xWc02119j+xr+xeECg+h574K1cPwwLrGhYXk2wfd5EwqwW+ESLyReB09LhP+l1DGxYgNT0b207vo3U14nfiDewAgMCfdXj82fkduyLQLm5NC80Cp6MeON8dEt703Q8/bpj7LGOWGj+XZRSWelVDclZ3kS20corzCULV5SUyN7lyiZMZR7mcgv7unchSXm9wxBl3ufblSWlSkkcGJtWhvHE/bKX8hwXW9Wv4fjfqcZcalSq3MWBsWmlShblPFqXeF1ZzqSVTpn/vzC7qWTEDCwpn6KKVfn/jH2YSrvMZVzOqbZzPrkzMXy24m/4PPBljO7ZUu24jeuXK/oMexU/3rTzfXzFcNX8ZTg3aT7+1NcPpae0ODC2W5dM1wEzFmKY+fpkqeu+joqtGEU3ruMX/Cd+PLm15EYTThGbJfUsOsuItcnA4MkGBN0fjXBgbPXa4tk/BCL3q2/kMPR1HDv4vygIfAHPPvFgSemUNXkFuGnHk3yXc+MAogLaY9D8/SVD+ju3YGtWICYND6rVSVclitWXnY8A36GYL4fxxd+znfHbkaX+PRveve5v0WorJmmygZzUE9gf0xMvY+DgfujQor7c5ijiGuFczD//Mt6b2M1Ux+gkTJNRGuLR0AUwatdW85C9vAMOjnoDyzO1uakOoibp6wUoxD6s++xnGOKPq7GdRdqfG2CL4Y9IKHedzVFkjWrDQRjZ7xEn+SPVFEG//wOePTgVPbVh6CdhiL2CMX9+FcFWL2lQhZr0wrQtFsPIvoHov/YeRhnX4K3gpvJBtc00ZL7FYhjfNzAMazESxvjJTv075L8uskHJpB5tok7yePR904iLDjs7MF+vBCLeG+t0/4OZbrxwGrsjesgPD15o5B+Cp/2zsW67qLJ0tGcxe/Y49BDXpO9fOz2MDz7LtpgZ70DaLNkrCJo9Cn2aOMnv9lY6lr+2DHdn70G29sFL/XCTMAgZYyci1qEfvFyR+m8ueBSid5/W/qZoX7ujMSZYXMu3I69WCB4Tjd3m1xT/j0aPQrD2/4HzYpKmark/USd5H9J+aAzfjr+RW8pqjocqvdlBTRQh5+AuZCMdsYYnTUO2bcveg/ghB8VWAXljBdOdnxwVWz00920L77I3opCxmWb4Ovq4yVmyhQ+jk1+zMn+gHBWb+W5VQRgySNzNSjB/uMnGpoNncbe5LzpWNGLq611ygw2iauI/HaqYvHYUFn/adA3HUkNvNH2wPho/1Lxk5qjGXH70OPxa2usTaiMER+wp+RQuvs7uRIT6R9I7YifOZs1EcL16DorNfO2rTJlGcRGu/wAEPR2AFmqydExsaprWalQv4LuL95c6uB+bv/9v1CPruNhM7uDyuW9R2LCflVsrOjq2Sng1xEO+v5SZafwj8k5eQsNOfmjJv7SkE//pUMXM9Yxb9yBLriRTnJ+KxK3HEThpKLo3eRCP9x6AoMLd2LzjG22Fm+L8g1i9di8a1vKt8arvAQfFZq7HPI6tnx2Xq/7cQf4/PsHW3L54beBj6iMcFZtK+50C61Z/aqoVdabYNOKuTd9XUL7m6N9pFj7bliYnO8njlhWIPzzbFvW8HkXvYaIUbCt2aLW/6vYDm7D28yYYNuBJO02GIo8gZ3kTWXfvkpKREKmEihVqxFeH15SYfTmmVWE0Pyk5SfNKtovVcSI3KxmXfpHb60i51XwEx8V271KakhA5RL6uj9JhwnJln7YikJkDj1vZ3+n91YrMHPk7tVyJyBrn+Z22CY1UEjLEeknSzVNKkuV2sSJTQpppNSsinf5D/EfmayIiInIi9h67IiIiIp2YpImIiJwUkzQREZGTYpImIiJyUkzSRERETopJmoiIyEkxSRMRETkpJmkiIiInxSRNRETkpJikiYiInBLw/wG4ayMB1mk4KAAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify a property of electrons demonstrated by this experiment.</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 energy <em>E</em> of each electron in the beam is about 7 × 10<sup>−11 </sup>J.</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>The de Broglie wavelength for an electron is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>h</mi><mi>c</mi></mrow><mi>E</mi></mfrac></math>. Show that the diameter of an oxygen-16 nucleus is about 4 fm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the result in (a)(iii), the volume of a tin-118 <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mmultiscripts><mtext>Sn</mtext><mprescripts></mprescripts><mn>50</mn><mn>118</mn></mmultiscripts></mfenced></math> nucleus. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>wave properties ✓</p>
<p><em><br>Accept reference to diffraction or interference.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>440 x 10<sup>6</sup> x 1.6 x 10<sup>-19</sup> <em><strong>OR</strong> </em>7.0 × 10<sup>-11</sup> «J» ✓</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>.</mo><mn>63</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow><mrow><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow></mfrac></math> <em><strong>OR </strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>440</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac></math> <em><strong>OR </strong> </em>2.8 × 10<sup>-15 </sup>«m» seen ✓</p>
<p>read off graph as 46° ✓</p>
<p>«Use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mi>λ</mi><mrow><mi>sin</mi><mi>θ</mi></mrow></mfrac></math>=» 3.9 × 10<sup>-15</sup> m ✓</p>
<p> </p>
<p><em>Accept an angle between 45 and 47 degrees.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP2</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>∝</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>∝</mo><mi>A</mi></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><mfenced><mfrac><msub><mi>A</mi><mrow><mi>S</mi><mi>n</mi></mrow></msub><msub><mi>A</mi><mi>O</mi></msub></mfrac></mfenced><msubsup><mi>r</mi><mi>O</mi><mrow><mo> </mo><mn>3</mn></mrow></msubsup></math> or equivalent working ✓</p>
<p>2.3 to 2.5 × 10<sup>-43 </sup>«m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><msub><mi>R</mi><mtext>o</mtext></msub><mo>×</mo><msup><mi>A</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup></math> ✓</p>
<p>volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sn</mtext><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mi>π</mi><msup><mi>R</mi><mn>3</mn></msup></math> <em><strong>OR</strong> </em>5.9 x 10<sup>-15</sup> seen ✓</p>
<p>8.5 × 10<sup>-43</sup> «m<sup>3</sup>»✓</p>
<p>answer to 1 or 2sf ✓</p>
<p> </p>
<p><em>Although the question expects candidates to work from the oxygen radius found, allow <strong>ALT 2</strong> working from the Fermi radius.</em></p>
<p><em><strong>MP4</strong> is for any answer stated to 1 or 2 significant figures.</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;">
<p>ai) Well answered.</p>
<p>aii) Well answered.</p>
<p>aiii) This was generally well done but quite a few attempted the small angle approximation. Probably worth a mention in the report.</p>
<p>b) Most gained credit from the first alternative solution, trying to use the data as the question intended. There were the inevitable slips and calculator mistakes. Most got the fourth mark.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br>