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<h2>HL Paper 2</h2><div class="specification">
<p>Curling is a game played on a horizontal ice surface. A player pushes a large smooth stone across the ice for several seconds and then releases it. The stone moves until friction brings it to rest. The graph shows the variation of speed of the stone with time.</p>
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" alt></p>
<p style="text-align: left;">The total distance travelled by the stone in 17.5 s is 29.8 m.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the coefficient of dynamic friction between the stone and the ice during the last 14.0 s of the stone’s motion.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The diagram shows the stone during its motion <strong>after</strong> release.</p>
<p><img 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"></p>
<p>Label the diagram to show the forces acting on the stone. Your answer should include the name, the direction <strong>and</strong> point of application of each force.</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><em><strong>ALTERNATIVE 1</strong></em></p>
<p>«deceleration» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{3.41}}{{14.0}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>3.41</mn>
</mrow>
<mrow>
<mn>14.0</mn>
</mrow>
</mfrac>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = 0.243\,{\text{m}}\,{{\text{s}}^{ - 2}}">
<mo>=</mo>
<mn>0.243</mn>
<mspace width="thinmathspace"></mspace>
<mrow>
<mtext>m</mtext>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math></span>»</p>
<p><em>F</em> = 0.243 × <em>m</em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu = \frac{{0.243 \times m}}{{m \times 9.81}} = 0.025">
<mi>μ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.243</mn>
<mo>×</mo>
<mi>m</mi>
</mrow>
<mrow>
<mi>m</mi>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.025</mn>
</math></span></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>distance travelled after release = 23.85 «m»<br>KE lost = 5.81<em>m</em> «J»</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\mu _{\text{d}}} = \frac{{{\text{KE lost}}}}{{mg \times {\text{distance}}}} = \frac{{5.81m}}{{23.85mg}} = 0.025">
<mrow>
<msub>
<mi>μ</mi>
<mrow>
<mtext>d</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>KE lost</mtext>
</mrow>
</mrow>
<mrow>
<mi>m</mi>
<mi>g</mi>
<mo>×</mo>
<mrow>
<mtext>distance</mtext>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5.81</mn>
<mi>m</mi>
</mrow>
<mrow>
<mn>23.85</mn>
<mi>m</mi>
<mi>g</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.025</mn>
</math></span></p>
<p><em>Award <strong>[3]</strong> for a bald correct answer.</em></p>
<p><em>Ignore sign in acceleration.</em></p>
<p><em>Allow ECF from (a) (note that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu = 0.0073">
<mi>μ</mi>
<mo>=</mo>
<mn>0.0073</mn>
</math></span> x candidate answer to (a) ).</em></p>
<p><em>Ignore any units in answer.</em></p>
<p><em>Condone omission of m in solution.</em></p>
<p><em>Allow g = 10 N kg<sup>–1</sup> (gives 0.024).</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>normal force, upwards, ignore point of application</p>
<p><em>Force must be labeled for its mark to be awarded. Blob at poa not required. <br>Allow OWTTE for normal force. </em><em>Allow N, R, reaction.<br>The vertical forces must lie within the middle third of the stone</em></p>
<p>weight/weight force/force of gravity, downwards, ignore point of application</p>
<p><em>Allow mg, W but not “gravity”. </em></p>
<p><em>Penalise gross deviations from vertical/horizontal once only</em></p>
<p>friction/resistive force, to left, at bottom of stone, point of application must be <strong>on</strong> the interface between ice and stone</p>
<p><em>Allow F, μR. Only allow arrows/lines that lie on the interface. Take the tail of the arrow as the definitive point of application and expect line to be drawn horizontal. <br></em></p>
<p><em>Award <strong>[2 max]</strong> if any force arrow does not touch the stone </em></p>
<p><em>Do not award MP3 if a “driving force” is shown acting to the right. This need not be labelled to disqualify the mark. Treat arrows labelled “air resistance” as neutral.</em></p>
<p><em><img 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" alt></em></p>
<p> </p>
<p><em><strong>N.B:</strong> Diagram in MS is drawn with the vertical forces not direction of travel collinear for clarity</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">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Airboats are used for transport across a river. To move the boat forward, air is propelled from the back of the boat by a fan blade.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>An airboat has a fan blade of radius 1.8 m. This fan can propel air with a maximum speed relative to the boat of 20 m s<sup>−1</sup>. The density of air is 1.2 kg m<sup>−3</sup>.</p>
</div>
<div class="specification">
<p>In a test the airboat is tied to the river bank with a rope normal to the bank. The fan propels the air at its maximum speed. There is no wind.</p>
</div>
<div class="specification">
<p>The rope is untied and the airboat moves away from the bank. The variation with time <em>t</em> of the speed <em>v</em> of the airboat is shown for the motion.<br><br></p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why a force acts on the airboat due to the fan blade.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that a mass of about 240 kg of air moves through the fan every second.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the tension in the rope is about 5 kN.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the airboat has a maximum speed under these conditions.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the distance the airboat travels to reach its maximum speed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the mass of the airboat.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>there is a force «by the fan» on the air / air is accelerated «to the rear» ✓</p>
<p>by Newton 3 ✓</p>
<p>there is an «equal and» opposite force on the boat ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>air gains momentum «backward» ✓</p>
<p>by conservation of momentum / force is rate of change in momentum ✓</p>
<p>boat gains momentum in the opposite direction ✓</p>
<p> </p>
<p><em>Accept a reference to Newton’s third law, e.g. N’3, or any correct statement of it for <strong>MP2</strong> in <strong>ALT 1</strong>.</em></p>
<p><em>Allow any reasonable choice of object where the force of the air is acting on, e.g., fan or blades.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><msup><mi>R</mi><mn>2</mn></msup></math> <em><strong>OR</strong></em> «mass of air through system per unit time =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>v</mi><mi>ρ</mi></math> seen ✓</p>
<p>244 «kg s<sup>−1</sup>» ✓</p>
<p> </p>
<p><em>Accept use of Energy of air per second = 0.5 ρΑv<sup>3</sup> = 0.5 mv<sup>2</sup> for <strong>MP1</strong>.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«force = Momentum change per sec = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>v</mi><mn>2</mn></msup><mi>ρ</mi></math> = » 244 x 20 <em><strong>OR</strong> </em>4.9 «kN» ✓</p>
<p> </p>
<p><em>Allow use of 240</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>resistive forces increase with speed <em><strong>OR</strong> </em>resistive forces/drag equal forward thrust ✓</p>
<p>acceleration/net force becomes zero/speed remains constant ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that area under the graph is distance covered ✓</p>
<p>«Distance =» 480 - 560 «m» ✓</p>
<p> </p>
<p><em>Accept graphical evidence or calculation of correct geometric areas for <strong>MP1</strong>.</em></p>
<p><em><strong>MP2</strong> is numerical value within range.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>calculation of acceleration as gradient at <em>t</em> = 0 «= 1 m s<sup>-2</sup>» ✓</p>
<p>use of <em>F=ma <strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4900</mn><mn>1</mn></mfrac></math>seen ✓</p>
<p>4900 «kg» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> can be shown on the graph.</em></p>
<p><em>Allow an acceleration in the range 1 – 1.1 for <strong>MP2</strong> and consistent answer for <strong>MP3</strong></em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.</em></p>
<p><em>Allow use of average acceleration = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>40</mn></mfrac></math></em><br><br><em>or assumption of constant force to obtain 11000 «kg» for<strong> [2]</strong></em></p>
<p><em>Allow use of 4800 or 5000 for <strong>MP2</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The majority succeeded in making use of Newton's third law to explain the force on the boat. The question was quite well answered but sequencing of answers was not always ideal. There were some confusions about the air hitting the bank and bouncing off to hit the boat. A small number thought that the wind blowing the fan caused the force on the boat.</p>
<p>bi) This was generally well answered with candidates either starting from the wind turbine formula given in the data booklet or with the mass of the air being found using <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi><mi>A</mi><mi>v</mi></math>.</p>
<p>1bii) Well answered by most candidates. Some creative work to end up with 240 was found in scripts.</p>
<p>1ci) Many candidates gained credit here for recognising that the resistive force eventually equalled the drag force and most were able to go on to link this to e.g. zero acceleration. Some had not read the question properly and assumed that the rope was still tied. There was one group of answers that stated something along the lines of "as there is no rope there is nothing to stop the boat so it can go at max speed.</p>
<p>1cii) A slight majority did not realise that they had to find the area under the velocity-time graph, trying equations of motion for non-linear acceleration. Those that attempted to calculate the area under the graph always succeeded in answering within the range.</p>
<p>1ciii) Use of the average gradient was common here for the acceleration. However, there also were answers that attempted to calculate the mass via a kinetic energy calculation that made all sorts of incorrect assumptions. Use of average acceleration taken from the gradient of the secant was also common.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A small metal pendulum bob is suspended at rest from a fixed point with a length of thread of negligible mass. Air resistance is negligible.</p>
<p>The pendulum begins to oscillate. Assume that the motion of the system is simple harmonic, and in one vertical plane.</p>
<p>The graph shows the variation of kinetic energy of the pendulum bob with time.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>When the 75 g bob is moving horizontally at 0.80 m s<sup>–1</sup>, it collides with a small stationary object also of mass 75 g. The object and the bob stick together.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in m, the length of the thread. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label on the graph with the letter X a point where the speed of the pendulum is half that of its initial speed.</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 mass of the pendulum bob is 75 g. Show that the maximum speed of the bob is about 0.7 m s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the combined masses immediately after the collision.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the collision is inelastic.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.</p>
<p style="text-align:center;"><img 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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="text-align:left;">The speed after the collision of the bob and the object was measured using a sensor. This sensor emits a sound of frequency <em>f</em> and this sound is reflected from the moving bob. The sound is then detected by the sensor as frequency <em>f</em>′.</p>
<p style="text-align:left;">Explain why <em>f</em> and <em>f</em>′ are different.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iv.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies T as 2.25 s ✔</p>
<p>L = 1.26 m ✔</p>
<p>1.3 / 1.26 «m» ✔</p>
<p><em>Accept <span style="text-decoration:underline;">any</span> number of s.f. for MP2.</em></p>
<p><em>Accept <span style="text-decoration:underline;">any</span> answer with 2 or 3 s.f. for MP3</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>X labels any point <span style="text-decoration:underline;">on the curve</span> where <em>E<span style="font-size:11.6667px;"><sub>K</sub> </span></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> of maximum/5 mJ ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> mv<sup>2</sup> = 20 × 10<sup>−3</sup> seen <em><strong>OR </strong></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> × 7.5 × 10<sup>-2</sup> × <em>v</em><sup>2</sup> = 20 × 10<sup>-3</sup> ✔</p>
<p>0.73 «m s<sup>−1</sup>» ✔</p>
<p><em>Must see at least 2 s.f. for MP2</em>.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.40 «m s<sup>-1</sup>» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>initial energy 24 mJ and final energy 12 mJ ✔</p>
<p>energy is lost/unequal /change in energy is 12 mJ ✔</p>
<p>inelastic collisions occur when energy is lost ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>graph with same period but inverted ✔</p>
<p>amplitude one half of the original/two boxes throughout (by eye) ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mention of Doppler effect ✔</p>
<p>there is a change in the wavelength of the reflected wave ✔</p>
<p>because the wave speed is constant, there is a change in frequency ✔</p>
<div class="question_part_label">b.iv.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was well approached by candidates. The noteworthy mistakes were not reading the correct period of the pendulum from the graph, and some simple calculation and mathematical errors. This question also had one mark for writing an answer with the correct number of significant digits. Candidates should be aware to look for significant digit question on the exam and can write any number with correct number of significant digits for the 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;">
<p>This question was well answered. This is a “show that” question so candidates needed to clearly show the correct calculation and write an answer with at least one significant digit more than the given answer. Many candidates failed to appreciate that the energy was given in mJ and the mass was in grams, and that these values needed to be converted before substitution.</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates fell into some broad categories on this question. This was a “show that” question, so there was an expectation of a mathematical argument. Many were able to successfully show that the initial and final kinetic energies were different and connect this to the concept of inelastic collisions. Some candidates tried to connect conservation of momentum unsuccessfully, and some simply wrote an extended response about the nature of inelastic collisions and noted that the bobs stuck together without any calculations. This approach was awarded zero marks.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates drew graphs that received one mark for either recognizing the phase difference between the gravitational potential energy and the kinetic energy, or for recognizing that the total energy was half the original energy. Few candidates had both features for both marks.</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was essentially about the Doppler effect, and therefore candidates were expected to give a good explanation for why there is a frequency difference. As with all explain questions, the candidates were required to go beyond the given information. Very few candidates earned marks beyond just recognizing that this was an example of the Doppler effect. Some did discuss the change in wavelength caused by the relative motion of the bob, although some candidates chose very vague descriptions like “the waves are all squished up” rather than using proper physics terms. Some candidates simply wrote and explained the equation from the data booklet, which did not receive marks. It should be noted that this was a three mark question, and yet some candidates attempted to answer it with a single sentence.</p>
<div class="question_part_label">b.iv.</div>
</div>
<br><hr><br><div class="specification">
<p>A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="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 non-uniform electric field, with field lines as shown, exists in a region where there is no gravitational field. X is a point in the electric field. The field lines and X lie in the plane of the paper.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by electric field strength.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is placed at X and released from rest. Draw, on the diagram, the direction of the force acting on the electron due to the field.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force per unit charge</p>
<p>acting on a small/test positive charge</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontally to the left</p>
<p><em>Arrow does not need to touch X</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>proton moves to the right/they move in opposite directions</p>
<p>force on each is initially the same</p>
<p>proton accelerates less than electron initially «because mass is greater»</p>
<p>field is stronger on right than left «as lines closer»</p>
<p>proton acceleration increases «as it is moving into stronger field»</p>
<p><em><strong>OR</strong></em></p>
<p>electron acceleration decreases «as it is moving into weaker field»</p>
<p><em>Allow ECF from (b)</em></p>
<p><em>Accept converse argument for electron</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.44.22.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/01"></p>
<p>The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.</p>
</div>
<div class="specification">
<p>In another test, the block hangs in equilibrium at the end of the same elastic rope. The elastic constant of the rope is 400 Nm<sup>–1</sup>. The block is pulled 3.50 m vertically below the equilibrium position and is then released from rest.</p>
</div>
<div class="specification">
<p>An elastic climbing rope is tested by fixing one end of the rope to the top of a crane. The other end of the rope is connected to a block which is initially at position A. The block is released from rest. The mass of the rope is negligible.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.44.22.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/01"></p>
<p>The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.</p>
</div>
<div class="specification">
<p>At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.</p>
</div>
<div class="specification">
<p>For the rope and block, describe the energy changes that take place</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>At position B the rope starts to extend. Calculate the speed of the block at position B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude of the average resultant force acting on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the magnitude of the average force exerted by the rope on the block between B and C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>between B and C.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the block to return to the equilibrium position for the first time. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the block as it passes the equilibrium position. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>use of conservation of energy</p>
<p><strong><em>OR</em></strong></p>
<p><em>v</em><sup>2</sup> = <em>u</em><sup>2</sup> + 2<em>as</em></p>
<p> </p>
<p><em>v</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 60.0 \times 9.81} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>60.0</mn>
<mo>×</mo>
<mn>9.81</mn>
</msqrt>
</math></span><strong>»</strong> = 34.3 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of impulse <em>F</em><sub>ave</sub> × Δ<em>t</em> = Δ<em>p</em></p>
<p><strong><em>OR</em></strong></p>
<p>use of <em>F</em> = <em>ma</em> with average acceleration</p>
<p><strong><em>OR</em></strong></p>
<p><em>F</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{80.0 \times 34.3}}{{0.759}}">
<mfrac>
<mrow>
<mn>80.0</mn>
<mo>×</mo>
<mn>34.3</mn>
</mrow>
<mrow>
<mn>0.759</mn>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<p>3620<strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (a).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>upwards</p>
<p>clearly longer than weight</p>
<p> </p>
<p><em>For second marking point allow ECF from (b)(i) providing line is upwards.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>3620 + 80.0 × 9.81</p>
<p>4400 <strong>«</strong>N<strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from (b)(i).</em></p>
<p><strong><em>[</em></strong><strong><em>2 marks]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential energy (of block) into kinetic energy (of block)</p>
<p> </p>
<p><em>Must</em><em> see names of energy (gravitational potential energy and kinetic energy) – Allow for reasonable variations of terminology (eg energy of motion for KE).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(loss in) gravitational potential and kinetic energy of block into elastic potential energy of rope</p>
<p> </p>
<p><em>See note for 1(c)(i) for naming convention.</em></p>
<p><em>Must see either the block or the rope (or both) mentioned in connection with the appropriate energies.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>k can be determined using EPE = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kx</em><sup>2</sup></p>
<p>correct statement or equation showing</p>
<p>GPE at A = EPE at C</p>
<p><strong><em>OR</em></strong></p>
<p>(GPE + KE) at B = EPE at C</p>
<p> </p>
<p><em>Candidate must clearly indicate the energy associated with either position A or B for MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>T</em> = 2<em>π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{80.0}}{{400}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>80.0</mn>
</mrow>
<mrow>
<mn>400</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> = 2.81 <strong>«</strong>s<strong>»</strong></p>
<p>time = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{T}{4}">
<mfrac>
<mi>T</mi>
<mn>4</mn>
</mfrac>
</math></span> = 0.702 <strong>«</strong>s<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for kinematic solutions that assume a constant acceleration.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><em>ω</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2\pi }}{{2.81}}">
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>2.81</mn>
</mrow>
</mfrac>
</math></span> = 2.24 <strong>«</strong>rad s<sup>–1</sup><strong>»</strong></p>
<p><em>v </em>= 2.24 × 3.50 = 7.84 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>kx</em><sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em>mv</em><sup>2</sup> <strong><em>OR</em></strong> <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>400 × 3.5<sup>2</sup> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>80<em>v</em><sup>2</sup></p>
<p><em>v = </em>7.84 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[0] </em></strong><em>for kinematic solutions that assume a constant acceleration.</em></p>
<p><em>Allow ECF for T from (e)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>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 company delivers packages to customers using a small unmanned aircraft. Rotating horizontal blades exert a force on the surrounding air. The air above the aircraft is initially stationary.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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" width="319" height="179"></p>
<p>The air is propelled vertically downwards with speed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. The aircraft hovers motionless above the ground. A package is suspended from the aircraft on a string. The mass of the aircraft is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>95</mn><mtext> kg</mtext></math> and the combined mass of the package and string is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>45</mn><mo> </mo><mi>kg</mi></math>. The mass of air pushed downwards by the blades in one second is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi>kg</mi></math>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the value of the resultant force on the aircraft when hovering.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, by reference to Newton’s third law, how the upward lift force on the aircraft is achieved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math>. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power transferred to the air by the aircraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a(iv).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">zero </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">Blades exert a downward force on the air </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0"><br>air exerts an equal and opposite force on the blades </span><span class="fontstyle3">«</span><span class="fontstyle0">by Newton’s third law</span><span class="fontstyle3">»<br></span><span class="fontstyle4"><em><strong>OR</strong></em><br></span><span class="fontstyle0">air exerts a reaction force on the blades </span><span class="fontstyle3">«</span><span class="fontstyle0">by Newton’s third law</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<p><em><span class="fontstyle5"><br>Downward direction required for </span><strong><span class="fontstyle4">MP1</span></strong><span class="fontstyle4">.</span></em></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«</span><span class="fontstyle1">lift force/change of momentum in one second</span><span class="fontstyle0">» <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi></math> </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mi>v</mi><mo>=</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>95</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>45</mn></mrow></mfenced><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> ✓</span></p>
<p><span class="fontstyle4"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>1</mn><mo> </mo><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> <em><strong>AND </strong></em></span><span class="fontstyle1">answer expressed to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> sf only </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle5"><em><br>Allow</em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">8</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">2</mn></math> <em>from </em></span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn><mo mathvariant="italic"> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">2</mn></mrow></msup></math>.</p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="fontstyle0">power <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>rate</mi><mo> </mo><mi>of</mi><mo> </mo><mi>energy</mi><mo> </mo><mi>transfer</mi><mo> </mo><mi>to</mi><mo> </mo><mi>the</mi><mo> </mo><mi>air</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfrac><mrow><mo>∆</mo><mi>m</mi></mrow><mrow><mo>∆</mo><mi>t</mi></mrow></mfrac><msup><mi>v</mi><mn>2</mn></msup><mo>»</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>1</mn><mo>.</mo><mn>7</mn><mo>×</mo><mn>8</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup></math> ✓</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">W</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><span class="fontstyle0">Power <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mi>Force</mi><mo> </mo><mo>×</mo><mo> </mo><mi>v</mi><mo> </mo><mi>ave</mi><mo>»</mo><mo>=</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>95</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>45</mn></mrow></mfenced><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn><mo>×</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>1</mn></mrow><mn>2</mn></mfrac></math> ✓</span> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">W</mi><mo>»</mo></math> ✓</span></p>
<div class="question_part_label">a(iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">vertical force = lift force – weight </span><span class="fontstyle2"><em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>.</mo><mn>4</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo>»</mo><mo> </mo></math></span><span class="fontstyle4">✓</span></p>
<p><span class="fontstyle0">acceleration <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>95</mn></mrow></mfrac><mo>=</mo><mn>4</mn><mo>.</mo><mn>6</mn><mo> </mo><mo>«</mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo><mo> </mo></math></span><span class="fontstyle4">✓</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally answered well with the most common incorrect answer being the weight of the aircraft and package. The question uses the command term 'state' which indicates that the answer requires no working.</p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The question required candidates to apply Newton's third law to a specific situation. Candidates who had learned the 'action and reaction' version of Newton's third law generally did less well than those who had learned a version describing 'object A exerting a force on object B' etc. Some answers lacked detail of what was exerting the force and in which direction.</p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was answered well with many getting full marks. A small number gave the wrong number of significant figures and some attempted to answer using kinematics equations or kinetic energy.</p>
<div class="question_part_label">a(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>HL only. It was common to see answers that neglected to average the velocity and consequently arrived at an answer twice the size of the correct one. This was awarded 1 of the 2 marks.</p>
<div class="question_part_label">a(iv).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Well done by a good number of candidates. Many earned a mark by simply using the correct mass to find an acceleration even though the force was incorrect.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The moon Phobos moves around the planet Mars in a circular orbit.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the origin of the force that acts on Phobos.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why this force does no work on Phobos.</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 orbital period <em>T</em> of a moon orbiting a planet of mass <em>M</em> is given by</p>
<p style="text-align:center;"><span style="background-color:#ffffff;"><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\frac{{{R^3}}}{{{T^2}}} = kM">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mi>k</mi>
<mi>M</mi>
</math></span></span></p>
<p>where <em>R</em> is the average distance between the centre of the planet and the centre of the moon.</p>
<p>Show that <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The following data for the Mars–Phobos system and the Earth–Moon system are available:</p>
<p>Mass of Earth = 5.97 × 10<sup>24</sup> kg</p>
<p>The Earth–Moon distance is 41 times the Mars–Phobos distance.</p>
<p>The orbital period of the Moon is 86 times the orbital period of Phobos.</p>
<p>Calculate, in kg, the mass of Mars.</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 graph shows the variation of the gravitational potential between the Earth and Moon with distance from the centre of the Earth. The distance from the Earth is expressed as a fraction of the total distance between the centre of the Earth and the centre of the Moon.</p>
<p style="text-align:center;"><img src="data:image/png;base64,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"></p>
<p style="text-align:left;">Determine, using the graph, the mass of the Moon.</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>gravitational attraction/force/field «of the planet/Mars» ✔</p>
<p><em>Do not accept “gravity”</em>.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the force/field and the velocity/displacement are at 90° to each other <strong><em>OR</em></strong></p>
<p>there is no change in GPE of the moon/Phobos ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATE 1</strong></em></p>
<p>«using fundamental equations»</p>
<p>use of Universal gravitational force/acceleration/orbital velocity equations ✔</p>
<p>equating to centripetal force or acceleration. ✔</p>
<p>rearranges to get <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="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<p><em><strong>ALTERNATE 2</strong></em></p>
<p>«starting with <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:center;text-decoration:none;text-indent:0px;white-space:normal;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{R^3}}}{{{T^2}}} = kM">
<mfrac>
<mrow>
<mrow>
<msup>
<mi>R</mi>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>T</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mi>k</mi>
<mi>M</mi>
</math></span><span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">»</span></span></p>
<p>substitution of proper equation for T from orbital motion equations ✔</p>
<p>substitution of proper equation for M <em><strong>OR</strong></em> R from orbital motion equations ✔</p>
<p>rearranges to get <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="k = \frac{G}{{4{\pi ^2}}}">
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mi>G</mi>
<mrow>
<mn>4</mn>
<mrow>
<msup>
<mi>π</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{m_{{\text{Mars}}}} = {\left( {\frac{{{R_{{\text{Mars}}}}}}{{{R_{{\text{Earth}}}}}}} \right)^3}{\left( {\frac{{{T_{{\text{Earth}}}}}}{{{T_{Mars}}}}} \right)^2}{m_{{\text{Earth}}}}">
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mrow>
<mtext>Mars</mtext>
</mrow>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>Mars</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>R</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>T</mi>
<mrow>
<mi>M</mi>
<mi>a</mi>
<mi>r</mi>
<mi>s</mi>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msub>
<mi>m</mi>
<mrow>
<mrow>
<mtext>Earth</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</math></span></span> or other consistent re-arrangement ✔</p>
<p>6.4 × 10<sup>23</sup> «kg» ✔</p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>read off separation at maximum potential 0.9 ✔</p>
<p>equating of gravitational field strength of earth and moon at that location <em><strong>OR <img src="data:image/png;base64,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">✔</strong></em></p>
<p>7.4 × 10<sup>22</sup> «kg» ✔</p>
<p><em>Allow ECF from MP1</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>This was generally well answered, although some candidates simply used the vague term “gravity” rather than specifying that it is a gravitational force or a gravitational field. Candidates need to be reminded about using proper physics terms and not more general, “every day” terms on the exam.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates connected the idea that the gravitational force is perpendicular to the velocity (and hence the displacement) for the mark. It was also allowed to discuss that there is no change in gravitational potential energy, so therefore no work was being done. It was not acceptable to simply state that the net displacement over one full orbit is zero. Unfortunately, some candidates suggested that there is no net force on the moon so there is no work done, or that the moon is so much smaller so no work could be done on it.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was another “show that” derivation. Many candidates attempted to work with universal gravitation equations, either from memory or the data booklet, to perform this derivation. The variety of correct solution paths was quite impressive, and many candidates who attempted this question were able to receive some marks. Candidates should be reminded on “show that” questions that it is never allowed to work backwards from the given answer. Some candidates also made up equations (such as T = 2𝝿r) to force the derivation to work out.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was challenging for candidates. The candidates who started down the correct path of using the given derived value from 5bi often simply forgot that the multiplication factors had to be squared and cubed as well as the variables.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was left blank by many candidates, and very few who attempted it were able to successfully recognize that the gravitational fields of the Earth and Moon balance at 0.9r and then use the proper equation to calculate the mass of the Moon.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A chicken’s egg of mass 58 g is dropped onto grass from a height of 1.1 m. Assume that air resistance is negligible and that the egg does not bounce or break.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>impulse</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the kinetic energy of the egg just before impact is about 0.6 J.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the egg is likely to break when dropped onto concrete from the same height.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>force × time</p>
<p><em><strong>OR</strong></em></p>
<p>change in momentum ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>k</sub> = mgh = 0.058 × 9.81 ×1.1 = 0.63 J ✔</p>
<p><em>Allow use of g = 10 m s<sup>−2</sup> (which gives 0.64 «J»)</em></p>
<p><em>Substitution and at least 2 SF must be shown</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>initial momentum = <em>mv</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 0.058 \times 0.63} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>0.058</mn>
<mo>×</mo>
<mn>0.63</mn>
</msqrt>
</math></span> «= 0.27 kg m s<sup>−1</sup>»</p>
<p><em><strong>OR</strong></em></p>
<p><em>mv</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.058 \times \sqrt {2 \times 9.81 \times 1.1} ">
<mn>0.058</mn>
<mo>×</mo>
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>9.81</mn>
<mo>×</mo>
<mn>1.1</mn>
</msqrt>
</math></span> «= 0.27 kg m s<sup>−1</sup>» ✔</p>
<p>force = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{change in momentum}}}}{{{\text{time}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>change in momentum</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>time</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.27}}{{0.055}}">
<mfrac>
<mrow>
<mn>0.27</mn>
</mrow>
<mrow>
<mn>0.055</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>4.9 «N» ✔</p>
<p><em>F − mg</em> = 4.9 so <em>F </em>= 5.5 «N» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>«<em>E</em><sub>k</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span>mv<sup>2</sup> = 0.63 J» v = 4.7 m s<sup>−1</sup> ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta v}}{{\Delta t}}">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
</mfrac>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{4.7}}{{55 \times {{10}^{ - 3}}}}">
<mfrac>
<mrow>
<mn>4.7</mn>
</mrow>
<mrow>
<mn>55</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «85 m s<sup>−2</sup>» ✔</p>
<p>4.9 «N» ✔</p>
<p><em>F − mg</em> = 4.9 so <em>F</em>= 5.5 «N» ✔</p>
<p> </p>
<p><em>Accept negative acceleration and force.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>concrete reduces the stopping time/distance ✔</p>
<p>impulse/change in momentum same so force greater</p>
<p><em><strong>OR</strong></em></p>
<p>work done same so force greater ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>concrete reduces the stopping time ✔</p>
<p>deceleration is greater so force is greater ✔</p>
<p> </p>
<p><em>Allow reverse argument for grass.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Plutonium-238 (Pu) decays by alpha (α) decay into uranium (U).</p>
<p>The following data are available for binding energies per nucleon:</p>
<p style="padding-left: 30px;">plutonium 7.568 MeV</p>
<p style="padding-left: 30px;">uranium 7.600 MeV</p>
<p style="padding-left: 30px;">alpha particle 7.074 MeV</p>
</div>
<div class="specification">
<p>The energy in b(i) can be transferred into electrical energy to run the instruments of a spacecraft. A spacecraft carries 33 kg of pure plutonium-238 at launch. The decay constant of plutonium is 2.50 × 10<sup>−10</sup> s<sup>−1</sup>.</p>
</div>
<div class="specification">
<p>Solar radiation falls onto a metallic surface carried by the spacecraft causing the emission of photoelectrons. The radiation has passed through a filter so it is monochromatic. The spacecraft is moving away from the Sun.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the binding energy of a nucleus.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the axes, a graph to show the variation with nucleon number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of the binding energy per nucleon, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>BE</mtext><mi>A</mi></mfrac></math>. Numbers are not required on the vertical axis.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some unstable nuclei have many more neutrons than protons. Suggest the likely decay for these nuclei.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy released in this decay is about 6 MeV.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The plutonium nucleus is at rest when it decays.</p>
<p>Calculate the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>kinetic energy of alpha particle</mtext><mtext>kinetic energy of uranium</mtext></mfrac></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the power, in kW, that is available from the plutonium at launch.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spacecraft will take 7.2 years (2.3 × 10<sup>8</sup> s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> State and explain what happens to the kinetic energy of an emitted photoelectron.</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> State and explain what happens to the rate at which charge leaves the metallic surface.</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>the energy needed to «completely» separate the nucleons of a nucleus</p>
<p><em><strong>OR</strong></em></p>
<p>the energy released when a nucleus is assembled from its constituent nucleons ✓</p>
<p> </p>
<p><em>Accept reference to protons and </em><em>neutrons.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve rising to a maximum between 50 and 100 ✓</p>
<p>curve continued and decreasing ✓</p>
<p> </p>
<p><em>Ignore starting point.<br></em></p>
<p><em>Ignore maximum at alpha particle.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>At a point on the peak of their graph ✓</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>beta minus «decay» ✓</p>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct mass numbers for uranium (234) and alpha (4) ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>234</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>600</mn><mo>+</mo><mn>4</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>074</mn><mo>-</mo><mn>238</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>568</mn></math> «MeV» ✓</p>
<p>energy released 5.51 «MeV» ✓</p>
<p> </p>
<p><em>Ignore any negative sign.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>K</mi><msub><mi>E</mi><mi>α</mi></msub></mrow><mrow><mi>K</mi><msub><mi>E</mi><mi>U</mi></msub></mrow></mfrac><mo>=</mo></math>»<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>α</mi></msub></mrow></mfrac><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>m</mi><mi>U</mi></msub></mrow></mfrac></mfrac></mstyle></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>m</mi><mi>U</mi></msub><msub><mi>m</mi><mi>α</mi></msub></mfrac></math> ✓</p>
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>234</mn><mn>4</mn></mfrac><mo>=</mo></math>» <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>.</mo><mn>5</mn></math> ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer.</em></p>
<p><em>Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>117</mn><mn>2</mn></mfrac></math> for <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>number of nuclei present <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>33</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mn>238</mn></mfrac><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>«</mo><mo>=</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>»</mo></math> ✓</p>
<p>initial activity is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><msub><mi>N</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>8</mn><mo>.</mo><mn>347</mn><mo>×</mo><msup><mn>10</mn><mn>25</mn></msup><mo>«</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo> </mo><mtext>Bq</mtext><mo>»</mo></math> ✓</p>
<p>power is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>08</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup><mo>×</mo><mn>5</mn><mo>.</mo><mn>51</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>≈</mo><mn>18</mn></math> «kW» ✓</p>
<p> </p>
<p><em>Allow a final answer of 20 </em>kW<em> if 6 </em>MeV<em> used. </em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong> and <strong>MP2</strong>.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>available power after time <em>t</em> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><msup><mi>e</mi><mrow><mo>−</mo><mn>2</mn><mo>.</mo><mn>50</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></msup><mo>=</mo><mn>17</mn><mo>.</mo><mn>0</mn></math> «kW» ✓</p>
<p> </p>
<p><em><strong>MP1</strong> may be implicit.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 17.4 </em>kW<em> from unrounded power from <strong>(c)(i)</strong>.</em></p>
<p><em>Allow 18.8 </em>kW<em> from 6 </em>MeV<em>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>stays the same ✓</p>
<p>as energy depends on the frequency of light ✓</p>
<p> </p>
<p><em>Allow reference to wavelength for <strong>MP2</strong>.</em></p>
<p><em>Award <strong>MP2</strong> only to answers stating that KE decreases due to Doppler effect.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>decreases ✓</p>
<p>as number of photons incident decreases ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.</p>
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"></p>
<p>The mass of ions ejected each second is 6.6 × 10<sup><span style="font-size: small;">–6 </span></sup>kg and the speed of each ion is 5.2 × 10<sup><span style="font-size: small;">4</span></sup> m s<sup><span style="font-size: small;">–1</span></sup>. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.</p>
</div>
<div class="specification">
<p>An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.</p>
</div>
<div class="specification">
<p>In practice, the ions leave the spacecraft at a range of angles as shown.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the initial acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Estimate the maximum speed of the spacecraft.</p>
<p>(ii) Outline why the answer to (i) is an estimate.</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>Outline why scientists sometimes use estimates in making calculations.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ions are likely to spread out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>change in momentum each second = 6.6 × 10<sup>−6</sup> × 5.2 × 10<sup>4</sup> «= 3.4 × 10<sup>−1 </sup>kg m s<sup>−1</sup>» ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}">
<mfrac>
<mrow>
<mn>3.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>740</mn>
</mrow>
</mfrac>
</math></span> =» 4.6 × 10<sup>−4</sup> «m s<sup>−2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) <strong>ALTERNATIVE</strong><em><strong> 1:</strong></em></p>
<p>(considering the acceleration of the spacecraft)</p>
<p>time for acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «4.6 × 10<sup>6</sup>» «s» ✔</p>
<p>max speed = «answer to (a) × 4.6 × 10<sup>6</sup> =» 2.1 × 10<sup>3</sup> «m s<sup>−1</sup>» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>(considering the conservation of momentum)</p>
<p>(momentum of 30 kg of fuel ions = change of momentum of spacecraft)</p>
<p>30 × 5.2 × 10<sup>4 </sup>= 710 × max speed ✔</p>
<p>max speed = 2.2 × 10<sup>3 </sup>«m s<sup>−1</sup>» ✔</p>
<p> </p>
<p>(ii) as fuel is consumed total mass changes/decreases so acceleration changes/increases<br><em><strong>OR</strong></em><br>external forces (such as gravitational) can act on the spacecraft so acceleration isn’t constant ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>problem may be too complicated for exact treatment ✔</p>
<p>to make equations/calculations simpler ✔</p>
<p>when precision of the calculations is not important ✔</p>
<p>some quantities in the problem may not be known exactly ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ions have same (sign of) charge ✔</p>
<p>ions repel each other ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the forces between the ions do not affect the force on the spacecraft. ✔</p>
<p>there is no effect on the acceleration of the spacecraft. ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<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.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>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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pVGjx7tbalbBLklCgoKvKWgzZs3qaRkv44cOVIaul988YWKina4ywcOHNTBgwfcZWPZsqXe0umde26UYmNjvbWKNm7coO7d4721isz91dWtW/dyr9WyZSudc04Tdzk+/jvOeznXXQ5VJ3br1q10m2GWO3Xq5K0BDYvP59OKFSs0YcIEbwsiUeiEq75qKgnyemCueR04EAzZtWvXOoFcon379mnNmtWlAbx+/bpypeJOnTqrWbNmTlAXOY/Z7209e7Vt2849Az759xE6MWjbtq2io1u4wW+W27RprQsu6Oo+JrhO6QaRjyC3gylomZpKgrwBMC1Lt24N/iFNQO/YsUOfffaZPv/8c+fnRvdmmBAydu360v2JutOxY2ft2fNVafhfccWVbi1Aly5d1L27OQno4AY+JX1EAoLcDgS5ZULXj03VdmHhFn38ca67Hqq6NiXnbdtoCGYzc2nBXOM3J1qm9N6790XOCUAnJScnu2F/3nnn0Q4AdYIgtwNBHqFCpetPPvlEn376qVvVvXjxonIHeZydzjuvvb744nM35C+++BIlJSU5P5Pdknx9tVpFw0SQ24EgjwCh0F6+fLkWLVrklLJXuKVsE9pcj0Z1hQI+OflipaVdpj59+qhHjx6EO74xgtwOBHk9MMG9fv16p4S9WPPmfSi/f6WaN2+uQ4cOeY+IXOYab/PmzbR3794KtQJlW4Cfc845atmypbtsJCUle0tBpuFcVQ2+evfu7S1VznxhT9X9zLSeN+0CKmPaDZRlGv1t2PAfb820GzjRwO/kBn+GbY3+TIM887f63veu03XXXafLLruMYEe1EeR2IMjriLm2vWzZMr311luaP//DiAhu04WrbFctU5KLiopyq2xjY893r8W2aNFC0dHRFbpd1WfL6/ocEKZsi38jdNJg/r6HDx92Gxd+9dVXKi7e64Z9qIGhqV2JiWmt7dvr532HmPfRrFlTDRky1A32Sy65hGvtqBJBbgeCvJYtXbpU06ZNc8O7rphScygwQo2lTOnYlIrNumkoZULasLHRlI0ju5Ud5CbU5W/nzp1ubUDZxoqmR4GpsamL0r45mWzatJluvPFGff/76erXr593DxBEkNuBIK9KkU9ZaeOkKXP0p3TnC511s+7XE1rhrFQ9VMkJCxcu0GOPPeZe+/766yPe1ppjDvimattUZ5ubac184YUXloZ0fZaY8c2FSvyhXgmmoeP27dvcho5G6Dp4TfvWt77l1rw89thvdNttt3lbcbaL6CAvd4zuIh0vkv/97eo4MFWxtTav5hEV+Zdqe8crlRrb1NtW/wjyatlS7SA3v9CsrBFuaasmSlWhBm9XX32NevTo6YZ1z5491a5dO/oZn2VCjSJNdf7GjRu1dOkSt3Rvqu9D18LPlAl00/r99dffUMeOHb2tOFvZE+St5c8eovQ/D5Dv44eUGhycscYd9U9S3/S5uss3S6NSo72t9a++g7xBzUduSuE333yje2D9JiFuQtuUpAcMuNH5x3la7747R/PmzXf/ODNnvqZx48a5paWLL76YED8LmUsgpqGameVo+PDheuGFqVq0aLH7/Xj7bZ9eeeVVPfDAKPekzzDhHi5zXr1p02e64orLnDB/3dsKAFWr3SAvKdC87BHqFdfZva7aK2uK5hUUe3eaKpLXNHZgT/e+uLg0ZWX75C/yqsHN2V5csrJ8W4Lrp2FCfOTIu8NqwGaCOyGhh1OCH+lOQ7d06TJ98skqvfzyy+6BmsCunPl7oTwT8Nddd71++ctfuid9oXCfOvUlt2Fb69atwwp2E+i/+tUjuv/++92zfaBmfamFY/spbnCOCo57m3RcxQvHOcfrHymnwBxHT3OMLlUSLI1nr5V2T1J69wHK9u9xDuH3Ka7XCGW/MlYDSzPgRS33L9SUrDRvn4M01rfO2YPHVM/7JimrV/Dx7v0zclXkvMdgaXySdmutstMvVEq2X0fdp/jlK5MzcQPHaoa/yPk0hqnNTVavzBHKdPfZU4Nz1nn3NRy1F+THC+V7+Ef68bRoPfXPjSrMn6vRmqkfD35GC4uPqsT/ojLTJ2vnTa9qxaat2rTiD0peO0HpmS/KXxLer9lUed53332nDXET3IY5sIaC25S4TUnblLK4po2aZML95ptvVnZ2tlatWqP33/+HW9Nj+pibceBP5/jx406Ir3cvFZmpLE01K6GOmtFGqdd/T1F5H2jJhtBxc7f8H8zX/pTrdVV80zCO0dFKHTVLvlG9nd0+JN/GuSeqvfd/pLkbLtUf8zcp/4OndNWSJzU0/Vl9OdynTYX/cp7TRDPuf0J/dU8c9sg/+V6lP7pe/Xz5zslwofOc27RzwnBlTs7VodSH9LHvIeed99Yo36fKG5WqJiW5mpx5hx5de618+YXOc/L1wbBdmpB+ryY7JxMh++fv1sWv/cv5DG/riYHdGlZVtKPWrpEfL8hRev+npCfekS+z50m/OHM2mK6MNVma58tUgndn8Dl/UtJ0n8Zf+FG1G7vNmTPHOdDd461VZAL88suvUGbmXbrsssvp7nOGzFlvfV0LaihMK/r33ntPL7887ZTtOcx315xwbtmyxe2BsXr1auf7/q7bwPKqq2jl3tCZXhUdOsRqypQp3pYaVLxQYy+7R2tGe8focutttTisY/TJ18iPOiXyB5V2/1d6Yt7/U2ZCc+fJ65STPljj2k8sPY6Xu+b9nY/Lvx/3FQ+pIGeE+k+M1/Tlj6vff/5Q5hr5uc5HeFyXZWzQ6NBrGN7rTEx6ScvHx2u+yY7PHyr3OWpag23sFvwD5ahvqEVjWUf9yu47WH++6x19bM6qvM3lvlgD/62R1QzyZ599VpMnZ3tr5aWm9tHvf/8Mg3DUIIK8ZpkT0dGjH3H7vlfGDL5z8ve3bHc6NFwffvihOzbC7373O29LTSpboMpQh8VlQrFbfpjH6KqC3LnbKcmnx5o9BBstP947p3SfZYP8gRZ/dU4S/ld57gudLN3dzy3bp5QJ8ibBkB8X7FFSwQ3POXnRR/+sZkPpM0Fjt7IO7NHOGuy+a/rpmu5CpgEbEKmios5V48bh/Suay0B8r3Fm2qjvkNuU6FavbytTre6VbCtTw8foirrqzul5biCWvz3nnQxUIuonmv4vU61+0nNqMbgjzVlTtX7jjTcpMzPTbcAG1DfTrmP58n/qt7/9rdd3veqqddOOw8jNzXW7Ii1Z8lHpiHXDh2e4P9Ew1WrVuuFWQw/V2/91p3q98pb2PvVXvZAe5xyvwz1Gn3mJPFi1Plxv3zpTy8dfqxMDTJ9Q7vGlVevzdat5P9cGp4cur/pdl89EfZfITevY2nFsc2D2PZcGulx4f2D2tsPO+rbAgl/fEujS5YeBV9fvD+xbOTkwoMulgRGTlwR2HHPu3rEkMHmE8/gBkwMr9zkbdswOjOiSFBgxu9DZWWFg9oikQJcRswM7gnsvZ9euXc5+O532dtFFvQPJyRcFnnpqQiAvLy9w4MABbw9A7TPf0wUL5gcefPDBSr+fld1uueWWwNChQ93bjBkz3O+t2Q/ODrNnzw48+uij3lptOBhY/+oPg9+3C38dWLDXOfa6joV5jP7aWf15mX14611+Hpi942t3j6Hj+MWTVjr3Bn298tnAxV1uCExauc9Z+yqwclK685xbAr9esM15B2Vec9CrgfVmg/uaVwXGLPjCPD0Q2LciMGlAD+c9/TawYIeTM4HDgR0rpgZGXNgjMOjVT519nDo7asr69evd32F9qb2q9UZxSn/mNb06skSPXt5dcV3TlLEiWeN9zyoj4VxFp/5UOb4H1OG9Hyuta2d1TXtQq3uPkS/np0qNDr+a0XTzOeecU4/0s3fvHncc7hdeeF5Dhw5Rz54Jbil95syZWrVqlVtKAmqKuY5tGqg9/fRTztn693TllVcoI+NOzZr1lveIU2vcuLE7QIwT/HrzzTdLu0TSuwI1p7nir7peKc5S1K3fU2rL0LG3UZjH6CZqf/l/K/OCN5RxUUq1uw2XF6PUB6bKNz5ZKzLS1DWuzGtO+2GwVqB9moZnttaMjBTFZflUFH2pHsiZqfF9lisjzcmZuO5Ky8hV76f+T9MyTq4JbrgsGdmtel566UU9++wz32gylFatYtygN62B+/e/zh3BzUxo0dnCsdBR90xom5bla9asKZ0K9+DBQ2c0uuDjjz+hn/zkJ94azkaMtW6HBttqvb6YL/0999xdIy16Q+FuGhX17Zum5ORk9ep1oTuE5tkc8Gdzq/XQWOxmaFbTFcwM1RqakMdczz6T4DYaNWrklrhnzHjttNPJouEjyO1AkNcCU0U+a9Yst0rz6NGjZ3xwPVko4A0zHGfHjp3cEnxcXBc35M10ow15RLiGHuTmn9IwYb1hwwZ34pQdO7Y7wb3KDWujpr9TJsDNHPL/8z+jNXLkSG8rznYEuR0I8loUahn83HPPuQfhuph/3BzoTUndzIxmXHHFlW6JPj7+O+rQoYNiYzu4YW+Y7TZe77Q1yMvOZW5C2lSHm0lQTJV4KKiNTp06O4+tu8933XU36LvfvVZ33kkLdJRHkNuBIK8j5iD+t7+9q7///e/y+1d6W+tP9+7x2rhxg7cmJSdfrJiYGHfe8tjY80unQm3atGmFKtaTBwepa/Ud5OYEzQRwiAlnM2iGmWN837597rJp1GgGWCkqKirtqmWmnm3WrHnpXPH1wYxtYE4oBw/+vn7wgx8w0iBOiSC3A0FeD0xJzFSXmn+SDz6Ye8aNkuqKCX+j7AmAYQLfTLFqmOpZczJghE4IQpo1a1ahBqBbt27upYBwmC+sGW0sHGbqz88/Lz+P944dO7yloDVrVntLKtfGYdmypd5SkKn1iI2NdQLxcL2GcnWErpubEQZNI8qrr77a+Vv1ILxRLQS5HQjyCBAK9pUrV7pV8YsXL3JLb6HqcQSFTiRCzPzb/I5OCF0///a3m7uNI6+55holJSUR3PjGCHI7EOQRylTFb9682Q34ZcuWaf36dW4VbV1fP0XkKdvgzVwSSUzs7fZoMKHdpUsX+nmjxhDkdiDILWP+YOaarOkvbLoemYBfu/ZfblWwKcWb67c2VNPj1Mr+Lc3YAubShemZEB8f77ZZaOg9ExAZCHI7EOQNSKhV9ObNm5w/6JZKW0RHQoOrs93JDQ3L9iwwJWozRkCosSGla9QngtwOBPlZ5uQuUKGW1qah14EDB51S4AG3lF+2sZcJHhsadtUH87s5+Vq9KUGbxnAtW7ZS69at3QZ9wVBubX3XP5xdCHI7EOQ4pZO7WhnmBMAwjfQOHz7snhiYWZKM0MmAsX///tKagKqEWoBXx8mt5av7XPMeq9OuwJSMQ0wIn3NOcNrCpKRk92eLFi0UHR3t3KJKAzmkvrvkAbWBILeDmatj0KCbCXLUj8pOFE7HnHmG2/2MoAXCZybdGTbsNuXlraYGKYJNnDhRmzZt0tSpU70tdYsgR9jO5rHWgbp22223uZeCJk2aRDfGCBQ62Xr33Tnu7IT1gSAHgAhm2tX88Id3uMt33z3SvbyEyGAue8ycOV1Tpjyn9PR0b2vdI8gBIMKZS2Bz5851gwORo1WrVrr11lvr/dIhQQ4AgMUaeT+BajPXyAEAkYEgBwDAYgQ5AAAWI8gBALAYQQ4AgMVotQ4AgMUokQMAYDGCHAAAixHkAABYjCBH2BgQBgAiB0EOAIDFCHIAACxGkAMAYDGCHAAAizEgDAAAFqNEDgCAxQhyAAAsRpAjbPQjB4DIQZADAGAxghwAAIsR5AAAWIwgBwDAYvQjBwDAYpTIAQCwGEEOAIDFCHKEjX7kABA5CHIAACxGkAMAYDGCHAAAixHkAABYjH7kAABYjBI5AAAWI8gBALAYQY6w0Y8cACIHQQ4AgMUIcgAALEaQAwBgMYIcAACLEeQAAFiMAWEAALAYJXIAACxGkAMAYDGCHGFjQBgAiBwEOQAAFiPIAQCwGEEOAIDFCHIAACxGP3IAACxGiRwAAIsR5AAAWIwgR9joRw4AkYMgBwDAYgQ5AAAWI8gBALAYQQ4AgMXoRw4AgMUokQMAYDGCHAAAixHkCBv9yAEgchDkAABYjCAHAMBiBDkAABYjyAEAsBj9yAEAsBglcgAALEaQAwBgMYIcAACLEeQIGwPCAEDkIMgBALAYQQ4AgMUIcgAALEaQAwBgMQaEAQDAYpTIAQCwGEEOAIDFCHKEjX7kABA5CHIAACxGkAMAYDGCHAAAixHkAABYjH7kAABYjBI5AAAWI8gBALAYQY6w0Y8cACIHQQ4AgMUIcgAALEaQAwBgMYIcAACL0Y8cAACLUSIHAMBiBDkAABYjyBE2+pEDQOQgyAEAsBhBDgCAxQhyAAAsRvczAAAsRokcAACLEeQAAFiMIAcAwGIEOQAAFiPIAQCwGEEOAIC1pP8P17Srf9W8QVQAAAAASUVORK5CYII="></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>Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the ground state. Photons are emitted and are incident on a photoelectric surface as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_12.49.40.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p>The photons cause the emission of electrons from the photoelectric surface. The work function of the photoelectric surface is 5.1 eV.</p>
</div>
<div class="specification">
<p>The electric potential of the photoelectric surface is 0 V. The variable voltage is adjusted so that the collecting plate is at –1.2 V.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the energy of photons from the UV lamp is about 10 eV.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the maximum kinetic energy of the emitted electrons.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.</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 variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the equipotential lines at –0.4 V and –0.8 V.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.</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><em>E</em><sub>1</sub> = –13.6 <strong>«</strong>eV<strong>»</strong> E<sub>2</sub> = – <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{13.6}}{4}">
<mfrac>
<mrow>
<mn>13.6</mn>
</mrow>
<mn>4</mn>
</mfrac>
</math></span> = –3.4 <strong>«</strong>eV<strong>»</strong></p>
<p>energy of photon is difference <em>E</em><sub>2</sub> – <em>E</em><sub>1</sub> = 10.2 <strong>«</strong>≈ 10 eV<strong>»</strong></p>
<p> </p>
<p><em>Must see at least 10.2 eV.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>10 – 5.1 = 4.9 <strong>«</strong>eV<strong>»</strong></p>
<p>4.9 × 1.6 × 10<sup>–19</sup> = 7.8 × 10<sup>–19</sup> <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Allow </em>5.1 <em>if </em>10.2 <em>is used to give</em> 8.2×10<sup>−19</sup> <strong>«</strong>J<strong>»</strong>.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>EPE produced by battery</p>
<p>exceeds maximum KE of electrons / electrons don’t have enough KE</p>
<p> </p>
<p><em>For first mark, accept explanation in terms of electric potential energy difference of electrons between surface and plate.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4.9 <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Allow 5.1 if 10.2 is used in (b)(i).</em></p>
<p><em>Ignore sign on answer.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>two equally spaced vertical lines (judge by eye) at approximately 1/3 and 2/3</p>
<p>labelled correctly</p>
<p><img src="images/Schermafbeelding_2018-08-13_om_14.47.13.png" alt="M18/4/PHYSI/HP2/ENG/TZ1/08.c.i/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>kinetic energy at collecting plate = 0.9 <strong>«</strong>eV<strong>»</strong></p>
<p>speed = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{2 \times 0.9 \times 1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>2</mn>
<mo>×</mo>
<mn>0.9</mn>
<mo>×</mo>
<mn>1.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>9.11</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>31</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span><strong>»</strong> = 5.6 × 10<sup>5</sup> <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Allow ECF from MP1</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A longitudinal wave travels in a medium with speed 340 m s<sup>−1</sup>. The graph shows the variation with time <em>t</em> of the displacement <em>x</em> of a particle P in the medium. Positive displacements on the graph correspond to displacements to the right for particle P.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>Another wave travels in the medium. The graph shows the variation with time <em>t</em> of the displacement of each wave at the position of P.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="specification">
<p>A standing sound wave is established in a tube that is closed at one end and open at the other end. The period of the wave is <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>. The diagram represents the standing wave at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math> and at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>. The wavelength of the wave is 1.20 m. Positive displacements mean displacements to the right.</p>
<p style="text-align: left;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the wave.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, for particle P, the magnitude and direction of the acceleration at <em>t</em> = 2.0 m s.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the phase difference between the two waves.</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>Identify a time at which the displacement of P is zero.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the amplitude of the resultant wave.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the tube.</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>A particle in the tube has its equilibrium position at the open end of the tube.<br>State and explain the direction of the velocity of this particle at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>8</mn></mfrac></math>.</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>Draw on the diagram the standing wave at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>T</mi><mn>4</mn></mfrac></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo></math>«s» or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>250</mn><mo> </mo></math>«Hz» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mo>=</mo><mn>340</mn><mo>×</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>36</mn><mo>≈</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo> </mo></math>«m» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong>.<br>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϖ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mi>T</mi></mfrac><mo>=</mo><mo>»</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac></math> <em><strong>OR </strong></em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>57</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></math> «s<sup>−1</sup>» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>a</mtext><mo>=</mo><mo>«</mo><msup><mi>ϖ</mi><mn>2</mn></msup><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>57</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfenced><mn>2</mn></msup><mo>×</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>=</mo><mn>14</mn><mo>.</mo><mn>8</mn><mo>≈</mo><mo>»</mo><mn>15</mn></math> «ms<sup>−2</sup>» ✓</p>
<p>«opposite to displacement so» to the right ✓</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«±» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mo>/</mo><mn>90</mn><mo>°</mo></math> <em><strong>OR</strong></em> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mi mathvariant="normal">π</mi></mrow><mn>2</mn></mfrac><mo>/</mo><mn>270</mn><mo>°</mo></math> ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.5 «ms» ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>8.0 <em><strong>OR</strong> </em>8.5 «μm» ✓</p>
<p><em><br>From the graph on the paper, value is 8.0. From the calculated correct trig functions, value is 8.49.</em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>L</em> = «<math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>λ</mi><mo>=</mo></mstyle></math>» 0.90 «m» ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>to the right ✓<br><br></p>
<p>displacement is getting less negative</p>
<p><em><strong>OR</strong></em></p>
<p>change of displacement is positive ✓</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal line drawn at the equilibrium position ✓</p>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</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>
<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 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Flb1CKJztrXUotkrzmGfbZgxEbdBS+lrCNaTx8pEFVgz6E6pURy+jgOHNFj8tjh0GqHwsfvLIr3fIt6ZTXwA44f+K4LgYuIiIg6w0upRHTWbq5FEs1sohZJ9DkStUgiDIlO2s2dtbs2cGTznWPjEDiq3ahD7Wj9/xPzDVbk5mxHVaNd2v0USjPexmadAVEhPtIGYxE2Pwy23HfxQZWIRGIgxixkbPbuNHCJ19/TdwMSERH1dQxEHRBNTKIWqaNb/n/2s59d4Zb/5jvHfODt2XKj/GXKaNb+aWbI41ZrAzAvYwNiTyzHBM8B0AwYhZlfTEb2tgSEe4mPaDAC5v0JBbEnET9hmBTOboV+5j8Rmv0XPNuF/km33367MkdERETudPlZZs1ETclV7tJviRD0zTffyLf8i1ol0dwmmt7uvfdeedyfwMBAufbpZhIdx0VfKdE8SERERO4xEHUj0YwmHnj79ddfy48gER22RXPVpEmT5EefjBkz5oZ3bhZNfKJWi4/tICIi6hgDUQ8TfXjaPuU/PDxcrkW6EU/5F/2eRCjr6fMQERH1ZQxEN5ioRTp06BCOHDmCzz77TB48UgSW++67D35+fpgwYYJ8F1x3EWMuiWYz3nZPRETUMQaiXqC5Fqn5Kf+C6LB9vU/5F48tEQMy8vMiIiK6MgaiXkh01j5+/Di++uor7N+/X65FEp21RRPbXXfdhTvvvLNLtUgiaIl9xVACRERE1DEGoj5A1PRUV1fj6NGjci2S6Kw9Z84cPPDAA3Lt0S9/+Uu3TWKiqcxqtcpDBwiig7VolhPDCRAREdFlHIeoD3D3lH8x/pEIQ6IWqO1T/sXAkSJEiY7crs1tolkuLCxMfjwJERERXcYaon7C3S3//v7+MBqNiIiIkG/5Hz16tLI1kJGR0VJzREREpHYMRP2YGCyyrq5OHjjyvffew4EDB5Q1TgxFRERETgxEKiEeLxIVFaUsXcZQRERExD5EqiFqiZrdc889chASd7HFx8crpUREROrFGiKVEB2um2/bFx20iYiI6DIGIiIiIlI9NpkRERGR6jEQUd/SWI60iKUw2S4pBURERNePgUiNGqtgSomSmz81Gj0iUnJhtl1UVrqyo9G8HhGaCKSZG5Wym0V6LZYdSHs6HkllDENERNS9GIjUxn4cpmeeQMaAZbA2OdBkzcG08hTMXvkRTtmVbRT2U4V4ZnYinI+b7Q2GYEpKOlL9lEUiIqJuwkCkKnbUl72NpVnjELvwPuikT1+rm4nnVy0Esoqw518uNS9ScCp88Y/IsinLN0wjzGkRSu2Vy2QsREPAfYgM6PyhtkRERFeLgUhVzuLbyi9gMzyIMP/BSpkWXpGvwep4CzG6gUrZRZwqTMXSo7/GJwUvwX2FzCXYTEug0RuRtikFEUpw0Rs34ktzKdYbg5QwE4UUU5UUc9potKA4zQh9c+ARxym2SNt5IHjZTvlOxlZTTgx0yq5ERETdjYFIVc7jzOkGYHgtDuY2h5i2fYjsaKz6O1YsPYbEtGcwc8xQpbwDtmJsPzwVbzf8hIZD2ZhVvBTTQtbitPETNDl+QEXqLVg390XkW84rOwjfo/SVBTBsH4d3rBekwHMGh1YPRLphZZvtiIiIbgwGIlU5h7qaOiAvB1trH0VekwOOpr1YNeAdhCx8BxbRh6ixAm/99ys4kfgilgR7O3e7ojDExv8KAR4D4REwFTOCdEDcU0iIHCn9cXljUkQ4/HAatQ2uHaGV1wEvDPMUtVJeGL8oE1ZHPhYFNNdcERER3TgMRGpkeA4vPDNd7kME7UiEL5wPQ1EuPvzqO5jf+hOS8DTSloTAw7l1J3zgLYcaiXYovH2HwC9oDEY4SzowEoblqxBXnYgQzwHQG9PwgekfHdzp1sbAYCw77Nq8R0REdP0YiFTldowJGg34esPT5ZPXenrDFw04/f1+7HxrO1DmDCqib88tIUk4gjIkhXjCP82M7rnhXQuP8UbkWM+guqQQG2YD25Y+jBD9bKwoPYU2N7sRERH1OAYiVRmCX0yZBt2J47A2Xo4d9oY61GAcAv/jASw73Loz808VqfBDOFIrGnB4WTC6t17GCwGRcxDz62XIOXkImYYDeD1nD/6lrCUiIrpRGIhURQuv0Ggk4l28mf+N884v+ymUZW/BgUX/F1Etd571MDEWUnyQfEdaudxMJgZd3INdBwDDjF/iDudWRERENwwDkdp4hCIx7y+IrP4DPMVdZgPuwStNT6HsjWiMvFF/DdoxiF6didd9P8RU/a3QaAbAc0IefF8vRPbC8fyjJCKiG45PuyciIiLV4/+MExERkeoxEBEREZHqMRARERGR6jEQERERkeoxEBEREZHqMRARERGR6jEQERERkeoxEBEREZHq9WAgqoeleD2Meo08mKNGEwRj2g5YXJ6h1V6bffRGrC+3uTzs090xTV17SjoRERFRB3ooENlRX7oG4YZP4LvhEBocDjRZ0zFy+28R/kwhTrnNRHY0mjPxlPEI5uy9AIejCQ3bJuPDqYuRbq5zbmH5AAmGLCBpN6xNzcdcitl/3i1FJSIiIqJr00OB6BQ+zcmHLe4pPBszHh5SiVY3E8+vWghkvYcdh887N2vlLKp3foiyoCmYqBskLWvhMel+POy3HW/tPIJLOI/Duz9BkZ8Rv0+YDp30yrW6+7AwNgy23E9RUX+lmiciIiKijvVQIBqNmJzDcOTEQKeUXL9GnKw+CkwfB/1ApQiDMW5SKPxsh3GsxrXZ7BJspiVyk1vaphREyM1rGvnp6l+aS7HeGKQ0uUUhxVTlfOo7ERERqVYP9iFqqxYVO4pg0/ljrK+oAWprCAIjHkX4gUoclPsE2dG4/3+x/cjDWBLhh4E4h7oaZ9NZe6dR23BJmXdhK8b2w1PxdsNPaDiUjVnFSzEtZC1OGz9Bk+MHVKTegnVzX0S+xV2NFREREanFDQpEon9QLl5ZdwGLNjyFcC93p9XC4+4YJDy0C3NH3QqNZgA8QxJRnZyI/wr2Vra5WmGIjf8VAjwGwiNgKmYE6YC4p5AQOVI6mzcmRYTDr6MwRURERKpxQwKR/VQhnpmdhTsz/443YsZ0cNI6mNOfxtJLy3CooQkOuSN2ERaW/xfmpJVfY7OWD7w9lfY17VB4+w6BX9AYjHCWEBEREcl6OBDZ0WgxYfkTyTi6MB1rFk6UO1i7VV+J/PQqzJoTifEezpfl7DQ9BWVv/S+qL92OMUGj5fL2RsCnOfgQERERXaUeDET1sJhWYnbgH1HzaA7yVs+S7wy7dgPh6TMCKK7AoZY7yi7h9PHDONJhvyQiIiKizvVQILqIU6YVCJ+bDaRmYuNzztvkr8hrCuYljkfx1g9Rrgy0aLd9huzcSoQvuR+BAwfDP+xBGGzbkPPBN3ITmt22ExkZH0IX+wBC3PZLIiIiIupcz6SI+t14c+lG2KT/ypKmwlO57d05+cNo+k7a6DuYjP7Q+KfBLPdp9kZw4iZsizyBFL3oVK3BAH0amhbmIS8x1DmWUcCvkVEwGyfig+RjDtAb8UXoWmx7Ngxe4hBERERE10DjEL2Xr4IIKle5CxEREVGvxnYmIiIiUj0GIiKiPs5uM+Mjs+uDsInoajEQERH1ZZfMSL8vBM/utDIQEV0HBiIiIiJSPQYiIqKbxnm3rd64BptSopQ7cfWISDHB0thc33MRNrMJaS0PpRbrc2EWw5NcMiNtfAiSjgBHkkJwS8tdu0R0tRiIiIhuMtvmnTg89Q00OJrQUJEErFuKhHwL7PJzIDdiQcgfcWDG36X1DjgaihBbsw4hCzbCfP5uLKuqQKof4JdagZ8OL0MwB+0nuiYMREREN5thPuKjx8ND+kr2uPshxBqAol3f4F+oRXn+uygzPIcXmh995DERC194Doayd5FfXivvTkTXj4GIiOhm8/WGZ/O3sfIgapn9exzbZ5XSUTwCB1we4HZAYDyKUIeaunPO7YjoujEQERH1crrkEpwRzWWtpsPIienogddEdLUYiIiIeivtcIydrIct91NUtDzUmoh6AgMREVGv5YPQeY8j3JaNV9aUwCYykd2G8vVG6DXzkGU5Dwz8OcZN98PZ02dw1rkTEV0DBiIiol5LC4/gp5FXsRahX0ghSPQjGqBH9L4gbKh4AwsDBkvb3IFpxlgErpuJYZolMNl43z3RteDDXYmIiEj1WENEREREqsdARERERKrHQERERESqx0BEREREqsdO1UREvZT4vm1LfP+2LXf9Tu6OdfyOJzViDRERUR8jAovr5Eosf/XVV3j11VfdrnOdXHVUTqQWrCEiIuql2tboCJ19/547dw6PPfYYtm7diurqagQEBChriOhKWENERNSPfPzxx3IYElJTU+WfRNQ51hAREfVSV1tDVFtbiwcffBB79+5VSoAdO3bAYDAoS0TUEdYQERH1E3l5ea3CkLBy5Uq5GY2Irow1REREvdTV1BBZLBYEBgYqS63l5OQgLi5OWSIidxiIiIh6qattMnPF72qiq8MmMyIiIlI9BiIiIiJSPQYiIiIiUj0GIiIiIlI9BiIiIiJSPQYiIiIiUj0GIiIiVamHpXg9jHqNfGu+RhMEY5oJZttFZb0bdhvMOSmIkLeXpogU5JhtsCurXdltxVgREYU0c6NSomi0oDjNCH3zMfRGpJnMsLk7CNFNwEBERKQidssHSDBkAUm7YW1yoMmajpHbl2L2n3dLUcmdOpjTFyMkewhWWS/IYxs15T2A6mW/Q7q5TtnGyW77HG88n4jXy9qGq/Ow5K+EIV067R4rmhwXYH1nHLbPfQp/Lvte2Ybo5mIgIiJSjfM4vPsTFPkZ8fuE6dBJVwCt7j4sjA2DLfdTVNS7qa6pr0R+eiUMsfMRrhskF2l10zD34Tqk51cqIcpZ6/Tb+/6KprBfIVwuc2E/ht1bdsMv8fdICNVJF55B0IXPR6zBitwdX3cQxIhuLAYiIiLVaMTJ6qPA9HHQD1SKMBjjJoXCz3YYx2rcNJv9WIca2xD4eg91uWAMhn5cIGwFlfj2klg+g4PvHcGMjzKw7JGpuFPexkWjFdUHhkin/TlaTqsdhUmzpGPsO4Ya1xxmM8EoN+O9iZQIfUvz2vovzfhyfXOTmx4RKSZYGtneRt2HgYiISDXOoa6mdTPXZadR2yCnm9aGesNXdxY1dT+69Bmqw6E9FcDZWpw5K0pHIyZzAxaN93KubksOVcp8W0dq0dAu1xzE5u01mPp2FRwNB5A5qxKJ02Zj+eknYG5qQkNFErBuKRLyLW77MRFdCwYiIiLqmNcUzEucgqLcLSiTO15fhK18C3JyzYCtFnU/9kQk0cEQG4foAClgefgjbMYEqexRJCREQKfVwmPS/XjYzyZlKdeQRnR9GIiIiOgKvBGcuAl7Hj2KJ/S3QqMZiwUFw2FcvQjw88eYES2NYN3ItYluIDy9fXrwXERODERERKpxO8YEjVbm2xoBH88OAodWh9DncmB1OOBwWLFz7Uyger8UUnzg2ZWryIgxCPJT5tvq6jGIehj/DImIVGMgPH1GAMUVONRyR9klnD5+GEd0/hjr67yLrBV7FbKi9NCnlF6+G8z+PY7tq0P4rInQd+Uqoh0KH7+zKN7zrcsdZT/g+IHvoJs8Fr68ElEvwD9DIiLVGAz/sAdhsG1DzgffQAydaLftREbGh9DFPoAQLzeXBO1YhM0Xt+W/iw+qRJyph6XkY+w68iASHpsMD+dWV9buGBdhK81CxmZvxEbdhQ66YhPdUAxEREQqog34NTIKZuNEfBA8NRoM0BvxRehabHs2TAkm38Fk9IfGPw1m+aazwQhY+Ab2JF3CygnDoNEMQ/g7wBP/eA0xI93UKLklHWPen1AQexLx8jFuhX7mPxGa/Rc8Gz5c2Ybo5tI4xLCjV0GMCXGVuxAR0TUQ37dtdfX7l9/VRFeHNURERESkegxEREREpHoMRERERKR6DERERESkegxEREREpHoMRERERKR6DERERESkegxERERE1AllwE6jCTalpL/p0sCMycnJyhyQmpqKpKQked7b2xsrVqyQ54mIqHtdzcCM+/btQ15enrLU+rv63nvvRUxMjDxPdG1EIIrAXKyDNScGOqW0P+lSINqwYQMSEhKUpcsKCgr4j4yIqIdc7UjV0dHR2Lp1q7J0WXV1NQICApQlomvR/wNRl5rM4uPjcc899yhLTnPmzMFDDz2kLBER0c320ksvKXOXZWRkMAz1WhdhK98Io14jh1+N3og1a4zQa5bAZLsE2EwwaoLwuPH/SGVim3nIspyH3VaOnJQo5z7SpDemwWS2wS4f85K02xKpXDmGuzLluMa0N5ESoVeOE4UUU5X8wF9ZowXFaeK1iHV6RKRsxp4TZ5WV/VOXAtFtt92G559/XllyElWxopyIiHqHyZMntzSTCeJ/ZBcsWKAsUe9iR6N5IxZMfQtYfQANjguwFobi0Jub2/TROYi8E/djW8M5WCtfxEO+XyN9QTSW1zyKPdYLcDRZUTj5AJaGLEa6uU7ZpysOYvP2Gkx9uwoOxw+oSL0F6+a+iHwpcAF1ML+VCMP2kdhQfUY6hxlrfS3ILeuvvYecutypWjSNiVohQfyDmz59ujxPRES9h+v/vIp5Hx8fZYl6l1qU57+LMsNzeGHhRHhgEHSh8Xhh9W+U9c10MMQ+hLs9BkN39y8xtKIQ6WVhWP1CPEJ1g6SruA6hzyzHakMl0vMrUa/s1Tlx3DhEB3hJ8964+9EYGFCJXQdPA/WVyE+vvLxenCPeiNj+2E7m4qruMlu3bp3888knn5R/EhFR7yICUE5ODrs19HaXjqOywAy/WZMwruVKPAi+Y/3b9M8ZAl/vocrF+iy+rfwCNr9QTBo3WC6RaYdj7GQ9bPuOocbZbtYFrseVDuHpDV9l/tK3lSiwBWLWpFGXQ4LXLzB1lp+y0D91ORCJNsbAwEB5XvxsbrvkxIkTJ049M7njbru2k9FolDtXDxkyxO16Tjdn6jnnUFdzNc1l5E6XA5G4s4ETJ06cOHHidG1TKwPHYMrcYBwp3o+jLbU6F1Fz7PAVxvkZgl9MmQbdkXLsPyr6+ijsP0qB6Cx0k8fC1+1V/TysR6uV+c4N/MUUzNVVo3j/SaWjtkQ5R3/W5UBERERE3cUHofMeR3jReryafRCNopN11Ra8uvJ9Zb07WniFRiMxfDdWvpqJcttFKajYUP7G61hZNAWJ86bAS9pmqLcPdPgcWz8Wd42JO9ly8GZ6mXKMLvCagnmJU1C0MhXZVfUu52Cn6is6d+6cPE6RyWRSSoiI6HqIwXA3b94sf79Sf6WFR/DTyNuzBFgZBE/NAHj+99cIijUo6zvgEYrEvEK87vshpupvhWaAHtH7grChYhMSg72lDaTQFJ6Abdm/wol4cdxbEbyxAWGdHbcVbwQnbkLF68ORO2GYdI5gpNQEIDa8f/eq7tLAjB0RIWjNmjXYu3cvB2kkIuomIhCJkabFbfPr16/nXb2qcR6WrDgErvRHSdVqRHqxEedGuqZ322KxyCOizp07Vw5DRETU/cT3a1hYGBYvXix/71J/8j1KU0KgiXgZpaLpSzSZWf6BzNxKhCdGI5Rh6Ia76hoiUSskghAREd1Yu3fvZm1RPyJGnM798yosXFeklBiQnP0Kno0NhY556Ia7piYz8X8qokrX9Zk5bDIjIuoezU1mzcTYb2JAXD6Cg6jnXFMGFf8oCwsL5RDU9hlnRETUPcT3q6gV2rRpE8MQUQ+7rko5USO0a9cu+eGBRETUfcRo0+L7lU1kRDfGdd1lRkRERNQfsNsWERERqR4DEREREakeAxERERGpHgMR9REXYSt9GRH+aTBfUopc2G3FWBERhTRzo1LSAbsN5pwURDQ/gToiBTlm2+UHGBIRkSoxEFEfIB5OuAnPP/ES3D2e0G77HG88n4jXy8Ror1dSB3P6YoRkD8Eq6wX56dNNeQ+getnvkG6uU7YhIiI1YiCi3q3RguK0xbjP7cMJ62EpXo/f3vdXNIX9CuFKaYfqK5GfXglD7HyE6wbJRVrdNMx9uA7p+ZXS0YiISK0YiKh3aziI9w5E4qONiXhk6n8ohc3O4OB7RzDjowwse2Qq7lRKO/RjHWpsQ+DrPdTlD38w9OMCYSuoxLeuTXE2E4yaIBjT3kRKhN7ZvKY3Yv2XZny53gi93OSmR0SKCZZGNrgREfV1DETUu+likJljxHgPd3+qoxGTuQGLxnspy50Y6g1f3VnU1P3o0meoDof2VABna3HmbNtgcxCbt9dg6ttVcDQcQOasSiROm43lp5+AuakJDRVJwLqlSMi3sA8SEVEfx0BE6uE1BfMSp6AodwvK5KdLi75JW5CTawZstaj7sW2s0cEQG4foAClwefgjbMYEqexRJCREQKfVwmPS/XjYz4Yjta4Bi4iI+iIGIlIRbwQnbsKeR4/iCf2t0GjGYkHBcBhXLwL8/DFmxEBlu2auzWsD4ent08F2RETU1zEQkbpodQh9LgdWhwMOhxU7184EqvdLQccHnvzXQESkWrwEkHrYq5AVpYc+pfTyHWX273FsXx3CZ02Env8aiIhUi5cAUg/tWITND4Mt9118UCUiUT0sJR9j15EHkfDYZHg4tyIiIhViIKJ+7DuYjP7QtIxuPRgBC9/AnqRLWDlhGDSaYQh/B3jiH68hZqRzXCIiIlInjUMM10tERESkYqwhIiIiItVjICIiIiLVYyAiIiIilQP+P+LS1vHBGG6/AAAAAElFTkSuQmCC"></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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8xi8gAIA9JGMQDmiSee8H34PMBFOX78eHVzeVGCIFUgXrEel3qNSdvj0eWPMQ0jA7fugGsWnRuAyXoaGhrUa3DttdeqVEzgV0AVc0Fjuk/duOoMIAR5narQ6iQQA4wCRyq8XjZdHAAFwkP0RYHxBRid7EfjhhsLIoUbHKJlwsWJxgi9qz179qj02jVr1qi0TvS6AAShY8eO6jUaKi0YGG26a9cuVScK5dezs7PV6FNmX6UOOi/4XjHnePz32qVLF+ncubOajlOD94BTp06p3wpTgmLWN8wVgrkbvLimdIHM+HsIIgGBuOuuu2TKlCnGXQe471GGQ2cKmi4OgALhMWgMMcinoKBApcChIqwXQgFxwsArNARIo/R7II4WhbVr16pGBseEmbMgBhhLkuzNrXu6unFDLw3zVqA8OcWidXAt6MYK8y2gBw6R7devX0rXJBrmo0ePKoGP39c999zj+LWNz2qtUcX1gI4PxMuUDpBm9erV6nqHiCKN3I8OYqpQIHwCPSDkR+OGQk8ZvTCnGzR8BnqD+AxggjC4fd5aeCCGOHe4G7wS4aCg3R0ADTlKaTvZkMJKraioOP8b4/tP162K3xWFIzEnRFFRkb320pjmQsXxoGYb4n2///3vg9NxgUAQ/0BmAzIZkEWEnwMZRch6aktWA/aFtFqk1On9IcUO9Wv8BnngOBZ9TJfLC3eClp+ZKIskSuA6Q50fXBteZP3g+8a1rD+zrSnf2A/+H49UfkPcQxgrgc/34nwTgXOOP3+vvnunoAVhEOhdHzhwQI2a3blzp+oFxy4o5Qe+1MTl2icPd4F+P/zx/fv3l759+xrRU0HvCXNK+NWbj7da0IuLWn0puGUwSvfkyZO+JUnAlYVsvrbE3/C/uL7bGleIt5i8sqJhReGagxUbf83hWHB/J2MFmQAFwmC0fx039okTJ+y1F6Ozekyr/6QbJoAb0+/jQyODwncI0AfFB5wuEEXU1sJMZ367WrSbCMeEkuZeuzvddq21dOlOmzZNddbiRQ3fQYcOHVSGXhDcTBQI4gq4GZGxZVraIW5QJAmg0Vy1apURKcdugPPEGBdgWrAWQo16ZbguLmUV6MC3GyKSKDgPi7tnz54pdRrwHVdXV8vevXvlrbfeUhl4OCdU4G3tukInBbE3v+OByUCBII6je60mN8A6j96EnrXToHHFOaGxMqFoXSLiBaxl1WB9/F5YGRCL+Ay4+PTqRG5dneKrU4FhGcOCh8Ake61DnCorKwPhZqJAEEeBMLz22mvq2aReayKC0JCmipeNqxO0vF60cPt1/HATffrpp8oFdPjwYXvtBfQgwXQGaeIzRo4cqeKMpkOBII6Bmzxo80jonqwpJaLTQbtugiIOGlw3sDqRzICGGY+wuv40etCcaXHDllAgiCMEURw0YRCJoFkOLQny9dMWIIioDoDfzGRYrI+kjQ74BXWSIRwzArk4BwTXgwZcFkEXh2PHjimBhlBDsMMOYhY6nmE0sCAIaSsY/IPLqC0D+0wD5xDEc8HgKwwEDCI4bhy//s7TP5dG62z1Nqs4/yb1W0rmA1bJgdP2NnPAgL8gNL+0IEibQU8PPm9M/2h6QDoZcA44F7iZgtKLhdUDgugaw7Frt5K+fmCFYj2C1anTJA1VL8qjw38q+waslJrGU1I564RM+ceNcrDJfoshwGpFqiviRiZDgSBtBi4NBNvCNDIZ54LAIcZKmA4aF7hn0KgGEQxUaxlzQGYQ0qORyZSySDdUysp/+Lkcm1Uizz12h2S26yhZvWPCs++P8lGDYQoRA1VnUUrdZCgQpE2gcUJtewyGCxsYG4GG1/TeHQZcoYxDkEaEo9FHzATAakgUs0IGEzoeGHWdPP8nB3/9jMyWR+WZRwZJc3H4L+Vsfeyzaj+T+j+bJxDoiNCCIKFEN05BDEpfDjS4EAldlsFEkBKKfPwgWW/ItEIQGoPELgc6HnA1Jd2AnvkfKZlfIXn3j5JbO9rNWtMRqfiPCpHsb0mva65oXmcQN9xwg3KxGY0diyAkaXRV0LDjZxXQ1kCAE/MYt7U6qh8gCI1jTiUAjarEqMZ6eRqt0zvmWpkISid4ZBbusMwLUzeD4zMZWhAkZdCzRomBsINzNNGK2Lp1qyoHYfogq3hgDSBmlUowfdSoUaqkxeWtiM+kcnu51GbOlR2nG9Hixh6NEhMNyYz93dw3y3Y5mQcC1bCsTIUCQVJCZ5cEMd8+VfQ5muYnRmOLsu5BAnWHUr1m4L6Eq2/jxo32mkvw5VHZXfa+ZN5/lwzqpJs0LRqTZc69fYxt6CDyKO1hKhQIkhKvvPKKKmMcFVCn6bINlIdogQ6C9YBjTVdcYUXMmzfvfGA7ISePyr5D2fL9278tnexVTR//t/z7izUyfNZYyT0vGuaBgoCJaj6ZAgWCJA1uUtysqHEfFeDKwTmbMi4iKAKNEelIVcXcB+kAKwJzjLca2L6ys3TPtF8r6mXPr16QF2SczLhvgLHuJQ0m/TIVCgRJGtykuFnDmLl0KZDRhHPGPNd+A5GCWA0aNMheYybIsEIWEp6dGEA5evTo1seldMyW20d9XV793S75uOmvUvv6s/LT2V/I3PVzZex1f2O/yUxQKhzlxk2FAkGSBgIxbNgweyk6oEHGNJF+g8lpEHswfdwDSmI7JQ4AU+euWbPm0m6mdr1k7MIlMvnwdLm+/dfkttJOUlT9kjw54jo2cGnCaq4kaTIyMqSuri5QA7OcAA2TCfX7EZwOQgVQNwjSLGypAKsQbjhTm2EKLEkKBBtxg0ZNHADOGVNT+p2OiGkt9fzjJoFG7sEHH1RWg1sgmHvo0CF7KTyY7q6lQJCkQM2Y3Nxceyl64NwxR7KfwM3So0cPe8kMIA56Lg1kHLmF6b76sEKBIEnxySefSE5Ojr0UPXDuJ06csJe8B9YLLDjTepzxEy25eWwQRpNLn6QD4kqmDpajQJCkQO+td+/e9lL0QODVzwleMA2niWMfMNrci1LjWnxMSTd2ki5duqjf10QoECRp0s1pDzIojOcncPH17NnTXvIXBO11Q+2laKGnffz4cXuJeAEFgiQFauJEWSD8BoOpECj3G4yORkYXstm8Bj1t4i0UCJIUu3btciyvPYiE2QeeLBgdfeutt6qie1G+FqIEBYKQJIjS6PFLMXTo0PPPGBMTD5bjH/E4va3leq+3xePENnQ84q3z+G14xNPaNjegQBCSBGEMjqZKcxntC494vNzWcr3X2+Jxalu8RdZyWzytbXMDCgRJisGDBxtdt95tEByNwhwYhMRDgSBJgaqmpqbiRQGU2KipqbGXosmpU6fsV8QrKBAkaaIsECdPnrRf+QPmLz527Ji9FE1MHEkedigQJClQ6sDkiU3cBqOoUQ/ILxDENG1mOy/RlVyZLOAtFAiSFN27d5eqqip7KXrg3DGa2i8QxNyyZUtkg+WYlpMxIO+hQJCkgIvD73LXfrJ582bp1auXveQPUR5JjFIvJlayDTsUCJIUKKmAHuwlJ20JMfqc/R4chqleo1rRFHWwsrOz7SXiFRQIkjSYevPAgQP2UnTATHpjx461l/yjf//+snXrVnspOsCthsFk/fr1s9cQr6BAkKQxZepNrzFlqtXLTr0ZUjAfeBCmWg0jnHKUJA0apq5du6p016hkk5h2zk8++aQS6ry8PHtN+IniOZsCLQiSNOjBwc2EqS+jAqrY4pxNEcTRo0fL888/by+FHwj0vHnzlEAQ76FAkJSIWgO1bt06uffee+0l/xkwYIB6RtntKKAFmu4lf6BAkJTQDRRKP4cdfY6mzeSWn58vGzZssJfCC4LTTz31lFECHTUoECRlMGApCnMj4BxNHJw1atQo1bMO+8hqZGyhBpiJU61GBQoESZk77rhDPZeXl6vnMLJp0yY1zag+V5NAPGThwoWhFmnEHmA9IHuJ+AcFgrSJxYsXy/z580NZ+kE3TiaXdkBGDwoIhlWkV65cqVxptB78hWmupM0g/RAUFRWp57BQWFioyjqggTIZuJgmTZok27ZtC1UQFwH4hx56SI25YXE+f6EFQdrMY489puozhakXi3NBwzthwgR7jbmgdz19+nSZM2eOvSb4wHqDOKxatYriYAC0IEhaoDHFCF8UkQv6RPZBPZcHH3xQbrnlFiUWQQbuypkzZ4biXMICLQiSFujFVlRUyLhx4wI9JSmOHe4anEvQhG7ZsmVqvEbQU49LSkrUM8XBHCgQJG2Q6QN//YIFCwIZtMYxo1HCw8SspcsBVwyyruDyC6pIrFixQj788EMldsQc6GIijhF/kwfFfwzLAcIWBrcGzgWW3NKlSwMldLhuYAGFLdgeBmhBEMdAA4uGFpVPg+Bu0g1qWHzecI1pSyIoiQO6U0FxMBNaEMRx0EhhHAEyUXRpDtOAKwYNKQacha1KqBY+uP2mTJlipDWnA9IgSBZn1DDfgmjYLy8U3CwZGRmSkVUkr59psjcQU0HjBHFAuiJcBybFJXAsOCaIA44xjCWkYUlgDAF65miETbPmMM4BViYsN4qD4cCCMJcvrJqyh2MWzgSrpPpzex0JCnV1ddbUqVOtMWPGWNXV1fZa/8Ax4Fhmz56tji0KlJWVwUOgnv3m3Llz1qJFi6zBgwdbe/bssdcSkwlIDOJq6XzVFfZrEhTgU169erVMmzZNpZDC34yBUF6Dz8SobxwDjgVlQqLi74Y1h3EdKHyHaVP9ynKC21HPyod4g6muR9ICWygcoNE6W73NKs6/SfVY8MjMX2KVV59u3lxTZuVLtpVfdqx5GXxl3TGrLD/bypyYb03MbP7/lo/s4krri8Yaq7Ks2MqPf8/wQmttZU3sCGzOVlvlxflWpr39K8dh/cWqqSyLO85Ma3jhOquy5i/2duIG6D0uX75cfed4jjVa9hb3wGfEfyaOIcpUVFQoCwoPvHYbfN+wXLTVZoIVSVLDOYE4vcMqzIw1tnPLrRq01Gf3WSVohPNKrGosJykQIj+wiitPWY01+6zdNX+2XUwPW2U1X8Te87lVXTLBkswHrJIDzQ1+Y02FtQSfkznX2nE69kGNR6yyB7D8qFX2UazR18ehtn9hna1cYg2Xm6z8kn3WWexAbx++xKo8e15iiEvAtYPGGm4GuJ/QUDnZcGNf2Cf2jc8oLS2NjDspWbRQ6O/HabGG+0j/xhSGYOOcQKjGPiYQxe81N7wtSVYgtKAodAxCC0QibNGw39NYXWLlxY4jr+TABYviPCetHYW3tfiMmKao/7nNKtxx0l5D3EY35PBJo4ePBh29TTQmqQgG3ov/wf9iH9gX9um08IQRfG+6IYdg4DW+t1QFA/vZvn37+fgC9kVhDgcOprmekaoXHpMRU16QWrlJ8ovnyphv95Xv/PA2yUSko3aTFGQVipT9l5SO69H8L19ZJ7Kp4LsyXhZLTWwhU73hy9hbpkvW+NhbalbIuMzmOERT7fvy8jtHpVGapP691TJlMXK+H1bv+buaf5WcQSvljvjP0TRVyQujRsiU8lp7RTzZkp/of4jrILMo1sjI3r17Zf/+/Wqeg1hDoyaLAZ07d5acnBz1uqqqSurr69VrPR8CynKj+mr//v1VLSVmxaQOMp1QePHdd99VkxHt2rVLzcXQpUsXtX3IkCHquaGhQf1GALWrtmzZIjFBkNzcXDVv9I033hj4mlwkDiUTTnK22toR6829pGMAw5+wdsC/n6wFkV9m1TRvjdHSgviLVbPjCWu4ihusUr3Gsh0fWJVxFsQXlcVWdsvP0TQesEryMq3Mwh2Wjki0Br4ePvjgg4+wPy6F81lMHfvIiHHj5N6flspH1SWS98aLUvrOCXvjV/my5rCklFPRdFi2Pv1vUl24XrY8/aDK0Bg34jo5XX3YfoNIu6uujtkC5+ST+j/H7IsWtOsmNwzIktoXX5PKJMZTxL4fPgx58Pfw/8HfILyPS+GYQDR9vEmmZN0sBUvfllrV9p6RgxVvyz4ZKMNuukbkys7SPfOQvLrldalqaJKm2rdl+bJSOaT+O0l0A7/zLams/WtsRewzNi2Rny9+v3l7jHbf+p48/EBXKZ+/QjZ/HHtP08fyetHdkpHxY3nhYAfJ/fHfy/DatfLzp3Y0H2dTrexcWiBZavv/Ne+EEEKIcwLR7rp7ZOHLhdL9PydIVvuMWIP8Den3Yjf5ReWzMrnP34p0Gio/eXmd3H9srvS7qr20v22VNA4dLc1e5mTpJsN/8qws6blRvpf1tdhn5MjD731THi3Ol0yplPcO1McOpJeMe7ZMymedlenXx97T/nr53jsDZK06jg7S8bZHZUPl05L7TkwUcJzts2TsBzfLCn2chBBCFKzFRAIBSq3wUvUX/gbRIyAjqUnUSdQw6bpKxFkw6jlR/SaKQ/SgQJBAgpIRKN1QUFBgryFOgVTXHj16qNIoJhVaJN5DgSCBAO4NgNx7zME8dOhQlatP3GPGjBlKhGFRAP0bkOjAGAQJBGicFi1aJPPmzbPXEC/BYDgMimNzES1oQZDAMHr0aNVQtQSNFh/OPTAyvSWYfIhEDwoECQwoEb1582YpKytTpTiI+8Bqq6urU4NSSfSgQJBAgJ6tBo0V5hRYvny5vYY4DSw11McqKio6P3dG/G9AogFjECTQIGjdp08fe4k4Ab9ToqFAEEIISQhdTCQQMMXSf/gbRA8KBCGEkIRQIAghhCSEAkFIyhyXTQXfkoyCTVKrZj18RDIyHpFNtV/a21uAmRMzviUFm47HFuL/lxCzoUCQQGBuLsUVkjluZez4Vp6fErd1esi40j+KdX5a3eDAfJboQYEghBCSEAoEIYloOCivPoOZBjH5VeyRVSDPvHpQGuzNF2jpYmqK/et2eabg5ub/y7hb5vz723Ks+c0xErinsO/Vc+S7+rO+WySbDp6x3x/j/KyHzduzChbIU9g/3VTEZSgQhFzEp/L6zydK3u96y/qav4hlnZYDC6+QJXnz5deXm5a2oVJWPvyo/K77Aqk+2yiNNf8s3feVyxv25oTUviq/++Pt8m+x91tn35NiWSvjZ2yUg2rq3np5f8mDcnvxFbLwwGmxGmtk84DDsmzdfvWvhLgJBYKQi/hc6j+pjz13km9chbhCJ8l5oERqrF/LA61OS9skZ3ZuliVvDJT7p4yWPh3bSbvM78iUgh9eJt4w9Pz7pWN/+bv7h4qU75T9J2IWyZnd8usluyVv4WyZnNMpdsdmSu4/zpWFeUGLYJAgQoEg5CKuk7y5/yT51bNk0FXtJavgGdm46RV5v/av9vZLcU7+d/c7UpudK7f01kLSTjr1GyTft5cSc7V0VkIErpCrOjfXPgJf/u9uKavtK9+/5foLN2u7bnLDgCx7gRD3oEAQchHtpGNOgZTWnJbqHZtlxQ9FXp7+AxmU9UMpev3jmJ1ASDSgQBBySTpJnxFjZNy9P5XSjw5ISd4++UXpe3LC3noxHeTbA78jmYd2yoeHL8Qqms7Wyyf261S54tsDZXxmtbz64UcXhKnpUznyQY29QIh7UCAIaUnTUdk05WbJKnhOdiq3EjKT3pM394nkDbtRrm1+VwLaSafcsTJreIXMX/QfUtXQJE21b8uzi5ZKuf2OlOk0UH48a6CUzy+WtVXIbDojVWuLZX4585eI+1AgCGlJu14ydmGJ/KL7f8rtWV+TjIz2clW/DdL9F5tl7eSc1m+ajrkya8Pm2P9ukH5XtZf2Wf8in9ycJ8PtzanTWW6btVrem/2lzO/3jdix5Mg/VPeW+4czSE3ch+W+CQkaTVXywqgRMn/Aeql6eoR0slcT4jS0IAgxmTOvy5ysLPlu0atSq4IQZ+Tg5nXyYvlAmfXjgRQH4ioUCEJMptNQ+cnLT0vuOwWS1R4jqb8hfZc3yuTK1TLrts72mwhxB7qYCCGEJIQWBCGEkIRQIAghhCSEAkEIISQhFAhCCCEJEPl/9jgTvyYcYNgAAAAASUVORK5CYII="></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>A metal sphere is charged positively and placed far away from other charged objects. The electric potential at a point on the surface of the sphere is 53.9 kV.</p>
</div>
<div class="specification">
<p>A small positively charged object moves towards the centre of the metal sphere. When the object is 2.8 m from the centre of the sphere, its speed is 3.1 m s<sup>−1</sup>. The mass of the object is 0.14 g and its charge is 2.4 × 10<sup>−8 </sup>C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by electric potential at a point.</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 electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV. Determine the radius of the sphere.</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>Comment on the angle at which the object meets equipotential surfaces around the sphere.</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>Show that the kinetic energy of the object is about 0.7 mJ.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether the object will reach the surface of the sphere.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the work done per unit charge ✓</p>
<p>In bringing a small/point/positive/test «charge» from infinity to the point ✓</p>
<p> </p>
<p><em>Allow use of energy per unit charge for <strong>MP1</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of<em> Vr</em> = constant ✓</p>
<p>0.40 m ✓</p>
<p> </p>
<p><em>Allow <strong>[1]</strong> max if r + 2.8 used to get 0.47 m.</em></p>
<p><em>Allow <strong>[2]</strong> marks if they calculate Q at one potential and use it to get the distance at the other potential.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>90° / perpendicular ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>.</mo><msup><mn>1</mn><mn>2</mn></msup></math> <em><strong>OR </strong> </em>0.67 «mJ» seen ✓</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«p.d. between point and sphere surface = » (53.9 kV – 7.71) «kV» <em><strong>OR </strong></em>46.2 «kV» seen ✓</p>
<p>«energy required =» VQ « = 46 200 × 2.4 × 10<sup>-8</sup>» = 1.11 mJ ✓</p>
<p>this is greater than kinetic energy so will not reach sphere ✓</p>
<p> </p>
<p><em><strong>MP3</strong> is for a conclusion consistent with the calculations shown.</em></p>
<p><em>Allow <strong>ECF</strong> from <strong>MP1</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) Well answered.</p>
<p>b) Generally, well answered, but there were quite a few using r + 2.8.</p>
<p>ci) Very few had problems to recognize the perpendicular angle</p>
<p>cii) Good simple calculation</p>
<p>ciii) Many had a good go at this, but a significant number tried to answer it based on forces.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"><img src="blob:https://questionbank.ibo.org/55ba542d-3306-4ee7-8386-825edadb928d"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: center;"><img src="blob:https://questionbank.ibo.org/4e0f3fdc-c845-43ef-ba7c-39bab20625cf"></p>
<p> </p>
</div>
<div class="specification">
<p>As the train continues to move, the first diffraction minimum is observed when the light sensor is at a distance of 0.13 m from the centre of the fringe pattern.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A student investigates how light can be used to measure the speed of a toy train.</p>
<p style="text-align: center;"><img 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"></p>
<p>Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.</p>
<p>The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The slits are separated by 1.5 mm and the laser light has a wavelength of 6.3 x 10<sup>–7</sup> m. The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the speed of the train.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the width of one of the slits.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest the variation in the output voltage from the light sensor that will be observed as the train moves beyond the first diffraction minimum.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In another experiment the student replaces the light sensor with a sound sensor. The train travels away from a loudspeaker that is emitting sound waves of constant amplitude and frequency towards a reflecting barrier.</p>
<p><img 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"></p>
<p>The graph shows the variation with time of the output voltage from the sounds sensor.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Explain how this effect arises.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«light» superposes/interferes</p>
<p>pattern consists of «intensity» maxima and minima<br><em><strong>OR</strong></em><br>consisting of constructive and destructive «interference»</p>
<p>voltage peaks correspond to interference maxima</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="s = \frac{{\lambda D}}{d} = \frac{{6.3 \times {{10}^{ - 7}} \times 5.0}}{{1.5 \times {{10}^{ - 3}}}} = ">
<mi>s</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>λ</mi>
<mi>D</mi>
</mrow>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>5.0</mn>
</mrow>
<mrow>
<mn>1.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2.1 x 10<sup>–3 </sup>«m» </p>
<p> </p>
<p><em>If no unit assume m.</em><br><em>Correct answer only.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct read-off from graph of 25 m s</p>
<p><em>v</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{x}{t} = \frac{{2.1 \times {{10}^{ - 3}}}}{{25 \times {{10}^{ - 3}}}} = ">
<mfrac>
<mi>x</mi>
<mi>t</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 8.4 x 10<sup>–2</sup> «m s<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow ECF from (b)(i)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>angular width of diffraction minimum = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.13}}{{5.0}}">
<mfrac>
<mrow>
<mn>0.13</mn>
</mrow>
<mrow>
<mn>5.0</mn>
</mrow>
</mfrac>
</math></span> «= 0.026 rad»</p>
<p>slit width = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{d} = \frac{{6.3 \times {{10}^{ - 7}}}}{{0.026}} = ">
<mfrac>
<mi>λ</mi>
<mi>d</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.026</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 2.4 x 10<sup>–5</sup> «m»</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> for solution using 1.22 factor.</em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«beyond the first diffraction minimum» average voltage is smaller<br><br>«voltage minimum» spacing is «approximately» same<br><em><strong>OR</strong></em><br>rate of variation of voltage is unchanged</p>
<p> </p>
<p><em>OWTTE</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«reflection at barrier» leads to two waves travelling in opposite directions </p>
<p>mention of formation of standing wave</p>
<p>maximum corresponds to antinode/maximum displacement «of air molecules»<br><em><strong>OR</strong></em><br>complete cancellation at node position</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
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[N/A]
<div class="question_part_label">b.i.</div>
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[N/A]
<div class="question_part_label">b.ii.</div>
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[N/A]
<div class="question_part_label">c.i.</div>
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[N/A]
<div class="question_part_label">c.ii.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
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