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</div><h2>HL Paper 2</h2><div class="specification">
<div class="page" title="Page 35">
<div class="layoutArea">
<div class="column">
<p><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">This question is in </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-weight: bold;">two </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">parts. </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-weight: bold;">Part 1 </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">is about gravitational force fields. </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-weight: bold;">Part 2 </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">is about properties of a gas. </span></p>
<p><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPS'; font-weight: bold;">Part 1 </span><span style="font-size: 12.000000pt; font-family: 'TimesNewRomanPSMT';">Gravitational force fields </span></p>
</div>
</div>
</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State Newton’s universal law of gravitation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A satellite of mass <em>m</em> orbits a planet of mass<em> M</em>. Derive the following relationship between the period of the satellite <em>T</em> and the radius of its orbit <em>R</em> (Kepler’s third law).</p>
<p style="text-align: center;">\({T^2} = \frac{{4{\pi ^2}{R^3}}}{{GM}}\)</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 style="text-align: left;">A polar orbiting satellite has an orbit which passes above both of the Earth’s poles. One polar orbiting satellite used for Earth observation has an orbital period of 6.00 × 10<sup>3</sup>s.<br> Mass of Earth = 5.97 × 10<sup>24 </sup>kg<br> Average radius of Earth = 6.37 × 10<sup>6 </sup>m</p>
<p style="text-align: left;">(i) Using the relationship in (b), show that the average height above the surface of the Earth for this satellite is about 800 km.</p>
<p style="text-align: left;">(ii) The satellite moves from an orbit of radius 1200 km above the Earth to one of radius 2500 km. The mass of the satellite is 45 kg.</p>
<p style="text-align: left;">Calculate the change in the gravitational potential energy of the satellite.</p>
<p style="text-align: left;">(iii) Explain whether the gravitational potential energy has increased, decreased or stayed the same when the orbit changes, as in (c)(ii).</p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the (attractive) force between two (point) masses is directly proportional to the product of the masses;<br>and inversely proportional to the square of the distance (between their centres of mass); <br><em>Use of equation is acceptable:</em><br><em>Award<strong> [2]</strong> if all five quantities defined. Award <strong>[1]</strong> if four quantities defined.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(G\frac{{Mm}}{{{R^2}}} = \frac{{m{v^2}}}{R}\) so \({v^2} = \frac{{Gm}}{R}\);<br>\(v = \frac{{2\pi R}}{T}\);<br>\({v^2} = \frac{{4{\pi ^2}{R^2}}}{{{T^2}}} = \frac{{Gm}}{R}\);</p>
<p><strong>or</strong></p>
<p>\(G\frac{{Mm}}{{{R^2}}} = m{\omega ^2}R\)<em>;<br></em>\({\omega ^2} = \frac{{4{\pi ^2}}}{{{T^2}}}\);<br>\(\frac{{4{\pi ^2}}}{{{T^2}}} = \frac{{GM}}{{{R^3}}}\);<br><em>Award <strong>[3]</strong> to a clear response with a missing step.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \({R^3} = \frac{{6.67 \times {{10}^{ - 11}} \times 5.97 \times {{10}^{24}} \times {{6000}^2}}}{{4 \times {\pi ^2}}}\);<br><em>R</em>=7.13x10<sup>6</sup>(m);<br><em>h</em>=(7.13x10<sup>6</sup>-6.37x10<sup>6</sup>)=760(km);<br><em>Award <strong>[3]</strong> for an answer of 740 with π taken as 3.14.</em></p>
<p>(ii) clear use of \(\Delta V = \frac{{\Delta E}}{m}\) and \(V = - \frac{{Gm}}{r}\) <strong>or</strong> \(\Delta E = GMm\left( {\frac{1}{{{r_1}}} - \frac{1}{{{r_2}}}} \right)\);<br>one value of potential energy calculated (2.37×10<sup>9</sup> <em><strong>or</strong></em> 2.02×10<sup>9</sup> );<br>3.5×10<sup>8</sup> (J);<br><em>Award <strong>[3]</strong> for a bald correct answer.</em><br><em>Award <strong>[2]</strong> for 7.7x10<sup>9</sup>. Award <strong>[1]</strong> for 7.7x10<sup>12</sup>.</em><br><em>Award <strong>[0] </strong>for answers using mgΔh.</em></p>
<p>(iii) increased;<br>further from Earth / closer to infinity / smaller negative value;<br><em>Award<strong> [0]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>(a) Many candidates stated that the Newton’s law force is proportional to the masses of the objects in question, rather than the product of the masses.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This part was generally well done with most candidates coming to the correct outcome; too often steps were missed out in the derivations and this cost candidates mark. It is essential that they realise that a derivation must include every step. The presentation of this part left much to be desired in quite a large minority with mathematically incorrect statements being given.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) Most candidates were able to substitute values into the equation and rearrange it to find a value for R. Many then fail to subtract the radius of the Earth.</p>
<p>(ii) Very few candidates completed this part correctly. Confusion between potential and potential energy was common as were adding the height in kilometres to the radius of the Earth in metres. A sizeable minority of candidates attempted to use the mgh equation.</p>
<p>(iii) This part was quite well answered with most candidates realising that the increase in height meant an increase in potential energy. Several argued that the magnitude decreased but being a negative quantity this meant an increase.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">This question is about the thermodynamics of a car engine and the dynamics of the car.</p>
<p class="p1">A car engine consists of four cylinders. In each of the cylinders, a fuel-air mixture explodes to supply power at the appropriate moment in the cycle.</p>
<p class="p1">The diagram models the variation of pressure <em>P </em>with volume <em>V </em>for one cycle of the gas, ABCDA, in one of the cylinders of the engine. The gas in the cylinder has a fixed mass and can be assumed to be ideal.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-09-07_om_09.01.07.png" alt="M14/4/PHYSI/HP2/ENG/TZ2/09"></p>
</div>
<div class="specification">
<p>The car is travelling at its maximum speed of \({\text{56 m}}\,{{\text{s}}^{ - 1}}\). At this speed, the energy provided by the fuel injected into one cylinder in each cycle is 9200 J. One litre of fuel provides 56 MJ of energy.</p>
</div>
<div class="specification">
<p class="p1">A car is travelling along a straight horizontal road at its maximum speed of \({\text{56 m}}\,{{\text{s}}^{ - 1}}\). The power output required at the wheels is 0.13 MW.</p>
</div>
<div class="specification">
<p class="p1">A driver moves a car in a horizontal circular path of radius 200 m. Each of the four tyres will not grip the road if the frictional force between a tyre and the road becomes less than 1500 N.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">At point A in the cycle, the fuel-air mixture is at 18 °C. During process AB, the gas is compressed to 0.046 of its original volume and the pressure increases by a factor of 40. Calculate the temperature of the gas at point B.</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 class="p1">State the nature of the change in the gas that takes place during process BC in the cycle.</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 class="p1">Process CD is an adiabatic change. Discuss, with reference to the first law of thermodynamics, the change in temperature of the gas in the cylinder during process CD.</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 class="p1">Explain how the diagram can be used to calculate the net work done during one cycle.</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 class="p1">(i) Calculate the volume of fuel injected into one cylinder during one cycle.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Each of the four cylinders completes a cycle 18 times every second. Calculate the distance the car can travel on one litre of fuel at a speed of \({\text{56 m}}\,{{\text{s}}^{ - 1}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">A car accelerates uniformly along a straight horizontal road from an initial speed of \({\text{12 m}}\,{{\text{s}}^{ - 1}}\) to a final speed of \({\text{28 m}}\,{{\text{s}}^{ - 1}}\) in a distance of 250 m. The mass of the car is 1200 kg. Determine the rate at which the engine is supplying kinetic energy to the car as it accelerates.</p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Calculate the total resistive force acting on the car when it is travelling at a constant speed of \({\text{56 m}}\,{{\text{s}}^{ - 1}}\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>The mass of the car is 1200 kg. The resistive force <em>F </em>is related to the speed <em>v</em> by \(F \propto {v^2}\). Using your answer to (g)(i), determine the maximum theoretical acceleration of the car at a speed of \({\text{28 m}}\,{{\text{s}}^{ - 1}}\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Calculate the maximum speed of the car at which it can continue to move in the circular path. Assume that the radius of the path is the same for each tyre.</p>
<p class="p1">(ii) While the car is travelling around the circle, the people in the car have the sensation that they are being thrown outwards. Outline how Newton’s first law of motion accounts for this sensation.</p>
<div class="marks">[6]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">535 (K) / 262 (°C);</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">constant volume change / isochoric / isovolumetric / <em>OWTTE</em>;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Q</em>/thermal energy transfer is zero;</p>
<p>\(\Delta U = - W\);</p>
<p>as work is done by gas internal energy falls;</p>
<p>temperature falls as temperature is measure of average kinetic energy;</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">work done is estimated by evaluating area;</p>
<p class="p1">inside the loop / <em>OWTTE</em>;</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(1.6 \times {10^{ - 4}}{\text{ (litre)}}\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>one litre \( = \left( {\frac{1}{{4 \times 18 \times 1.64 \times {{10}^{ - 4}}}} = } \right){\text{ }}87{\text{ s of travel}}\);</p>
<p class="p1">\((87 \times 56) = 4.7{\text{ (km)}}\);</p>
<p class="p1"><em>Allow rounded 1.6 value to be used, giving 4.9 (km).</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">use of a kinematic equation to determine motion time \({\text{(}} = 12.5{\text{ s)}}\);</p>
<p class="p1">change in kinetic energy \( = \frac{1}{2} \times {\text{1200}} \times {\text{[2}}{{\text{8}}^2} - {\text{1}}{{\text{2}}^2}]{\text{ (}} = 384{\text{ kJ)}}\);</p>
<p class="p1">rate of change in kinetic energy \( = \frac{{{\text{384000}}}}{{{\text{12.5}}}}\); } <em>(allow ECF of 16<sup>2</sup></em> <em>from (28 </em>\( - \)<em> 12)<sup>2</sup></em> <em>for this mark)</em></p>
<p class="p1">31 (kW);</p>
<p class="p1"><strong><em>or</em></strong></p>
<p class="p1">use of a kinematic equation to determine motion time \(( = 12.5{\text{ s)}}\);</p>
<p class="p1">use of a kinematic equation to determine acceleration \(( = 1.28{\text{ m}}\,{{\text{s}}^{ - 2}})\);</p>
<p class="p1">work done \(\frac{{F \times s}}{{{\text{time}}}} = \frac{{1536 \times 250}}{{12.5}}\);</p>
<p class="p1">31 (kW);</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\({\text{force}} = \frac{{{\text{power}}}}{{{\text{speed}}}}\);</p>
<p class="p1">2300 <strong><em>or </em></strong>2.3k (N);</p>
<p class="p1"><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer.</em></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>resistive force \( = \frac{{2300}}{4}\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(\frac{{2321}}{4}{\text{ }}( = {\text{575)}}\); <em>(allow ECF)</em></p>
<p class="p1">so accelerating force \((2300 - 580 = ){\text{ }}1725{\text{ (N)}}\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)1741 (N);</p>
<p class="p1">\(a = \frac{{1725}}{{1200}} = 1.44{\text{ (m}}\,{{\text{s}}^{ - 2}})\)\(\,\,\,\)<strong><em>or</em></strong>\(\,\,\,\)\(a = \frac{{1741}}{{1200}} = 1.45{\text{ (m}}\,{{\text{s}}^{ - 2}})\);</p>
<p class="p1"><em>Award </em><strong><em>[2 max] </em></strong><em>for an answer of 0.49 (m</em>\(\,\)<em>s<sup>–2</sup> (omits 2300 N).</em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>centripetal force must be \( < 6000{\text{ (N)}}\); <em>(allow force 6000 N)</em></p>
<p class="p1">\({v^2} = F \times \frac{r}{m}\);</p>
<p class="p1">\(31.6{\text{ (m}}\,{{\text{s}}^{ - 1}})\);</p>
<p class="p1"><em>Allow </em><strong><em>[3] </em></strong><em>for a bald correct answer.</em></p>
<p class="p1"><em>Allow </em><strong><em>[2 max] </em></strong><em>if 4</em>\( \times \)<em> is omitted, giving 15.8 (m</em>\(\,\)<em>s<sup>–1</sup>)</em>.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>statement of Newton’s first law;</p>
<p class="p1">(hence) without car wall/restraint/friction at seat, the people in the car would move in a straight line/at a tangent to circle;</p>
<p class="p1">(hence) seat/seat belt/door exerts centripetal force;</p>
<p class="p1">(in frame of reference of the people) straight ahead movement is interpreted as “outwards”;</p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This simple gas law calculation was surprisingly badly done. Certainly similar questions have attracted better scores in previous examinations. Common errors included the inevitable failure to work in kelvin, and simple arithmetic errors.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates were able to describe the constant volume nature of the change in question.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Many candidates scored full credit in a question that has been well rehearsed in previous examinations. The zero change in thermal energy transfer was common and many were able to deduce that \(\Delta U\) is therefore equal to \( - W\). This led immediately to a deduction of temperature decrease.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Almost all recognised that the work done was related to some area under the graph. In a small minority of cases the exact specification of the area was too imprecise to gain the second mark.</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) It was common to see a correct value for the volume of fuel used though not a correct unit.</p>
<p class="p1">(ii) Many were able to arrive at a travel time for the fuel and therefore the distance travelled. However, routes were indirect and lengthy and few could see a direct way to the answer.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">There were at least two routes to tackle this problem. Some solutions were so confused that it was difficult to decide which method had been used. Common errors included: forgetting that the initial speed was \({\text{12 m}}\,{{\text{s}}^{ - 1}}\) not zero, power of ten errors, and simple mistakes in the use of the kinematic equations, or failure to evaluate work done \( = {\text{force }} \times {\text{ distance}}\) correctly. However, many candidates scored partial credit. Scores of two or three out of the maximum four were common showing that many are persevering to get as far as they can.</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) Many correct solutions were seen. Candidates are clearly comfortable with the use of the equation force = power/speed.</p>
<p class="p1">(ii) The method to be used here was obvious to many. What was missing was a clear appreciation of what was happening in terms of resistive force in the system. Many scored two out of three because they indicated a sensible method but did not use the correct value for the force. Scoring two marks does require that the explanation of the method is at least competent. Those candidates who give limited explanations of their method leading to a wrong answer will generally accumulate little credit. A suggestion (never seen in answers) is that candidates should have begun from a free-body force diagram which would have revealed the relationship of all the forces.</p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) The major problem here was that most candidates did not recognise that 1500 N of force acting at each of four wheels will imply a total force of 6 kN. Again, partial credit was available only if it was clear what the candidate was doing and what the error was.</p>
<p class="p1">(ii) Statements of Newton’s first law were surprisingly poor. As in previous examinations, few candidates appear to have learnt this essential rule by heart and they produce a garbled and incomplete version under examination pressure. The first law was then only loosely connected to the particular context of the question. Candidates have apparently not learnt to relate the physics they learn to everyday contexts.</p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is in <strong>two</strong> parts. <strong>Part 1</strong> is about fields, electric potential difference and electric<br>circuits. <strong>Part 2</strong> is about thermodynamic cycles.</p>
<p><strong>Part 1</strong> Fields, electric potential difference and electric circuits</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The magnitude of gravitational field strength <em>g</em> is defined from the equation shown below.</p>
<p>\[g = \frac{{{F_g}}}{m}\]</p>
<p>The magnitude of electric field strength <em>E</em> is defined from the equation shown below.</p>
<p>\[E = \frac{{{F_E}}}{q}\]</p>
<p>For each of these defining equations, state the meaning of the symbols</p>
<p>(i) <em>F</em><sub>g</sub>.</p>
<p>(ii) <em>F</em><sub>E</sub>.</p>
<p>(iii) <em>m</em>.</p>
<p>(iv) <em>q</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a simple model of the hydrogen atom, the electron is regarded as being in a circular orbit about the proton. The magnitude of the electric field strength at the electron due to the proton is <em>E</em><sub>p</sub> . The magnitude of the gravitational field strength at the electron due to the proton is <em>g</em><sub>p</sub>.</p>
<p>Determine the order of magnitude of the ratio shown below.</p>
<p>\[\frac{{{E_p}}}{{{g_p}}}\]</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
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<p>(i) the force exerted on a small/test/point mass; <br><em>Do not allow bald “gravitational force”.</em></p>
<p>(ii) the force exerted on a small/point/test positive charge; <br><em>To award <strong>[1]</strong> “positive” is required.</em><br><em>Do not allow bald “electric force”.</em></p>
<p>(iii) the size/magnitude/value of the small/point mass; <br><em>Do not accept bald “mass”</em>.</p>
<p>(iv) the magnitude/size/value of the small/point/test (positive) charge;<br><em>Do not accept bald “charge”.</em></p>
<p><em>In part (a) only penalize lack of “small/test/point” once, annotate as ECF.<br>It must be clear that the mass/charge in (iii) & (iv) refer to the object in (i) and (ii).</em></p>
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</div>
<div class="question_part_label">a.</div>
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<p><span style="font-size: 12.000000pt; font-family: 'Times New Roman';">\({E_p} = \frac{e}{{4\pi {\varepsilon _0}{r^2}}}\) and \({g_p} = \frac{{G{m_p}}}{{{r^2}}}\); </span><em><span style="font-size: 12pt; font-family: 'Times New Roman,Italic';">(both needed) <br></span></em><span style="font-size: 12pt; font-family: 'Times New Roman,Italic';">\(\frac{e}{{4\pi {\varepsilon _0}G{m_p}}}\left( { = \frac{{9 \times {{10}^9} \times 1.6 \times {{10}^{ - 19}}}}{{6.7 \times {{10}^{ - 11}} \times 1.7 \times {{10}^{ - 27}}}}} \right)\);<br>≈10<sup>28</sup>;</span></p>
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</div>
</div>
<p><em>Award <strong>[2 max]</strong> if response calculates ratio of force as this is an ECF from the </em><em>first marking point (10<sup>39</sup>) .</em><br><em>Award <strong>[3]</strong> for solution that correctly evaluates field strengths separately and </em><em>then divides.</em></p>
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</div>
</div>
<div class="question_part_label">b.</div>
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<h2 style="margin-top: 1em">Examiners report</h2>
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<p>In this part candidates were completely at a loss and could not state the meanings of the symbols in the definitions of gravitational or electric field strengths. This was a disappointing failure in what was meant to be an easy opener to the whole question.</p>
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</div>
<div class="question_part_label">a.</div>
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<p>Following (a) candidates failed widely on this part too. They often had little idea which data to use (mass and charge were frequently confused) and sometimes the meaning of the constants in the equations failed them too. This was compounded by arithmetic errors to make a straightforward calculation very hard for many.</p>
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</div>
</div>
</div>
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</div>
<div class="question_part_label">b.</div>
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<br><hr><br><div class="specification">
<p>The gravitational potential due to the Sun at its surface is –1.9 x 10<sup>11</sup> J kg<sup>–1</sup>. The following data are available.</p>
<table style="width: 441.4px; margin-left: 120px;">
<tbody>
<tr>
<td style="width: 422px;">Mass of Earth</td>
<td style="width: 558.4px;">= 6.0 x 10<sup>24</sup> kg</td>
</tr>
<tr>
<td style="width: 422px;">Distance from Earth to Sun</td>
<td style="width: 558.4px;">= 1.5 x 10<sup>11</sup> m</td>
</tr>
<tr>
<td style="width: 422px;">Radius of Sun</td>
<td style="width: 558.4px;">= 7.0 x 10<sup>8</sup> m</td>
</tr>
</tbody>
</table>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the gravitational potential is negative.</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 gravitational potential due to the Sun at a distance <em>r</em> from its centre is <em>V</em><sub>S</sub>. Show that</p>
<p style="text-align: center;"><em>rV</em><sub>S</sub> = constant.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the gravitational potential energy of the Earth in its orbit around the Sun. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the total energy of the Earth in its orbit.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An asteroid strikes the Earth and causes the orbital speed of the Earth to suddenly decrease. Suggest the ways in which the orbit of the Earth will change.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iv.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>potential is defined to be zero at infinity</p>
<p>so a positive amount of work needs to be supplied for a mass to reach infinity</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em><sub>S</sub> = \( - \frac{{GM}}{r}\) so <em>r</em> x <em>V</em><sub>S</sub> «= –<em>GM</em>» = constant because<em> G</em> and<em> M</em> are constants</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>GM</em> = 1.33 x 10<sup>20</sup> «J m kg<sup>–1</sup>»</p>
<p>GPE at Earth orbit «= –\(\frac{{1.33 \times {{10}^{20}} \times 6.0 \times {{10}^{24}}}}{{1.5 \times {{10}^{11}}}}\)» = «–» 5.3 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> unless answer is to 2 sf.</em></p>
<p><em>Ignore addition of Sun radius to radius of Earth orbit.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>work leading to statement that kinetic energy \(\frac{{GMm}}{{2r}}\), <em><strong>AND</strong></em> kinetic energy evaluated to be «+» 2.7 x 10<sup>33</sup> «J»</p>
<p>energy «= PE + KE = answer to (b)(ii) + 2.7 x 10<sup>33</sup>» = «–» 2.7 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em><br>statement that kinetic energy is \( = - \frac{1}{2}\) gravitational potential energy in orbit</p>
<p>so energy «\( = \frac{{{\text{answer to (b)(ii)}}}}{2}\)» = «–» 2.7 x 10<sup>33</sup> «J»</p>
<p> </p>
<p><em>Various approaches possible.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«KE will initially decrease so» total energy decreases<br><em><strong>OR</strong></em><br>«KE will initially decrease so» total energy becomes more negative</p>
<p>Earth moves closer to Sun</p>
<p>new orbit with greater speed «but lower total energy»</p>
<p>changes ellipticity of orbit</p>
<div class="question_part_label">b.iv.</div>
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<div class="question" style="padding-left: 20px;">
<p>centripetal force is required</p>
<p>and is provided by gravitational force between Earth and Sun</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> for statement that there is a “centripetal force of gravity” without further qualification.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
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<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
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<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">b.iv.</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>Rhodium-106 (\(_{\,\,\,45}^{106}{\text{Rh}}\)) decays into palladium-106 (\(_{\,\,\,46}^{106}{\text{Pd}}\)) by beta minus (<em>β</em><sup>–</sup>) decay. The diagram shows some of the nuclear energy levels of rhodium-106 and palladium-106. The arrow represents the <em>β</em><sup>–</sup> decay.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_06.42.36.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/09.d"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Bohr modified the Rutherford model by introducing the condition <em>mvr </em>= <em>n</em>\(\frac{h}{{2\pi }}\). Outline the reason for this modification.</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>Show that the speed <em>v </em>of an electron in the hydrogen atom is related to the radius <em>r </em>of the orbit by the expression</p>
<p>\[v = \sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} \]</p>
<p>where <em>k </em>is the Coulomb constant.</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>Using the answer in (b) and (c)(i), deduce that the radius <em>r </em>of the electron’s orbit in the ground state of hydrogen is given by the following expression.</p>
<p>\[r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}\]</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>Calculate the electron’s orbital radius in (c)(ii).</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>Explain what may be deduced about the energy of the electron in the <em>β</em><sup>–</sup> decay.</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>Suggest why the <em>β</em><sup>–</sup> decay is followed by the emission of a gamma ray photon.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the wavelength of the gamma ray photon in (d)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the electrons accelerate and so radiate energy</p>
<p>they would therefore spiral into the nucleus/atoms would be unstable</p>
<p>electrons have discrete/only certain energy levels</p>
<p>the only orbits where electrons do not radiate are those that satisfy the Bohr condition <strong>«</strong><span class="Apple-converted-space"><em>mvr</em> = <em>n</em>\(\frac{h}{{2\pi }}\)</span><strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{{m_{\text{e}}}{v^2}}}{r} = \frac{{k{e^2}}}{{{r^2}}}\)</p>
<p><strong><em>OR</em></strong></p>
<p>KE =Â \(\frac{1}{2}\)PE hence \(\frac{1}{2}\)<em>m</em><sub>e</sub><em>v</em><sup>2</sup> =Â \(\frac{1}{2}\frac{{k{e^2}}}{r}\)</p>
<p><strong>«</strong>solving for <em>v </em>to get answer<strong>»</strong></p>
<p>Â </p>
<p><em>Answer given – look for correct working</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>combining <em>v</em> =Â \(\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}} \)Â with <em>m</em><sub>e</sub><em>vr</em> =Â \(\frac{h}{{2\pi }}\)Â using correct substitution</p>
<p><strong>«</strong><span class="Apple-converted-space"><em>eg</em> \({m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}\)</span><strong>»</strong></p>
<p>correct algebraic manipulation to gain the answer</p>
<p>Â </p>
<p><em>Answer given – look for correct working</em></p>
<p><em>Do not allow a bald statement of the answer for MP2. Some further working eg cancellation of m or r must be shown</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><span class="Apple-converted-space"> <em>r</em> = \(\frac{{{{(6.63 \times {{10}^{ - 34}})}^2}}}{{4{\pi ^2} \times 8.99 \times {{10}^9} \times 9.11 \times {{10}^{ - 31}} \times {{(1.6 \times {{10}^{ - 19}})}^2}}}\)</span><strong>»</strong></p>
<p><em>r</em> = 5.3 × 10<sup>–11</sup> <strong>«</strong><span class="Apple-converted-space">m</span><strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the energy released is 3.54 – 0.48 = 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p>this is shared by the electron and the antineutrino</p>
<p>so the electron’s energy varies from 0 to 3.06 <strong>«</strong>MeV<strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the palladium nucleus emits the photon when it decays into the ground state <strong>«</strong>from the excited state<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Photon energy</p>
<p><em>E</em> = 0.48 × 10<sup>6</sup> × 1.6 × 10<sup>–19</sup> = <strong>«</strong><span class="Apple-converted-space">7.68 × 10<sup>–14</sup> <em>J</em></span><strong>»</strong></p>
<p><em>λ</em> = <strong>«</strong><span class="Apple-converted-space">\(\frac{{hc}}{E} = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{7.68 \times {{10}^{ - 14}}}}\) =</span><strong>»</strong> 2.6 × 10<sup>–12</sup><strong> «</strong><span class="Apple-converted-space">m</span><strong>»</strong></p>
<p>Â </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow ECF from incorrect energy</em></p>
<p><strong><em>[2 marks]</em></strong></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">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>A planet has radius <em>R</em>. At a distance <em>h </em>above the surface of the planet the gravitational field strength is <em>g </em>and the gravitational potential is <em>V</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by gravitational field strength.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <em>V </em>= –<em>g</em>(<em>R </em>+ <em>h</em>).</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>Draw a graph, on the axes, to show the variation of the gravitational potential <em>V</em>Â of the planet with height <em>h </em>above the surface of the planet.</p>
<p><img src="data:image/png;base64,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"></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>A planet has a radius of 3.1 × 10<sup>6</sup> m. At a point P a distance 2.4 × 10<sup>7</sup> m above the surface of the planet the gravitational field strength is 2.2 N kg<sup>–1</sup>. Calculate the gravitational potential at point P, include an appropriate unit for your answer.</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 diagram shows the path of an asteroid as it moves past the planet.</p>
<p>Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â <img src="images/Schermafbeelding_2018-08-14_om_07.33.17.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/06.c"></p>
<p>When the asteroid was far away from the planet it had negligible speed. Estimate the speed of the asteroid at point P as defined in (b).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The mass of the asteroid is 6.2 × 10<sup>12</sup> kg. Calculate the gravitational force experienced by the <strong>planet </strong>when the asteroid is at point P.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the <strong>«</strong>gravitational<strong>» </strong>force per unit mass exerted on a point/small/test mass</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>at height <em>h </em>potential is <em>V</em> = –\(\frac{{GM}}{{(R + h)}}\)</p>
<p>field is <em>g </em>=Â \(\frac{{GM}}{{{{(R + h)}^2}}}\)</p>
<p><strong>«</strong>dividing gives answer<strong>»</strong></p>
<p>Â </p>
<p><em>Do not allow an answer that starts with g = –</em>\(\frac{{\Delta V}}{{\Delta r}}\)<em> and then cancels the deltas and substitutes </em><em>R </em>+ <em>h</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>correct shape and sign</p>
<p>non-zero negative vertical intercept</p>
<p>Â </p>
<p><img src="images/Schermafbeelding_2018-08-14_om_07.26.11.png" alt="M18/4/PHYSI/HP2/ENG/TZ2/06.a.iii/M"></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>V</em> = <strong>«</strong><span class="Apple-converted-space">–2.2 × (3.1 × 10<sup>6</sup> + 2.4 × 10<sup>7</sup>) =</span><strong>»</strong> <strong>«</strong><span class="Apple-converted-space">–</span><strong>»</strong> 6.0 × 10<sup>7</sup> J kg<sup>–1</sup></p>
<p>Â </p>
<p><em>Unit is essential</em></p>
<p><em>Allow eg MJ kg<sup>–</sup></em><em><sup>1</sup> </em><em>if power of 10 is correct</em></p>
<p><em>Allow other correct SI units eg m</em><sup><em>2</em></sup><em>s<sup>–</sup></em><sup><em>2</em></sup><em>, N m kg<sup>–</sup></em><sup><em>1</em></sup></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total energy at P = 0 / KE gained = GPE lost</p>
<p><strong>«</strong><span class="Apple-converted-space">\(\frac{1}{2}\)<em>mv</em><sup>2</sup> + <em>mV</em> = 0 ⇒</span><strong>»</strong> <em>v</em> = \(\sqrt { - 2V} \)</p>
<p><em>v</em> = <strong>«</strong><span class="Apple-converted-space">\(\sqrt {2 \times 6.0 \times {{10}^7}} \) =</span><strong>»</strong> 1.1 × 10<sup>4</sup> <strong>«</strong><span class="Apple-converted-space">ms<sup>–1</sup></span><strong>»</strong></p>
<p>Â </p>
<p>Â </p>
<p><em>Award </em><strong><em>[3] </em></strong><em>for a bald correct answer</em></p>
<p><em>Ignore negative sign errors in the workings</em></p>
<p><em>Allow ECF from 6(b)</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>force on asteroid is <strong>«</strong><span class="Apple-converted-space">6.2 × 10<sup>12</sup> × 2.2 =</span><strong>»</strong> 1.4 × 10<sup>13</sup> <strong>«</strong><span class="Apple-converted-space">N</span><strong>»</strong></p>
<p><strong>«</strong>by Newton’s third law<strong>» </strong>this is also the force on the planet</p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>mass of planet = 2.4 x 10<sup>25</sup> <strong>«</strong>kg<strong>» «</strong>from <em>V</em> = –\(\frac{{GM}}{{(R + h)}}\)<strong>»</strong></p>
<p>force on planet <strong>«</strong><span class="Apple-converted-space">\(\frac{{GMm}}{{{{(R + h)}^2}}}\)</span><strong>»</strong> = 1.4 × 10<sup>13</sup> <strong>«</strong><span class="Apple-converted-space">N</span><strong>»</strong></p>
<p>Â </p>
<p><em>MP2 must be explicit</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>Part 2</strong> Motion of a rocket</p>
<p>A rocket is moving away from a planet within the gravitational field of the planet. When the rocket is at position P a distance of 1.30×10<sup>7</sup>m from the centre of the planet, the engine is switched off. At P, the speed of the rocket is 4.38×10<sup>3</sup>ms<sup>–1</sup>.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>At a time of 60.0 s later, the rocket has reached position Q. The speed of the rocket at Q is 4.25×10<sup>3</sup>ms<sup>–1</sup>. Air resistance is negligible.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to the energy of the rocket, why the speed of the rocket is changing between P and Q.</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>Estimate the average gravitational field strength of the planet between P and Q.</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>(i) An object is a distance<em> r</em> from the centre of a planet. Show that the minimum speed required to escape the gravitational field is equal to<br>\[\sqrt {2g'r} \]<br>where <em>g′</em> is the gravitational field strength at distance <em>r</em> from the centre of a planet.</p>
<p>(ii) Discuss, using a calculation, whether the rocket at P can completely escape the gravitational field of the planet without further use of the engine.</p>
<div class="marks">[5]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A space station is in orbit at a distance <em>r</em> from the centre of the planet in (e)(i). A satellite is launched from the space station so as just to escape from the gravitational field of the planet. The launch takes place in the same direction as the velocity of the space station. Outline why the launch velocity relative to the space station can be less than your answer to (e)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>gravitational potential energy is being gained;<br>this is at the expense of kinetic energy (and speed falls);</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {{\rm{acceleration}} = \frac{{\left( {v - u} \right)}}{t} = \frac{{4.25 \times {{10}^3} - 4.38 \times {{10}^3}}}{{60}} = } \right)\left( - \right)2.17\left( {{\rm{m}}{{\rm{s}}^{ - 2}}} \right)\);</p>
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<p><span style="font-size: 11.000000pt; font-family: 'Arial';">gravitational field strength <span style="font-size: 11.000000pt; font-family: 'SymbolMT';">= </span></span><span style="font-size: 11.000000pt; font-family: 'Arial';">acceleration of rocket (</span><span style="font-size: 11.000000pt; font-family: 'SymbolMT';">=</span><span style="font-size: 11.000000pt; font-family: 'Arial';">2.17 N kg</span><span style="font-size: 7.000000pt; font-family: 'Arial'; vertical-align: 3.000000pt;">–1</span><span style="font-size: 11.000000pt; font-family: 'Arial';">); } </span><em>(allow g <span style="font-size: 11.000000pt; font-family: 'SymbolMT';">=</span> a in symbols)</em></p>
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<p><em><strong><span style="font-size: 11pt; font-family: 'Arial,BoldItalic';">or </span></strong></em></p>
<p><span style="font-size: 11.000000pt; font-family: 'Arial';">computes potential difference from KE per unit mass change (5.61</span><span style="font-size: 11.000000pt; font-family: 'Arial';">\( \times \)10</span><span style="font-size: 7.000000pt; font-family: 'Arial'; vertical-align: 5.000000pt;">5</span><span style="font-size: 11.000000pt; font-family: 'Arial';">),<br>computes distance travelled (0.259 Mm), uses \(g = \frac{{\left( - \right)\Delta V}}{{\Delta r}}\);<br><em>g</em>=(\( - \))2.17(ms<sup>-2</sup>);<br></span></p>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(\left( {{\rm{gravitational force}}} \right){\rm{ = }}mg'{\rm{ = }}\frac{{{\rm{GMm}}}}{{{r^2}}}\);<br>\(\left( {{\rm{kinetic energy}}} \right){\rm{ = }}\frac{{{\rm{m}}{{\rm{v}}^{\rm{2}}}}}{2} = \frac{{GMm}}{r}\);<br>\({v^2} = 2\frac{{GM}}{{{r^2}}}r\left( { = 2g'r} \right)\);</p>
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<p><em><span style="font-size: 11pt; font-family: 'Arial,Italic';">Award </span><strong><span style="font-size: 11pt; font-family: 'Arial,BoldItalic';">[0] </span></strong></em><span style="font-size: 11.000000pt; font-family: 'Arial,Italic';"><em>for centripetal force argument as rocket is not in orbit.</em><br> </span></p>
<p><span style="font-size: 11pt; font-family: 'Arial,Italic';">(ii) </span><span style="font-size: 11.000000pt; font-family: 'Arial';">calculation of speed at a relevant distance </span><span style="font-size: 11.000000pt; font-family: 'Arial,Italic';">eg</span><span style="font-size: 11.000000pt; font-family: 'Arial';">: \(\sqrt {2 \times g' \times 13 \times {{10}^6}} = 7500\left( {{\rm{m}}{{\rm{s}}^{ - 1}}} \right)\);<br>speed is less than this so will not escape; } </span><em>(allow ECF from (d) which could lead to rocket able to escape)</em></p>
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<p><em><span style="font-size: 11pt; font-family: 'Arial,Italic';">Award </span><strong><span style="font-size: 11pt; font-family: 'Arial,BoldItalic';">[1 max] </span></strong><span style="font-size: 11pt; font-family: 'Arial,Italic';">for use of g</span><span style="font-size: 11pt; font-family: 'SymbolMT';">=</span><span style="font-size: 11pt; font-family: 'Arial,Italic';">9.81 and r which gives 16000 ms</span><span style="font-size: 7pt; font-family: 'Arial,Italic'; vertical-align: 3pt;">–1 </span></em><span style="font-size: 11.000000pt; font-family: 'Arial,Italic';"><em>.</em><br> </span></p>
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<p><span style="font-size: 11.000000pt; font-family: 'Arial';"> </span></p>
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<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
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<p><span style="font-size: 11.000000pt; font-family: 'Arial';">the satellite has velocity/kinetic energy as it is orbiting with the space station; </span></p>
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<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a planet near two stars of equal mass <em>M</em>.</p>
<p><img src="data:image/png;base64,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" alt></p>
<p>Each star has mass <em>M</em>=2.0×10<sup>30</sup>kg. Their centres are separated by a distance of 6.8×10<sup>11</sup>m. The planet is at a distance of 6.0×10<sup>11</sup>m from each star.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram above, draw <strong>two</strong> arrows to show the gravitational field strength at the position of the planet due to each of the stars.</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 the magnitude and state the direction of the resultant gravitational field strength at the position of the planet.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
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<div class="layoutArea">
<div class="column">
<p>two arrows each along the line connecting the planet to its star <em><strong>AND</strong></em> directed towards each star</p>
<p>arrow lines straight and of equal length</p>
<div class="page" title="Page 6">
<div class="section">
<div class="layoutArea">
<div class="column">
<p><em>Do not allow kinked, fuzzy curved lines.</em></p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(g = \ll \frac{{GM}}{{{r^2}}} = \frac{{6.67 \times {{10}^{ - 11}} \times 2.0 \times {{10}^{30}}}}{{{{\left( {6.0 \times {{10}^{11}}} \right)}^2}}} \gg \) <em><strong>OR</strong></em> 3.7×10<sup>-4</sup>Nkg<sup>-1</sup></p>
<p>\({g_{{\rm{net}}}} = \ll 2g\cos \theta = 2 \times 3.7 \times {10^{ - 4}} \times \frac{{\sqrt {{{6.0}^2} - {{3.4}^2}} }}{{6.0}} = \gg 6.1 \times {10^{ - 4}}{\rm{Nk}}{{\rm{g}}^{ - 1}}\)</p>
<p>directed vertically down «page» <em><strong>OR</strong></em> towards midpoint between two stars <em><strong>OR</strong></em> south</p>
<p><em>Allow rounding errors.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>This question is about a probe in orbit.</p>
<p>A probe of mass <em>m</em> is in a circular orbit of radius <em>r</em> around a spherical planet of mass <em>M</em>.</p>
<p style="text-align: center;"><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why the work done by the gravitational force during one full revolution of the probe is zero.</p>
<p> </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>Deduce for the probe in orbit that its</p>
<p>(i) speed is \(v = \sqrt {\frac{{GM}}{r}} \).</p>
<p>(ii) total energy is \(E = - \frac{{GMm}}{{2r}}\).</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>It is now required to place the probe in another circular orbit further away from the planet. To do this, the probe’s engines will be fired for a very short time.</p>
<p>State and explain whether the work done on the probe by the engines is positive, negative <strong>or</strong> zero.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>because the force is always at right angles to the velocity / motion/orbit is an equipotential surface; <br><em>Do not accept answers based on the displacement being zero for a full revolution.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) equating gravitational force \(\frac{{GMm}}{{{r^2}}}\);<br>to centripetal force \(\frac{{m{v^2}}}{r}\) to get result;</p>
<p>(ii) kinetic energy is \(\frac{{GMm}}{{2r}}\);<br>addition to potential energy −\(\frac{{GMm}}{{r}}\) to get result;</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the total energy (at the new orbit) will be greater than before/is less negative;<br>hence probe engines must be fired to produce force in the direction of motion / positive work must be done (on the probe); <br><em>Award <strong>[1]</strong> for mention of only potential energy increasing.</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>This question is in <strong>two</strong> parts. <strong>Part 1</strong> is about solar radiation and the greenhouse effect. <strong>Part 2 </strong>is about orbital motion.</p>
<p><strong>Part 1</strong> Solar radiation and the greenhouse effect</p>
<p>The following data are available.</p>
<p><img src="data:image/png;base64,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C4Cf9Gpk1YNTWq0bd07EZ6vbT5ka5f6kQkCCCCAAAKdVMDxfY29fVCIBiQuHX/lDVW1opOWu2qbXjDn2ex1k6ZmtqYBbCc9DlQLAQQQ6OICBLS6+BeA6iPQNgKfatuiX4UIUnxV/ft+qxW9sxpL7kjW4CsTg1TDpRNly/VMZRtMThskV1bZEKifX22GNpyIg2hWPJXFBh2bIIAAAh1WwPUnHT1sFdAyz9czIp//0nGxht2cJJ01euoej4PzSoc9QBQcAQQQQACBQALdlDwmU1dbTV/sucvx9frV1k89l4Tx/qT2rNuh40bYrPfosTGeOyuMYrMpAggggEC7CRDQajdqMkKg6wi4q7frxT11wSvsHKwR154ffBtba89VyuWXhGglFsXJaW2ViY1CCtQHkPJUVGW0vIv1K57KEmsL8kcAAQRiKmDOf5mlsUvfjaCn1jlKuT49yDDEMa0YmSOAAAIIINA5BBKv1oTRF4WoS53eXrtd1ZH00qp9Wy9uMeZWdl6r+3IubX0D2BAlZTUCCCCAQMcT+ErHKzIlRgCB+Bb4QlUbN4bonWXU4PxkJSW0brjBBgeHEr6brPO1y2jFFfjVMDntSI1p5RCHgXNogzV1ldq84fc65T6qVwvLdNCnwbkzJUvTb75E/a8bp7Skbm1QAM8ka1W5abN2vfa8inY3SZ+rS7JyNXL4TbotPcn2zYa75jU9eN8crY+DYFY8lcVTm/cIIIBApxVwflt9+xvnrCqrXlpmrc/o4KoJGvLOeD32yAxlpgbrhe2t5Liwn/o793sv7LCfzPPuy/rde1v1RFlV85xj9ef+UcP1o9vT1CfIZZS7pkLP/2antnldP0R23g6HsD7fN/bqt6vXqLy5B3Yb5Nt4jXTyyKtePmZZ2/f6KBwdtkUAAQQ6g0BPDR0/Qr3Lng5+//3+Rm2qmqhZqeeEUekvVFlSpHKXU72yMpUe7r17XN0/h1HtWG3qrlHFc2/o8CHfc2lvpU/5qa4cfH1Y9/mxqgb5IoBA1xP40t+MVzjVTu5jDOXh8ao+VuPxibcIINDlBdz7VXDNeBWFGO7HmVGod1aPkf3HVEFka4o1Km2RDgbZREpQeuF2FY+9oHkrV/lsXZpdpkCP1Jo3VDddkr9NW3P7Ny6qU8WsEcopO9GySaB33bJUcnCp0kINy9C8/1kdK39BTz/5S22wHfAxHxTN00PzMpUaLEjoqtCcS7K1IXSF1S2rVAcK0up7voUO+hj5T1iiJx+7IejDNRlTA9dVlmrmlGUeD7maK27jTdNxkEp+PFKLAz4M9UgqoH80yrJRT+oRZSzc55Ghnbe9lFm6Q0vSEzw2Phy6TgHr4pEMbxFAoEsIdOzr8TDOocZk8LbObyGPukvHiifG4Pfaxm97Y9lbzrvm+WmDljy0KPh1QK9hmrtqsXJ8A37Gw7wNix7Wzz2CYP48ds/b5p6h6jBYcyvWKufC46p4YqHmr9itYFdHzpTwA5Ve5TcfVhatVOGq4Pk07GM8EM2YrBnTcjTG18krUd8Pob6jjXVOsn1x55tBTD57/m5wDx+TQ0CmCHQigU+1efKNmrk72KgsZlBqpbYXDDPuxG2+jDmN5wyfagxJn6S8LVtsBsPa8P65udiRnRfi83mDWSmj0UxZoR7JX+fXaLa5yo1vnCl3aMUvZuu6Nm9A65sznxFAoDMIeF5/mvWJ1jUoQw52hm8HdUAgjgTcVW9oe4hgltF2Vuf3v8j+hW2o+vXuqwEhOygZwx68tte4dGt5OdOX6sMDm7VsSoZ6tSy28S5BaQX/ov1bFisz5Vwb29vbxF2zS49PHqaM7MaHWL0ylPdgqXZXG/OBGI0Hqo/9XhsLxusSv+cnRmv2srkaf9uT2l8XZFwHZ5qWfFiukvwsizSsymg+VCvWXePvD9Gbysj/xfs1ce6uIENEGTcauxbojqxFEQazPMvXXzkvf9AK/2iVxak+uasCHBPP8ja9N1q65W/U/mPv+gSzzPVmnT5StfF9XJKV4jOEprHftGe0+8NwAqNNefIXAQQQiDcBO0MFN5W54fw27tJrlbt0syqDneOadrH8G6vfa/O3/V+0sfAupffyO3lblLTp/DQ3eDDL3PPELi3OmqaS6pZWKmYDlPzbbtecoMEsc2fzvD1H9y+PZGhHc3+flzl07+iRygkRzDL3clWt05ysbOXvqjGauYT3cteU6a7hP9FMr2BW4zmy8VrpcMVK3dJ8bWbMy7b7ac0cPUq5xfuDXKOEVw62RgABBBA4X9fcMNjnnsVXxfgN3rJB5bV2f+3dqt29QVuN3r3OjDxNttGzq83vn32rFObneHveUF/8uv0qmTxK42a1BLPMoFVRhXEvaj5zOLBRczN6N9fUVfWs8q6foIL9nk9SmlfzBgEEEIiJAAGtmLCTKQKdVcAIgPyxWp+FrJ5D3Xuca3uIupDJffk89fhG6AdFrnfeU5XPsH1KSNWY2Y9qRobtdmONxTGGOky9RUvWPKz00FmHrIL5kGbq+Kla2TycX3/lrXpKs7I9hxRKVGrWY3q2aLxlAM5VtUITs0uDj1XuSFJa7kN6KKept1ngorlrNmmO7d5Uxg1L2XI9U/mFdYKud/X0Pc+GbAFmvbPV0lb4R7Usjcdk/bTQQcKU25SfOyh4INf4PmYWrNKi5u/juUrNL9bTDwwL0fvNyohlCCCAQDwKOJQ4Kk/ZvcM5eR5X+aoZal1gK1a/10a+Yx/QkpnXhnjw97+qK39UE3PDOFe69mr5zBfqz/sN1xGhGqB4fh+MoNaqhwOftz03Dfr+iNZMMefE/LoxPFGhNh442vhAzKqBRmNCriqtv3uGCsN4ONZQv/na1TyMoZmW/znSkXSDFj5fqEyvAKLx/Vk4SXdENDdb0MqzEgEEEOiiAjbP5cZ56sXNR+w1YHAf0Oon3jSG2L1IoyZeHXIkl3a7f27tEY6T5w311aifO3qSFjc/czCW9hqvVc/Pb+mBlTBIOc88qTzP6zRXpYpuySWo1drvAvsjgEDUBAhoRY2ShBBAQPpvfXL04+Z5HgKLdFPPHl8LvDrcNY5z1aNHkIkkmtI7a7Q4suw9lqCk/t9s2iq8vwkXqd/54TyUs0jefUhrZizweUhjsV39IiOQc81YjfS8wPTY1PX+LzW79FCIm4a/14V9Lwr+YK32Vc0bbz44Or+hd5DZ8rm6XEUTfHsPeWSuGm1//SPrvM3eYYfMXmbmv8PanT/Yc0ef9+aQfJWN2zbtY/79yGPYx8ZdIvGPelmMYzJoSugg4alTOm2rgeI56p7Y2OWw102amtkvesFfH2k+IoAAAjERcFyqOx8dZ9k4I3h5GgNbg8doTnGFjtn6TfVMMVa/10a+9fN9epbF+737wxXKzltnDNdnzlvRFBg6avRGnhe0d5fLnKPkra3Krz9nG63ajSH9lmz5fcM5tPoNLbu+pZW1d47mpyDnbf+NAyyp04nai5W3aauKZ49pGfq4voFGiVZlXWS9n/lwbGqhKuz0ujMewBXeZ3Gd5ByiCWMszpEJ6ZrpF0A0A3h5yikOdY1kXVyWIoAAAgj4CDi+r7G3Dwp+T2n0CK58bpuqbJyvm0d66T1CP7mmp09mPh/b/f7ZJ/+wP8b4eYNZXsOsJNtsgHLGo/TGtAwzpynNd9oC4zpt8nSfhjjhnLc9cuAtAggg0BYCBLTaQpU0EeiyAv+jutrPbdS+mxK7hzM5rI0kbW3ynzpV59tFy9zRafQY+7qtFPw2shtM89uxaYExtMLWx7X8fc8LS3PdYZU+tMp6CMGgeRo3Da+8rX9vSt7yr0Pnde8eNEhydvdmbTvRzbt3kNG767rHHgzSqt6l46+8YeuGxbJYkSwMahFJgpHuc45Sc/KC99Y7Xq5dVQF6sHll+2dVHzLHozdank++TUN9bzC8tuUDAggg0BEFjABP+nQtCBTsCFUlo4fPhoXZyrgqR4+Xhzt0XWx+rx0JPdQ9SL1cH1bp31y9NazwWT3dHBgynFJz9fSqyUaYK9DrsIqypxvzjRjzTE5YqZ1bFimzab4oR7LGFDzo01vJMx3jvP3O+yGuGTy3t3p/kTKLijRrUKLFyp5Km31v4HPjiY16uOiAdUOY5tS+UGXRwz4P4BpXXjxYAxOtGjQZPQcGDtaA5jSa3hjXSAWPaI3HMI1Na/iLAAIIIBCuQDclj8nU1aHadh5fr19t/TRE4p9q24r1Om7Oez39VqVa/bQ3pxCL++fmzCN8E8vnDWaRz6q69BH/Zw7OwRpx7fkWdQpwHj3xqlZusNnjziJVFiGAAALREiCgFS1J0kEAAUOg6UF8e2N8TT16NvZoCZr15zp1+n+CbtH+Kz/TW6/ts+zV5qoq0s9CPuixKPHho6qxittZbBpskXPgPVqaPcA78OX4lvp+76uBd/t/p1T3f4FXd+o1icN1d9ChHGu0bd07oefwqP1A731kzIkSqOV5p0akcggg0HUEjGDH4tUhehCF0DixWyuzR2rsrPXhza8Vl7/XDcPnrRyb7H3eNQgcP7hMVwS9zHGq1/Xz9eRjN/gPT5vwfV32/SDn7VZfM3xTfZOCDNucOEQjhgZabwTUSoq0Lcj8Ku7qtVpYctjyi9BtQF9923KNsTDQ/KrmMI2LXvOaUzVQEixHAAEEEAghkHi1JowO0BO3eVf/uaybVzW+cVdv14t7jAZ9vUZoQoZVgMVzj/i9f/YsZVy9r31NSwr2+j1zcA4drmssG4YYpbc8j9rvcRdX9acwCCDQ6QQIaHW6Q0qFEOiKAh5DtHW46v9Fp062TOjuXfxotJz2TtH+J2Ps8mmjlOzXOi6EdcBhHe3n3HG3DNXq387EyEaLwzd36m2X8XBydKbSA91gdFwkSo4AAgi0CJg9iFY927qgljGc0cGyuRo3/H5trgl0Pm3JsuFd/P1eOzOMXki5Po1IfIsd6LPzWs1YPNY/mFW/fazP2z01cEi/QCWXXPu0481As69+oaqNG1Vp2Uinm/r1+3bgoa6c31bf/tZRQNfuIq0ONOdn4JKyBgEEEEDAT6Cnho4fEaQXccMOwX93m37rneo9eqyN0Sni9f7ZDydOFhg9nY3GI+UW51JHYnedF24pbY86Em7CbI8AAgjYFyCgZd+KLRFAAIE2EAjeu8zZM9EYeC7Ml/u0Tn9uY6DyIMk6B05Ubqixy4Ps32VXhWqlGHJi5KYWh0kaOf4qY9ANXggggEAnFzCDWs9s1cb8YRHMqeVhYwyDM/P6CfYnLI+z3+ugD5WCBGfqBRzd1f08vxYoHjixfOvUt5OTZB1aMssVpOV+7U79KkDvLBkpRj4fazTmDoulKXkjgAAC8SPgSBmpWweGumMN8rvb9FtvNM64L+dSv17K/jWNz/tn/3LGyRL3R9r1So1FYUI0DLHYo2FRkGMZcB9WIIAAAtEVIKAVXU9SQ6CLCwS/uOziOAGqf4FGzrtbqZZjjxu9pCZeLatZKQIk1rDYVadTn7du3D9H3766MF6fjQWtfKxXhmqlGGKYhtq92mEOt9E7XcNSYjHPXKz9yB8BBLqmQKJSc5/RnopnNDUj8GxRIW3qJyx/2GZPLX6vQ3pGaYMvd++hbwRJy/WHI/rEoh2O61/f028tWpQ3JBVqPtZvKnlAoGYhMZjzM0j9WYUAAgh0aAFHP42eOCRwj9n6ygUaYtaY22nzhjBHp4jP++d4PYbuqje0/XjAk2ngYgdsTOPSZ4c/Dj2MfuCUWYMAAgi0WoCAVqsJSQABBFoEQgxr07JhlN99odO1doYZ+o4xz0OQeSSiXCq7yTmSc/XS66Wam5XSfCPgTMnS3NI1Wpje0yeZWlVu2qL3/mzx5MdnSz7GRsCReqvuywj0EM0oU8CJkZuGGzTmUbl9pFIIKMbmAJIrAgjETMCRNEw/W71Lu0vvVXovy5Yeoctm9NSaN+MFVds4TfJ7HZozGls4Enqoe7CEPqtWTZ3vAftCH+w7YExj30YvyzzbKC+SRQABBDq1gEOJo/KU3TvEedtqpAr3h9r03H5jbqfwRqfg/tnuF8qtuj9Wy3pg37M6uPBHSu6TFODfj7S4yvos7DpZawz4zAsBBBCInQABrdjZkzMCnVDgq0rq9x0b9Tqr2tNf2NjO7ibBxtH2SMOZoB7nxefPniMpTTkF23ToWI2qjX+HXl6qnPQkjyEXzEDWUuUOuULjZjyt8hMRtLLyoOBtWwqcr/SJI4IMnWUMr7R2u8XD1sbhBp1DNGFMP49j35ZlJW0EEEAg3gS6qU/6dBXvfVcbC++KKLDlen+tit86aaNi/F7bQGr7TSx7ltep5vCf2y5v10H97l95HNd2wKSMAAJdSsBxsYbdnBSiyr4jVRjBlrc2aZvRe8iZkafJqeGNTsH9cwju+tVnVPXeQSNgGOXXqVM67dsOJcpZkBwCCCAQTCA+n+wGKzHrEEAgjgWc+s4PB4WcFFZGe9uTp/7S/vW4eLAGJna0bi9nday8WHN+nNYYyJJ6ZYyK6AFf+4N31RwdSrhmrEYGaaXoen+jNlV5B3XdlS/oF7vr5Bw6XNd0uO9pVz3W1BsBBNpOwBiGcOzsCANbH2vr2rdVG7Jw/F6HJIrGBuclqmeIhvv+2YRqrHSeenT/O//dWIIAAgggEAOBc5Sak6f0UL/1x3fopeYGJ5+pfO0OnTBmDb76hiHhD7MfsJbcP7fQBB/JpltWaXODWrNRre1//zJbqR3tsUoLCu8QQKATCBDQ6gQHkSogEE8Cjgv7qX+oC1m5dfrUGeO/UXq5/qSjh627w7fk4FTvqwbKTv+xln1i+c5osVa5WQWThykje5E2VJmtiHsrPX+dtq+eosu/yRVkLI9OyLwd39fY2wc1DyHpv/1hla7Y6fGw9QtVvV6u44pw3jT/DFiCAAIIdBKBxsDWO79RSX6WLgl5jdFQbdeenXqr1saVBr/Xbf89Oa+7wm6nEfLa7uvqkWDzy2BZwzodqm7DHmCWebIQAQQQ6MQCiVdrwuiLQlSwpcFJU2M+9b5Fd4+6IMR+dlZz/+yvFLxxyNlDR/Un/51YggACCMS9AAGtuD9EFBCBDiaQOEQjhgaZP6i+OlGeSPTz0wr9zCpJN15/cccYxs1dozfmjdGQ0TNUtPt44xegt4YVPquncwcZbdh4xb9ANyWPydTVQZ61eT1sdX+kXa/UGDHLEfrJNb7zpsV/bSkhAgggYFugplijBsxWRbjj3ziSlJa7VFv3bdTcjN6hs3N9rKOf/Hfo7cTvtQ2k1m1y/KgOhWp31Loc2BsBBBBAIOYCPTV0/IiQo7W49mzQlup/1551O4zGfFGaO5j758iOPkMHRubGXgggEHMBAloxPwQUAIHOJnC+rrlhcJCeKQ31df3hiD6x0XDajo77kyM6HOrBWO90DUsJb1xuO3lHdxuzVVmxcq/6kfJerPIY67ohmLVybHLHCMhFF6XjppY4XHfn9A9cfteb+kXJAaOnYtP48UY86+brlELnu8BmrEEAgc4hcPaA9n3gPeyq7YolDFLO6q3amD8syFyFZmqf69Tp/7GXLL/X9pzaaqtuxoT0vsP0ftkYUvAbQVqFtLos3dSzx9danQoJIIAAAgi0CDhSRurWgee2LLB659qvF371pJ7f8rHU6rmDuX+2Ira97LNq1dRF6aGM7UzZEAEEEGi9AAGt1huSAgIIeAk4lDgqT9m+Dya8tjE+RO3iyaV///1+o3VXsFeC0qffGufjPBtjfW+6XzeOXqTyE57ROad6ZT2oJQSzgh3gOF13jlLGjVNqwOdxLh3fskl76j5tHD++A/UijFNxioUAAh1FoEbbX/+oFUMPG8MQ5j6l5/OHhGxAY0+E32t7Tm201Td6KMH3rtRxrnr0aE0Ljz+r+lBdkAJ3U2L3eG/oFKT4rEIAAQTiUcDRT6Mnhjo3G/dAmzZrj8uYEsCYd2tk2GPSNlWc++cmicB/v6nkAUHGd7Hdmz1wDqxBAAEEYiHge+sQizKQJwIIdDYBx6WaPP3a4A+ZXPu0483PolDzk3p/75Hg6fQaoQkZ5wffJqZrzYvxmZo441VjUlyfV69xWjAvnWEGfVg6ykdH8o2aEGwIzhM79OL6jdqxp07OjDxNTuXhWkc5tpQTAQRaI2A8zHrlDVW1qlGwMVRgbqEWZQR5UBNGEfm9DgMrypt2u/Iy/cAvdtVbg666MMo5eSb3HfVN+qrnAt4jgAACCLRawGbjVjMf5yDdOu77EY5Awv2zvUP1d0pIPC/Ipq1tYBQkaVYhgAACbShAQKsNcUkaga4rYF7I/kwPBB1uoE5vv7ZXta1Fqt1bHwwInMxFylw0XWkJfk9KAu/Szmvc1S/ogTkWwSwjJNh79FgNjeOytzNVB8zuAo2cdkuQseTrVL7kKZW7EnT1DUOU2AFrSJERQACBiASOr9evtn4a0a4tOwX7jQ03YBEsLTNHfq9b3MN75647pdMBd0nQlZd/z6IR1N/rwr4XWSxvSug/darOs0d703Kbf3sP0qALA3ahtpkImyGAAAII+Ak4Ltawm5P8FvsucA7N1Ojkbr6LbX3m/tkWk7FRqHNpNBoY2S0L2yGAAALREyCgFT1LUkIAAU8BxwBNWnZPkOHWJNeenXqrtjXNs92qfXOn3g74PMMcri9fc9J7epbM4r1T305OMqaFj8XrU21b9CtVWtaBIehicUSinaetseSdgzXi2njuRRhtFdJDAAEEjADREy+osjWXAQai4weX6QqrE3gEAQt+r9vmW/l/p0/p/wVKOuD5z2gcde1wXR0w5hTGHGl+eRsNhpiz0k+FBQgggEB0BM5RqjGUYHrA328zl/7KnjY8wsZ8HfH+OVbPG4xz6cDBGhDswB7foZfeOhlsC9YhgAACcSdAQCvuDgkFQqDzCDiSb9XyJTcFnrS9tcMOuo9oy9q9sowFGYzOlDw9Fe/D9QXtYfZ19UgIeifQeb4snbkmIceSb+348Z0Zj7ohgECnFji+VgtLD7ViLq1AOhEGLPi9DgTaiuUu/am6RmctUzAaHo3OVHqg+VMSh2hEwGF7z6r29BeWqdYvdP1JRw9b5yrRYCgwHGsQQACBKAgkXq0Joy8KmJBz4DiNTYlwqHXunwO6Wq64cKCuDDq/+cfaumKrqm01MHKrrvwJ5W+qboNrN8vSsxABBBCwFCCgZcnCQgQQiI5AN/UZ+7CempIaYMgYo3X2shWqqLN19eRTJONi6q3nteb9Mz7LGz/2ukmLfjFVg2wO1/fl7j30DeuUgiw9q+rih7S8KtADE2NX92md/jxw/Vz/+p5+Gygip1YOpxOk5B1v1afaPGueNtcEsW63SoVbFqNlXEamRvUKFJzkwVq7HToyQgCBOBM4o8qCeSrc34oBiD8/Lb/O3s5rdV/OpRHMy8HvdfS/IH9VzZF/t07WmD9lUt7VQeYJDTYM5FmdPPUX63TNpVbfi8atW/UgNXCOrEEAAQQQaBboqaHjRwQYdt0Yan3ijUqOcEaAjnr/HKvnDXJ8X2NvHxTgeUzDAXO9/0vNttHAyF1dqpy8VXrzvT8qwFOY5m8AbxBAAIG2FCCg1Za6pI0AAoZAogbNLta6/GHWPbVObNT8ReXGzBRhvurKtWTeRp2w2s0IZi1bt0xjkqzGILLawRiy6MJ+6h8o3mC0Kz609wOf+b6MgNr+lZpRELiHWH1Orjqd+vz/rDM1+pYFbrVs7lKjbeve8bEx831Fr34UD4Edq2rZCcJ9Wef2SAhyUe3b6tqc9HexCrcYAxadF/AgWRVGOluj6uMBI4bGPu1UloSr9JPRAcaS752uYZG2ULSuNUsRQACBjiPgqlTRLbkqiCioZTQs2bzBZ+jhc5U662caGajXTyiZGP1enz10VH8KVbY2WW/nvB0s43/X0Zq/Bt7AXa19v7UKWJrH6SFNCjF/iiM1Ww9nWbXyt7o2aymG+5MjOmx5+r9Io6aNCvEg9Qudro3X66yWOvIOAQQQiGeBgMP49r5Fd4+6IMKix+r+ufXnhdg8bzCZuyk5MztI40pzG6OB0cJcTQ3S88pdU6apE5epMnGcFsT7KDhmlXghgECnFiCg1akPL5VDIF4EEpWa+5TWFt+hS/ziES6dKHtUc4JcPPnVwng4snnWo9pwwv9JhTNlmsp2PhlWMKs+/YSL1O98v8I1Z+3a/YTmFO9vCC65a1SxPE83jl2hg+qpXj0D79ecgOWbUMGUBpuZVvn6V90jh0Pa+UbrhgFw157W5x4ptrz9s6oPBQs/2pnTwqGE7yYr8IxRZs+9h1VSaT4Aq1Vl8b2aOOM3+ooxFrvfA0r3GZ06FbgHnEL2cotiWVqQLN4FGks+QenTb1VqhC0ULTJiEQIIINDxBOqDWtnK31UT1hA25qTws70alhhD2F0/X8uzB0TQO6uJLQ5/r4MOn2eUO2hv8FAP4eyct5tsrP7W6t19ga853FVvaLtFwxLnwHu01NZx6qm0efnKtOjlHHgu1i9U9Xq5jvsV91xdMmWxjblV/6JTJ4MFtFobBPQrGAsQQACBzidgOYyv0Zjh9pFKifjeJ1b3z1E4L8TkeUPj1yohXXMWjbNuYNz8zTuuXTNGa+ysldpcfx/euKKuUpuX5mho2mztOnGBMhdNV5rNUXCak+YNAgggEGUBAlpRBiU5BBAIJGAMPzjsIW16/RlNzejts5F58XSH7moK3Pis9fpYt18ld96hma/7PqborfRpz2jnlhm2hxn0StdxqSZPvzZIr6HjKl84ToP6JCk5OV05K3YbvcMuUmbR45r0rWBX5Ef03vuBJlkNNeG5WULffH+nnhMe09yxvbyK7/3BbGE1Qv3NsvYbr5Jq34cyX+iDfQcCzGfRkJLrD0f0iVWcqPYDvRe0d1jwB1tN5QzYYq9pgxO7tHj0D5Xc54cat3CXTvQap4fzLIaPqvtYRz4LFt37s478MVgAzuidlzJStw48tyln/792y+K/p/cSq7HknYM14trAoT3vBPiEAAIIdGIBV5XW5440HqQUq8LG8LLNLYWbTwFmMGuB1q7KUp9gp2U7hFH/vXar9v19OhQs74/26X2/sRMbdnB/8Du963sq90zL9bGOfvLfnkta3geda8TczN55uyVB33cuHS9ZrjV+1xrGdu5DWvPYWr/Aktn4aG1pdoheUh75mA/iVub5N4py7dWLm4/4B0Hr3tFLW2o8EjDfNgQ7n3zgiiBDHDbuEvJap0bbX//IP1+fHPmIAAIIdG0Bi2F8nUM0YUy/VjQ6idH9czTOCzF53tD0DTQacaZP1wLLHs9N25h/z+hg2XLNrL8PN54lmM8TLh2jmavMZx9GMDL/aS1M7+m5A+8RQACBmAgQ0IoJO5ki0HUFHEnD9LPVb2r/lkLleQW2GgI3Q348W0XFW1XpNa+WMcxe5VaVGC2Drrp0nBbv9gxmGa1ts+appGKXih8Y1oqHWMbF8ajZWnS9b7AtwLFypuiW4jXGBd03A2zQtNjsbfSgHi8P0Orc6qFZ066+f+vz3KZNi8Zr3I1pIVpYmTubAbenlOM5nI/Zu6z4ET1Sctg3de/Px1dr2p3FXsfBXbNLj896QuXNDw+9d2n4ZD7YelT5ZZU+QyX6bOsYoEnL7lGqrc5tRj38WoKZ34n1mjPp4RDlafAv2BSkPK0ui0/dAn70H0veOXS4rol0WKyA+bACAQQQ6AgCRkOU/I3af8wYGra6XCX5WUbAwnyQskg5aZdp1KxfqqS0Qse8GlcYQ9CW/7r+eqChpXDTCclMa522PxOFYFY9XTR/r42expuWa86yN42BhoO8XG+qcNZTPsG8hnNd/kP+QSHvlA6raMq9ftca7prXlB/yPGnzvN2coREYypinjRUvKC+lsTGIEVhaPHGaPM+19dcMd+Zqsddcpw37rnv+/jAbHxkP4gbdr2fL5indq6dWwxBJdy3f1fg9abw2uG2GTy9+41pxwpM2gp12ry3CNWvG4w0CCCDQtQS8hvF1qrfViBvhirTr/XM0zwsxet7Q7Gv0eF68RkUTUoI04m3e2OeNeZ21RiW5rekB75MkHxFAAIFWCHzpb8YrnP3NCL3nq9q4CeWFAAIIRCxgdmHf8Dsd3ftrFXkFqoKlaD4QmaRJVw3RdbentSKIZZGHOZzhFKseYC3bOlPu0IpfzNZ19XN0HVbJj0dqcVWwptON+6bM0+6Xc9WnJamGd3XvquC2PBVVBZpa1biAnDJdd+eNVGpT9/5Q5TSDX796Uo8OS2ppAeeq0JxLsrXBRlFbithLmaU79JgW69LssqC9ulr2aXzXLUslB5cqLWDQyrxBKNXMKctUbjF8ZH0qVvVQGOZehRqsuRVrlZNkVaBIy+KVgY0Pn2rz5Bs1c7fZa8wI1JVu0BJaudlwYxMEEPAU6NDX4zXFGpW2TCezVmp7wTDv3jJmo4vSp/WLgjIdDBr9adIwrwemaMH8KUoLY97Mpr2D/43G73Uk56tuuiR/m7bmflMVs0Yop8xyttDARa+/1rhDKp6ojIX7Am9ntcbyvO1RB+OcnLnwYc3JSm04bubxemKh5tf3WrdK0GOZ774eq8J6a1w3blj0sH5eVhU8QNiUaK8MTV2Ur/vSPa6HmtZ5/fWop9fyUB+CXVuE2rd913v+bnAP37725IZAlxao3azcITNUriGau3ONd2PLSGHa5f65jc4Loe7jDZOoP2/wcjYa2pQV6hGjIZCday1nyng99sgMZaYmeqXCBwQQQMCOgOf1p7l9tK5BCWjZ0WcbBBBoFwF35VKlj37ab2ga78yNOYcKt6t4bKQTyXqnZv3JbAFeprK1xR5BNrMnWK5uuvyfNW5s44Mc650jW2rxEM+ZkqXpN1+hyzJvbglkeaVutvper5eeK9KGpmCY+cBoRqZ+9KNxbfBwzyvz6H2oD2ru1I7Va1oCW/X1mKSf3BKo7tHL3iulNi+LETgr/7luzF6nE73v0sa3ZjN/ltcB4AMCCNgRaKsbAzt5t3obM6B1/T7dtneVxgTsoWqe317W/qPvaE39MDeeuTaej/t9R4MCnh89t4/0Pb/XDXLmA71xWtNzUsDAobumQs+/sVe/9TyP1+9sNsj5qS7ve1n0r52CNYiqv4a4Sd/rf51uCxnIivT70fH28/zdiNbDhI6nQIkRQKD9BRoaiMzTz/XO6jGKWlikQ98/x+B5g9+BD3KtZTQGyZt8uXomcx71Y2MBAgiEJeB5/WnuGK1rUAJaYR0GNkYAgbYV8GwNHSQnAgFBcFgV7wINgdvV0pR1Kp89qKUHXbwXnPIhgEDcCLTVjUHcVDBOCsLvdZwcCIoRFQHP341oPUyISsFIBAEEEEAAAQQQQKBTCnhef5oVjNY1KHNodcqvC5VCoKMKXKCR8+dqmNf8CBZ1Ob5WC0sPMRm3BQ2L4l3gU21bsV7HndfqvpxLCWbF++GifAgg0IUF+L3uwgefqiOAAAIIIIAAAggggECcChDQitMDQ7EQ6KoCjqSxWrJonHoFBTAmAS+Yp8L9tUG3YiUCcSdQu1c79tTJOXS4rgk41FbclZoCIYAAAl1PgN/rrnfMqTECCCCAAAIIIIAAAgjEvQABrbg/RBQQga4m4FBC+oNaW3hT8KCWq1JFt+SqgKBWV/uCxGd9zUnqZ43UgD5JSu6TolGz1quyzu1T1rOq3rxBb7v6K3va8OiNH++TCx8RQAABBIII8HsdBIdVCCCAAAIIIIAAAggggEB8CxDQiu/jQ+kQ6KIC3dRn7JPavmWe0oMNP2gGtcaOUu7SzRbBgy5KR7XbX8B9SCXZt2tOWZVc9bmf0cGyuRo/Y5u8+hC6P9Sm5/bL1Ttdw1LOaf9ykiMCCCDQ1QX4ve7q3wDqjwACCCCAAAIIIIAAAh1cgIBWBz+AFB+Bzitg9NRKzVXxzpe0JCtFzoAVPa7yVTM07tJUo1fML1VSvJXgVkArVrSFgLtqm154/4xf0q49O/VWbVMvLbdqtxap9PhXlT79VqU6/DZnAQIIIIBAGwvwe93GwCSPAAIIIIAAAggggAACCLSxwFfaOH2SRwABBFonkJCqzIJtGjOlQs+XrVXJqt06YZmi2SvmcR001y2c7rNFL2WW7tCS9ASf5XxEoLUCbtX9sVqfWSXjqtOpz/9PMufKqivXsmVvGr2zJuvuURdYbc0yBBBAAIE2FeD3uk15SRwBBBBAAAEEEEAAAQQQaAcBAlrtgEwWCCDQegFHUpomzTb/ndWx8o16o/qvOrX31yrafbz1iZMCAhELOHRe9+4yO1w1DDfomdB/6lSdsbSuSiUzHtWGExcYgdVsemd5EvEeAQQQaDcBfq/bjZqMEEAAAQQQQAABBBBAAIE2EvjS34xXOGknGxPee76qj9V4fuQ9AggggAACXUugbpfmDJ9qBKz8Q1otEE71un6B1q7KUh+GG2xh4R0CCEQkwPV4RGxGAwN+ryOUY7dOIOD5u8E9fCc4oFQBAQQQQAABBBCIcwHP60+zqNG6BmUOrTg/8BQPAQQQQCDOBRLSNWdlni4JONGbEczKmKkVBWMJZsX5oaR4CCDQyQX4ve7kB5jqIYAAAggggAACCCCAQGcXIKDV2Y8w9UMAAQQQaGMBhxIGzdCm10s1f0qGejXnZgay7tTcwpe0fXWuUhPomtVMwxsEEEAgJgL8XseEnUwRQAABBBBAAAEEEEAAgSgJMORglCBJBgEEEEAAAQQQQACB9hBoq6Eb2qPs5IEAArER8PzdiNZwL7GpCbkigAACCCCAAAIIdAQBz+tPs7zRugalh1ZHOPqUEQEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBDowgIEtLrwwafqCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggEBHECCg1RGOEmVEAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBLqwAAGtLnzwqToCCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggg0BEECGh1hKNEGRFAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQACBLixAQ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" alt></p>
</div>
<div class="specification">
<p><strong>Part 2</strong> Orbital motion</p>
<p>A spaceship of mass <em>m</em> is moving at speed <em>v</em> in a circular orbit of radius <em>r</em> around a planet of mass <em>M</em>.</p>
<p><img 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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the Stefan-Boltzmann law for a black body.</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>Deduce that the solar power incident per unit area at distance <em>d</em> from the Sun is given by</p>
<p>\(\frac{{\sigma {R^2}{T^4}}}{{{d^2}}}\).</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>Calculate, using the data given, the solar power incident per unit area at distance <em>d</em> from the Sun.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>two</strong> reasons why the solar power incident per unit area at a point on the surface of the Earth is likely to be different from your answer in (c).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The average power absorbed per unit area at the Earth’s surface is 240Wm<sup>–2</sup>. By treating the Earth’s surface as a black body, show that the average surface temperature of the Earth is approximately 250K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the actual surface temperature of the Earth is greater than the value in (e).</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Identify the force that causes the centripetal acceleration of the spaceship.</p>
<p>(ii) Explain why astronauts inside the spaceship would feel “weightless”, even though there is a force acting on them.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the speed of the spaceship is \(v = \sqrt {\frac{{GM}}{r}} \).</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The table gives equations for the forms of energy of the orbiting spaceship.</p>
<p><img 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" alt></p>
<p>The spaceship passes through a cloud of gas, so that a small frictional force acts on the spaceship.</p>
<p>(i) State and explain the effect that this force has on the total energy of the spaceship.</p>
<p>(ii) Outline the effect that this force has on the speed of the spaceship.</p>
<div class="marks">[4]</div>
<div class="question_part_label">j.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>power/energy per second emitted is proportional to surface area;<br>and proportional to fourth power of absolute temperature / temperature in K;<br><em>Accept equation with symbols defined.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>solar power given by \(4\pi {R^2}\sigma {T^4}\);<br>spreads out over sphere of surface area \(4\pi {d^2}\);<br><em>Hence equation given.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\left( {\frac{{\sigma {R^2}{T^4}}}{{{d^2}}} = } \right)\frac{{5.7 \times {{10}^{ - 8}} \times {{\left[ {7.0 \times {{10}^8}} \right]}^2} \times {{\left[ {5.8 \times {{10}^3}} \right]}^4}}}{{{{\left[ {1.5 \times {{10}^{11}}} \right]}^2}}}\);</p>
<p>=1.4×10<sup>3</sup>(Wm<sup>-2</sup>);</p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>some energy reflected;<br>some energy absorbed/scattered by atmosphere;<br>depends on latitude;<br>depends on time of day;<br>depends on time of year;<br>depends on weather (<em>eg</em> cloud cover) at location;<br>power output of Sun varies;<br>Earth-Sun distance varies;</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power radiated=power absorbed;<br>\(T = {}^4\sqrt {\frac{{240}}{{5.7 \times {{10}^{ - 8}}}}} \left( { = 250{\rm{K}}} \right)\);</p>
<p><em>Accept answers given as 260 (K).</em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>radiation from Sun is re-emitted from Earth at longer wavelengths;<br>greenhouse gases in the atmosphere absorb some of this energy;<br>and radiate some of it back to the surface of the Earth;</p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) gravitational force / gravitational attraction / weight; <em>(do not accept gravity)</em></p>
<p>(ii) astronauts and spaceship have the same acceleration;<br>acceleration is towards (centre of) planet;<br>so no reaction force between astronauts and spaceship;</p>
<p><em><strong>or</strong></em></p>
<p>astronauts and spaceships are both falling towards the (centre of the) planet;<br>at the same rate;<br>so no reaction force between astronauts and spaceship;</p>
<div class="question_part_label">h.</div>
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<p>gravitational force equated with centripetal force / \(\frac{{GmM}}{{{r^2}}} = \frac{{m{v^2}}}{r}\);</p>
<p>\( \Rightarrow {v^2} = \frac{{GM}}{r} \Rightarrow \left( {v = \sqrt {\frac{{GM}}{r}} } \right)\);</p>
<div class="question_part_label">i.</div>
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<p>(i) thermal energy is lost;<br>total energy decreases;</p>
<p>(ii) since <em>E</em> decreases, <em>r</em> also decreases;<br>as <em>r</em> decreases <em>v</em> increases / <em>E</em><sub>k</sub> increases so <em>v</em> increases;</p>
<div class="question_part_label">j.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">The Stefan-Boltzmann law was poorly understood with few candidates stating that the absolute temperature is raised to the fourth power. </span></p>
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<div class="question_part_label">a.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">This question was poorly done with few candidates substituting the surface area of the sun or the </span><span style="font-size: 10.000000pt; font-family: 'Arial';">surface area of a sphere at the Earth’s radius of orbit. </span></p>
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<div class="question_part_label">b.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">Despite not being able to state or manipulate the Stefan-Boltzmann law most candidates could substitute values into the expression and calculate a result. </span></p>
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<div class="question_part_label">c.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">This question was well answered at higher level. </span></p>
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<div class="question_part_label">d.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">To show the given value there is the requirement for an explanation of why the incident power </span><span style="font-size: 10.000000pt; font-family: 'Arial';">absorbed by the Earth’s surface is equal to the power radiated by the Earth, few candidates were </span><span style="font-size: 10.000000pt; font-family: 'Arial';">successful in this aspect. Although most could substitute into the Stefan-Boltzmann equation they needed to either show that the fourth root was used or to find the temperature to more significant figures than the value given. </span></p>
<div class="question_part_label">e.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">A surprising number of candidates could not explain the greenhouse effect. A common misunderstanding was that the Earth reflected radiation into the atmosphere and that the atmosphere reflected the radiation back to the Earth. </span></p>
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<div class="question_part_label">f.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">(i) Most were able to state gravitational force, however a significant number stated gravity and consequently did not get the mark. </span></p>
<p><span style="font-size: 10.000000pt; font-family: 'Arial';">(ii) Many answers only discussed the astronauts and not the spaceship, missing points such as </span><span style="font-size: 10.000000pt; font-family: 'Arial';">‘falling at the same rate’ or ‘with the same acceleration’. </span></p>
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<div class="question_part_label">h.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">This was well answered with candidates able to adequately show in their explanation where the expression comes from. </span></p>
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<div class="question_part_label">i.</div>
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<p><span style="font-size: 10.000000pt; font-family: 'Arial';">ji) Most appreciated that the effect of the force would be to decrease the total energy. </span></p>
<p><span style="font-size: 10.000000pt; font-family: 'Arial';">jii) Very few appreciated that they should use the equations above to answer this part of the question. As a consequence, the most common answer discussed a decrease in kinetic energy and a decrease in speed. </span></p>
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<div class="question_part_label">j.</div>
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