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</div><h2>SL Paper 3</h2><div class="specification">
<p>An ideal nuclear power plant can be modelled as a heat engine that operates between a hot temperature of 612°C and a cold temperature of 349°C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the Carnot efficiency of the nuclear power plant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The nuclear power plant works at 71.0% of the Carnot efficiency. The power produced is 1.33 GW. Calculate how much waste thermal energy is released per hour.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss the production of waste heat by the power plant with reference to the first law and the second law of thermodynamics.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A wheel of mass 0.25 kg consists of a cylinder mounted on a central shaft. The shaft has a radius of 1.2 cm and the cylinder has a radius of 4.0 cm. The shaft rests on two rails with the cylinder able to spin freely between the rails.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.44.54.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06"></p>
</div>
<div class="specification">
<p>The stationary wheel is released from rest and rolls down a slope with the shaft rolling on the rails without slipping from point A to point B.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.47.09.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.a"></p>
</div>
<div class="specification">
<p>The wheel leaves the rails at point B and travels along the flat track to point C. For a short time the wheel slips and a frictional force <em>F </em>exists on the edge of the wheel as shown.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.49.45.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/06.b"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The moment of inertia of the wheel is 1.3 × 10<sup>–4</sup> kg m<sup>2</sup>. Outline what is meant by the moment of inertia.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In moving from point A to point B, the centre of mass of the wheel falls through a vertical distance of 0.36 m. Show that the translational speed of the wheel is about 1 m s<sup>–1</sup> after its displacement.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the angular velocity of the wheel at B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the effect of <em>F </em>on the linear speed of the wheel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the effect of <em>F </em>on the angular speed of the wheel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A constant force of 50.0 N is applied tangentially to the outer edge of a merry-go-round. The following diagram shows the view from above.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.31.00.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/06"></p>
<p>The merry-go-round has a moment of inertia of 450 kg m<sup>2</sup> about a vertical axis. The merry-go-round has a diameter of 4.00 m.</p>
</div>
<div class="specification">
<p>The merry-go-round starts from rest and the force is applied for one complete revolution.</p>
</div>
<div class="specification">
<p>A child of mass 30.0 kg is now placed onto the edge of the merry-go-round. No external torque acts on the system.</p>
</div>
<div class="specification">
<p>The child now moves towards the centre.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular acceleration of the merry-go-round is 0.2 rad s<sup>–2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the merry-go-round after one revolution, the angular speed.<span class="Apple-converted-space"> </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the merry-go-round after one revolution, the angular momentum.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the new angular speed of the rotating system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the angular speed will increase.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the work done by the child in moving from the edge to the centre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylinder is fitted with a piston. A fixed mass of an ideal gas fills the space above the piston.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.52.30.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/07._01"></p>
<p>The gas expands isobarically. The following data are available.</p>
<p style="text-align: center;">\[\begin{array}{*{20}{l}} {{\text{Amount of gas}}}&{ = 243{\text{ mol}}} \\ {{\text{Initial volume of gas}}}&{ = 47.1{\text{ }}{{\text{m}}^3}} \\ {{\text{Initial temperature of gas}}}&{ = -12.0{\text{ °C}}} \\ {{\text{Final temperature of gas}}}&{ = + 19.0{\text{ °C}}} \\ {{\text{Initial pressure of gas}}}&{ = 11.2{\text{ kPa}}} \end{array}\]</p>
</div>
<div class="specification">
<p>The gas returns to its original state by an adiabatic compression followed by cooling at constant volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the final volume of the gas is about 53 m<sup>3</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in J, the work done by the gas during this expansion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the thermal energy which enters the gas during this expansion.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch, on the <em>pV </em>diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the change in entropy of the gas during the cooling at constant volume.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The <em>P–V</em> diagram of the Carnot cycle for a monatomic ideal gas is shown.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The system consists of 0.150 mol of a gas initially at A. The pressure at A is 512 k Pa and the volume is 1.20 × 10<sup>–3</sup> m<sup>3</sup>.</p>
</div>
<div class="specification">
<p>At C the volume is <em>V</em><sub>C</sub> and the temperature is <em>T</em><sub>C</sub>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by an adiabatic process.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the two isothermal processes.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the temperature of the gas at A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The volume at B is 2.30 × 10<sup>–3</sup>\(\,\)m<sup>3</sup>. Determine the pressure at B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \({P_B}V_B^{\frac{5}{3}} = nR{T_C}V_C^{\frac{2}{3}}\)</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The volume at C is 2.90 × 10<sup>–3</sup>\(\,\)m<sup>3</sup>. Calculate the temperature at C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why a Carnot cycle is of little use for a practical heat engine.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A flywheel consists of a solid cylinder, with a small radial axle protruding from its centre.</p>
<p style="text-align: center;"><img 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"></p>
<p>The following data are available for the flywheel.</p>
<table style="width: 396.667px;">
<tbody>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel mass <em>M</em></td>
<td style="width: 208.667px;">= 1.22 kg</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Small axle radius <em>r</em></td>
<td style="width: 208.667px;">= 60.0 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Flywheel radius <em>R</em></td>
<td style="width: 208.667px;">= 240 mm</td>
</tr>
<tr>
<td style="width: 207px; padding-left: 90px;">Moment of inertia</td>
<td style="width: 208.667px;">= 0.5 MR<sup>2</sup></td>
</tr>
</tbody>
</table>
<p><br>An object of mass <em>m</em> is connected to the axle by a light string and allowed to fall vertically from rest, exerting a torque on the flywheel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The velocity of the falling object is 1.89 m s<sup>–1</sup> at 3.98 s. Calculate the average angular acceleration of the flywheel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the torque acting on the flywheel is about 0.3 Nm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Calculate the tension in the string.</p>
<p>(ii) Determine the mass <em>m</em> of the falling object.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A solid cylinder of mass <em>M</em> and radius <em>R</em> rolls without slipping down a uniform slope. The slope makes an angle <em>θ</em> to the horizontal.<br><img src="data:image/png;base64,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" alt><br>The diagram shows the three forces acting on the cylinder. <em>N</em> is the normal reaction force and <em>F</em> is the frictional force between the cylinder and the slope.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why <em>F</em> is the only force providing a torque about the axis of the cylinder.</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>(i) The moment of inertia of a cylinder about its axis is \(I = \frac{1}{2}M{R^2}\). Show that, by applying Newton’s laws of motion, the linear acceleration of the cylinder is \(a = \frac{2}{3}g\sin \theta \).</p>
<p>(ii) Calculate, for <em>θ</em>= 30°, the time it takes for the solid cylinder to travel 1.5 m along the slope. The cylinder starts from rest.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A block of ice is placed on the slope beside the solid cylinder and both are released at the same time. The block of ice is the same mass as the solid cylinder and slides without friction.</p>
<p>At any given point on the slope, the speed of the block of ice is greater than the speed of the solid cylinder. Outline why, using the answer to (b)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The solid cylinder is replaced by a hollow cylinder of the same mass and radius. Suggest how this change will affect, if at all, the acceleration in (b)(i).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Two of the brightest objects in the night sky are the planet Jupiter and the star Vega.<br>The light observed from Jupiter has a similar brightness to that received from Vega.</p>
</div>
<div class="specification">
<p>Vega is found in the constellation Lyra. The stellar parallax angle of Vega is about 0.13 arc sec.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the mechanism leading stars to produce the light they emit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the light detected from Jupiter and Vega have a similar brightness, according to an observer on Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by a constellation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline how the stellar parallax angle is measured.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the distance to Vega from Earth is about 25 ly.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A heat engine operates on the cycle shown in the pressure–volume diagram. The cycle consists of an isothermal expansion AB, an isovolumetric change BC and an adiabatic compression CA. The volume at B is double the volume at A. The gas is an ideal monatomic gas.</p>
<p style="text-align: center;"><img 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"></p>
<p>At A the pressure of the gas is 4.00 x 10<sup>6</sup> Pa, the temperature is 612 K and the volume is 1.50 x 10<sup>–4</sup>\(\,\)m<sup>3</sup>. The work done by the gas during the isothermal expansion is 416 J.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify why the thermal energy supplied during the expansion AB is 416 J.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the temperature of the gas at C is 386 K.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the thermal energy removed from the gas for the change BC is approximately 330 J.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the efficiency of the heat engine.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain at which point in the cycle ABCA the entropy of the gas is the largest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A cylindrical space probe of mass 8.00 x 10<sup>2</sup> kg and diameter 12.0 m is at rest in outer space.</p>
<p style="text-align: center;"><img 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"></p>
<p>Rockets at opposite points on the probe are fired so that the probe rotates about its axis. Each rocket produces a force <em>F</em> = 9.60 x 10<sup>3</sup> N. The moment of inertia of the probe about its axis is 1.44 x 10<sup>4</sup> kg\(\,\)m<sup>2</sup>.</p>
</div>
<div class="specification">
<p>The diagram shows a satellite approaching the rotating probe with negligibly small speed. The satellite is not rotating initially, but after linking to the probe they both rotate together.</p>
<p style="text-align: center;"><img 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"></p>
<p>The moment of inertia of the satellite about its axis is 4.80 x 10<sup>3</sup> kg\(\,\)m<sup>2</sup>. The axes of the probe and of the satellite are the same.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the linear acceleration of the centre of mass of the probe.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the resultant torque about the axis of the probe.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The forces act for 2.00 s. Show that the final angular speed of the probe is about 16 rad\(\,\)s<sup>–1</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the final angular speed of the probe–satellite system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the loss of rotational kinetic energy due to the linking of the probe with the satellite.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A hoop of mass <em>m</em>, radius <em>r</em> and moment of inertia <em>mr</em><sup>2</sup> rests on a rough plane inclined at an angle <em>θ</em> to the horizontal. It is released so that the hoop gains linear and angular acceleration by rolling, without slipping, down the plane.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw and label the forces acting on the hoop.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the linear acceleration <em>a</em> of the hoop is given by the equation shown.</p>
<p style="text-align: center;"><em>a</em> = \(\frac{{g \times \sin q}}{2}\)</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the acceleration of the hoop when <em>θ</em> = 20°. Assume that the hoop continues to roll without slipping.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the relationship between the force of friction and the angle of the incline.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The angle of the incline is slowly increased from zero. Determine the angle, in terms of the coefficient of friction, at which the hoop will begin to slip.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The pressure–volume (<em>pV</em>) diagram shows a cycle ABCA of a heat engine. The working substance of the engine is 0.221 mol of ideal monatomic gas.</p>
<p style="text-align: left;"><img 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"></p>
<p>At A the temperature of the gas is 295 K and the pressure of the gas is 1.10 × 10<sup>5</sup> Pa. The process from A to B is adiabatic.</p>
</div>
<div class="specification">
<p>The process from B to C is replaced by an isothermal process in which the initial state is the same and the final volume is 5.00 × 10<sup>–3<sub> </sub></sup>m<sup>3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the pressure at B is about 5 × 10<sup>5</sup> Pa.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the process BC, calculate, in J, the work done by the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the process BC, calculate, in J, the change in the internal energy of the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the process BC, calculate, in J, the thermal energy transferred to the gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why an efficiency calculation is important for an engineer designing a heat engine.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A monatomic ideal gas is confined to a cylinder with volume 2.0 x 10<sup>–3</sup> m<sup>3</sup>. The initial pressure of the gas is 100 kPa. The gas undergoes a three-step cycle. First, the gas pressure increases by a factor of five under constant volume. Then, the gas expands adiabatically to its initial pressure. Finally it is compressed at constant pressure to its initial volume.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10<sup>–3</sup> m<sup>3</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the axes, sketch the three-step cycle.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An astronomical reflecting telescope is being used to observe the night sky.</p>
<p>The diagram shows an incomplete reflecting telescope.</p>
<p><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the diagram, with a Newtonian mounting, continuing the <strong>two</strong> rays to show how they pass through the eyepiece.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When the Earth-Moon distance is 363 300 km, the Moon is observed using the telescope. The mean radius of the Moon is 1737 km. Determine the focal length of the mirror used in this telescope when the diameter of the Moon’s image formed by the main mirror is 1.20 cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Hubble Space reflecting telescope has a Cassegrain mounting. Outline the main optical difference between a Cassegrain mounting and a Newtonian mounting.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Sirius is a binary star. It is composed of two stars, Sirius A and Sirius B. Sirius A is a main sequence star.</p>
</div>
<div class="specification">
<p>The Sun’s surface temperature is about 5800 K.</p>
</div>
<div class="specification">
<p>The image shows a Hertzsprung–Russell (HR) diagram.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The mass of Sirius A is twice the mass of the Sun. Using the Hertzsprung–Russell (HR) diagram,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a binary star.</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>The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.</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 mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is <strong>not</strong> a main sequence star.</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>Determine the radius of Sirius B in terms of the radius of the Sun.</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>Identify the star type of Sirius B.</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>draw the approximate positions of Sirius A, labelled A and Sirius B, labelled B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>sketch the expected evolutionary path for Sirius A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A fixed mass of an ideal monatomic gas undergoes an isothermal change from A to B as shown.<br><img 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" alt><br>The temperature at A is 350 K. An identical mass of the same ideal monatomic gas undergoes an isobaric change from A to C.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) Calculate the temperature at C.</p>
<p>(ii) Calculate the change in internal energy for AC.</p>
<p>(iii) Determine the energy supplied to the gas during the change AC.</p>
<p>(iv) On the graph, draw a line to represent an adiabatic expansion from A to a state of volume 4.0×10<sup>−3</sup>m<sup>3</sup> (point D).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) State the change in entropy of a gas for the adiabatic expansion from A to D.</p>
<p>(ii) Explain, with reference to the concept of disorder, why the entropy of the gas is greater at C than B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A horizontal rigid bar of length 2<em>R</em> is pivoted at its centre. The bar is free to rotate in a horizontal plane about a vertical axis through the pivot. A point particle of mass <em>M</em> is attached to one end of the bar and a container is attached to the other end of the bar.</p>
<p>A point particle of mass \(\frac{M}{3}\) moving with speed <em>v</em> at right angles to the rod collides with the container and gets stuck in the container. The system then starts to rotate about the vertical axis.</p>
<p>The mass of the rod and the container can be neglected.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>A torque of 0.010 N m brings the system to rest after a number of revolutions. For this case <em>R</em> = 0.50 m, <em>M</em> = 0.70 kg and <em>v</em> = 2.1 m s<sup>–1</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down an expression, in terms of <em>M</em>, <em>v</em> and <em>R</em>, for the angular momentum of the system about the vertical axis just before the collision.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Just after the collision the system begins to rotate about the vertical axis with angular velocity <em>ω</em>. Show that the angular momentum of the system is equal to \(\frac{4}{3}M{R^2}\omega \).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, show that \(\omega = \frac{v}{{4R}}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine in terms of <em>M</em> and <em>v</em> the energy lost during the collision.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the angular deceleration of the system is 0.043 rad\(\,\)s<sup>–2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of revolutions made by the system before it comes to rest.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="question">
<p>The diagram shows two methods of pedalling a bicycle using a force <em>F</em>.</p>
<p style="text-align: center;"><img 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"></p>
<p>In method 1 the pedal is always horizontal to the ground. A student claims that method 2 is better because the pedal is always parallel to the crank arm. Explain why method 2 is more effective.</p>
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