科目：物理 Physics (9702)
年份：2016 夏季
试卷：Paper 41
总页数：24
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 19: Capacitance, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Answer all the questions in the spaces provided.
1 (a) By reference to the definition of gravitational potential, explain why gravitational potential is a negative quantity.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) Two stars A and B have their surfaces separated by a distance of $1.4 \times 10^{12} \, \text{m}$ , as illustrated in Fig. 1.1.
<div style="text-align: center;">
</div>
Fig. 1.1
Point P lies on the l5
A rock of mass 180 kg moves along the line joining the centres of the two stars, from star A towards star B.
(i) Use data from Fig. 1.2 to calculate the change in kinetic energy of the rock when it moves from the point where $x = 0.1 \times 10^{12} \, \text{m}$ to the point where $x = 1.2 \times 10^{12} \, \text{m}$ . State whether this change is an increase or a decrease.
change = ……………………………………………………………… J
………………………………………………………………………………… [3]
(ii) At a point where $x = 0.1 \times 10^{12} \, \text{m}$ , the speed of the rock is $v$ .
Determine the minimum speed $v$ such that the rock reaches the point where $x = 1.2 \times 10^{12} \, \text{m}$ .
minimum speed = …………………………………………………… m s $^{-1}$ 3
© UCLES 2016 9702/41/M/J/16 [Turn over6
2 (a) An ideal gas is assumed to consist of atoms or molecules that behave as hard, identical spheres that are in continuous motion and undergo elastic collisions.
State two further assumptions of the kinetic theory of gases.
1. ...............................................................................................................................
2. ...............................................................................................................................
[2]
(b) Helium-4 ( $^4_2\text{He}$ ) may be assumed to be an ideal gas.
(i) Show that the mass of one atom of helium-4 is $6.6 \times 10^{-24}$ g.
[1]
(ii) The mean kinetic energy $E_K$ of an atom of an ideal gas is given by the expression
$$
E_K = \frac{3}{2} kT.
$$
Calculate the root-mean-square 7 3 (a) State, by reference to displacement, what is meant by *simple harmonic motion*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A mass is undergoing oscillations in a vertical plane. The variation with displacement $x$ of the acceleration $a$ of the mass is shown in Fig. 3.1. <div style="text-align: center;">
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(c) A block of wood is floating in a liquid, as shown in Fig. 3.2.
<div style="text-align: center;">
</div>
Fig. 3.2
The block is displaced vertically and then released.
The variation with time $t$ of the displacement $y$ of the block from its equilibrium position is shown in Fig. 3.3.
<div style="text-align: center;">
</div>
Fig. 3.3
Use data from Fig. 3.3 to determine
(i) the angular frequency $\omega$ of the oscillations,
$$
\omega = \underline{\hspace{5cm}} \text{ rad s}^{-1} \text{ [2]}
$$
© UCLES 2016 9702/41/M/J/169 (ii) the maximum vertical acceleration of the block. maximum acceleration = ………………………………………… m s⁻² [2] (iii) The block has mass 120 g. The oscillations of the block are damped. Calculate the loss in energy of the oscillations of the block during the first three complete periods of its oscillations. energy loss = ………………………………………… J 3 © UCLES 2016 9702/41/M/J/16 [Turn over
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4 (a) (i) State what is meant by the specific acoustic impedance of a medium.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(ii) The intensity reflection coefficient $\alpha$ is given by the expression
$$
\alpha = \frac{(Z_2 - Z_1)^2}{(Z_2 + Z_1)^2}.
$$
Explain the meanings of the symbols in this expression.
$\alpha$ : ..............................................................................................................................11
Some data for muscle and bone are given in Fig. 4.2.
<table>
<tr>
<th></th>
<th>linear absorption coefficient/m⁻¹</th>
<th>specific acoustic impedance /kg m⁻² s⁻¹</th>
</tr>
<tr>
<td>muscle<br>bone</td>
<td>23<br>130</td>
<td>1.7 × 10⁶<br>6.3 × 10⁶</td>
</tr>
</table>
Fig. 4.2
Calculate the ratio $\frac{I_T}{I_0}$ .
ratio = ................................................... 5
© UCLES 2016 9702/41/M/J/16 [Turn over12
5 The variation with time $t$ of the voltage level of part of an analogue signal is shown in Fig. 5.1.
Fig. 5.1
The signal is sampled at 0.25 ms intervals. Each sample is converted into a four-bit digital number.
Fig. 5.2 lists various times $t$ at which the voltage level is sampled.
The digital number for time $t = 0$ is shown.
<table>
<tr>
<th>time $t$ /ms</th>
<td>0</td>
<td>0.25</td>
<td>0.50</td>
<td>0.75</td>
<td>1.00</td>
<td>1.25</td>
<td>1.50</td>
</tr>
<tr>
<th>digital number</th>
<td>1011</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
Fig. 5.2
(a) (i) On Fig. 5.2, underline the most significant bit (MSB) for the digital number at time $t = 013  Fig. 5.3 [3] (c) The transmitted signal in (b) has less detail than the original signal in Fig. 5.1. Suggest and explain two means by which the level of detail in the transmitted signal could be increased. 1. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 2. ............................................................................................................................... .........................................
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15 6 A solid metal sphere of radius $R$ is isolated in space. The sphere is positively charged so that the electric potential at its surface is $V_S$. The electric field strength at the surface is $E_S$. (a) On the axes of Fig. 6.1, show the variation of the electric potential with distance $x$ from the centre of the sphere for values of $x$ from $x = 0$ to $x = 3R$.  Fig. 6.1 [3] (b) On the axes of Fig. 6.2, show the variation of the electric field strength with distance $x$ from the centre of the sphere for values of $x$ from $x = 0$ to $x = 3R$.  Fig. 6.2 3 © UCLES 2016 9702/41/M/J/16 [Turn over
16 7 A student sets up the circuit shown in Fig. 7.1 to measure the charge on a capacitor C for different values of potential difference across the capacitor. <div style="text-align: center;">  </div> Fig. 7.1 The variation with potential difference $V$ of the charge $Q$ stored on the capacitor is shown in Fig. 7.2. <div style="text-align: center;">  </div> Fig. 7.2 (a) State and explain how Fig. 7.2 indicates that there is a systematic error in the readings of one of the meters. ............................................................................................................................... ............................................................................................................................... ...
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(b) Use Fig. 7.2 to determine the capacitance, in $\mu$ F, of capacitor C.
$$
\text{capacitance} = \underline{\hspace{5cm}} \, \mu\text{F} \, [3]
$$
(c) Use your answer in (b) to determine the additional energy stored in the capacitor C when the potential difference across it is increased from 6.0 V to 9.0 V.
$$
\text{energy} = \underline{\hspace{5cm}} \, \text{J} \, [3]
$$
[Total: 8]
© UCLES 2016 9702/41/M/J/16 [Turn over18 8 The circuit of an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in Fig. 8.1. Fig. 8.1 (a) Explain why point P is known as a virtual earth. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) Derive an expression, in terms of the resistances $R_1$ and $R_2$, for the gain of the amplifier circuit. Explain your working. [3] © UCLES 2016 9702/41/M/J/16
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(c) A relay and the output terminals of the amplifier circuit are shown in Fig. 8.2.
Fig. 8.2
On Fig. 8.2, show how the relay may be connected to the amplifier output so that the relay operates only when $V_{OUT}$ is positive. 3
© UCLES 2016 9702/41/M/J/16 [Turn over20 BLANK PAGE © UCLES 2016 9702/41/M/J/16
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9 A thin rectangular slice of aluminium has sides of length 65 mm, 50 mm and 0.10 mm, as shown in Fig. 9.1.
<div style="text-align: center;">
</div>
Fig. 9.1 (not to scale)
Some of the corners of the slice are labelled.
A current $I$ of 3.8 A is normal to face RSXY of the slice.
In aluminium, the number of free electrons per unit volume is $6.0 \times 10^{28} \, \text{m}^{-3}$ .
A uniform magnetic field of magnetic flux density $B$ equal to $0.13 \, \text{T}$ is normal to face QRYZ of the aluminium slice in the direction from Q to P.
A Hall voltage $V_H$ is developed across the slice and is given by the expression
$$
V_H = \frac{BI}{ntq}.
$$
(a) Use Fig. 9.1 to state the magnitude of the distance $t$ .
$t = \underline{\hspace{5cm}} \, \text{mm} \, [1]$22 10 (a) A coil of insulated wire is wound on a copper core, as illustrated in Fig. 10.1. insulated wire copper core Fig. 10.1 An alternating current is passed through the coil. The heating effect of the current in the coil is negligible. Explain why the temperature of the core rises. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ......................................................................................................................
23 The magnets do not touch the sides of the tubes. Explain why magnet B takes much longer than magnet A to fall through the tube. .................................................................................................................... .................................................................................................................... .................................................................................................................... .................................................................................................................... .................................................................................................................... ......................................................................
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11 The variation with time $t$ of the sinusoidal current $I$ in a resistor of resistance $450\,\Omega$ is shown in Fig. 11.1.
Fig. 11.1
Use data from Fig. 11.1 to determine, for the time $t = 0$ to $t = 30\,\text{ms}$ ,
(a) the frequency of the current,
$$
\text{frequency} = \underline{\hspace{5cm}}\,\text{Hz [2]}
$$
(b) the mean current,
$$
\text{mean current} = \underline{\hspace{5cm}}\,\text{A [1]}
$$
(c) the root-mean-square (r.m.s.) current,
$$
\text{r.m.s. current} = \underline{\hspace{5cm}}\,\text{A [2]}
$$
© UCLES 2016 9702/41/M/J/1625 (d) the energy dissipated by the resistor. energy = ................................................... J 2 © UCLES 2016 9702/41/M/J/16 [Turn over
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12 Some of the electron energy bands in a solid are illustrated in Fig. 12.1.
<div style="display: flex; align-items: center; gap: 10px;">
<div style="width: 200px; height: 30px; background-color: #e0e0e0; border: 1px solid #000;"></div>
<div style="width: 200px; height: 30px; background-color: #e0e0e0; border: 1px solid #000;"></div>
</div>
$\left. \begin{array}{l} \text{conduction band} \\ \text{(partially filled)} \\ \\ \text{forbidden band} \\ \\ \text{valence band} \end{array} \right\}$
Fig. 12.1
(a) In isolated atoms, electron energy levels have discrete values.
Suggest why, in a solid, there are energy bands, rather than discrete energy levels.
............................................................................................................................ 27 13 Copper-66 is a radioactive isotope. When a nucleus of copper-66 decays, the emissions include a $\beta^-$ particle and a $\gamma$ -ray photon. The count rate produced from a sample of the isotope copper-66 is measured using a detector and counter, as illustrated in Fig. 13.1.  Fig. 13.1 (a) State three reasons why the activity of the sample of copper-66 is not equal to the measured count rate. 1. ............................................................................................................................... 2. ............................................................................................................................... 3. ......................................................................................................