科目：物理 Physics (9702)
年份：2013 冬季
试卷：Paper 42
总页数：20
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Section A
Answer all the questions in the spaces provided.
For Examiner's Use
1 (a) Define gravitational potential at a point.
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(b) The Moon may be considered to be an isolated sphere of radius $1.74 \times 10^3$ km with its mass of $7.35 \times 10^{22}$ kg concentrated at its centre.
(i) A rock of mass 4.50 kg is situated on the surface of the Moon. Show that the change in gravitational potential e5
2 The product of the pressure $p$ and the volume $V$ of an ideal gas is given by the expression
$$
pV = \frac{1}{3} N m <c^2>
$$
where $m$ is the mass of one molecule of the gas.
(a) State the meaning of the symbol
(i) $N$ ,
................................................................................................................... [1]
(ii) $<c^2>$ .
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(b) The product $pV$ is also given by the expression
$$
pV = N k T.
$$
Deduce an expression, in terms of the Boltzmann constant $k$ and the thermodynamic temperature $T$ , for the mean kinetic energy of a molecule of the ideal gas.
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3 A metal ball is suspended from a fixed point by means of a string, as illustrated in Fig. 3.1.
<div style="text-align: center;">
</div>
Fig. 3.1
The ball is given a small displacement and then released. The variation with time $t$ of the displacement $x$ of the ball is shown in Fig. 3.2.
<div style="text-align: center;">
</div>
Fig. 3.2
(a) (i) State two times at which the speed of the ball is a maximum.
time = ……………………… s and time = ……………………… s [1]
(ii) Show that the maximum speed of the ball is approximately $0.08 \, \text{m} \, \text{s}^{-1}$ .
© UCLES 2013
9702/42/O/N/13
[2]
For Examiner's Use7
(b) The variation with displacement $x$ of the potential energy $E_p$ of the oscillations of the ball is shown in Fig. 3.3.
<div style="text-align: center;">
</div>
Fig. 3.3
(i) On the axes of Fig. 3.3, sketch a graph to show the variation with displacement $x$ of the kinetic energy of the ball. [2]
(ii) The amplitude of the oscillations reduces over a long period of time. After many oscillations, the amplitude of the oscillations is 0.60 cm.
Use Fig. 3.3 to determine the total energy of the oscillations of the ball for oscillations of amplitude 0.60 cm. Explain your working.
energy = ........................................ J [2]
© UCLES 2013 9702/42/O/N/13 [Turn over
For Examiner's Use
Note: The image placeholder is used since actual image extractio8
4 An $\alpha$ -particle and a proton are at rest a distance $20\,\mu\mathrm{m}$ apart in a vacuum, as illustrated in Fig. 4.1.
<div style="text-align: center;">
</div>
Fig. 4.1
(a) (i) State Coulomb’s law.
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(ii) The $\alpha$ -particle and the proton may be considered to be point charges. Calculate the electric force between the $\alpha$ -particle and the proton.
force = ...9
(ii) A point P is distance $x$ from the $\alpha$ -particle along the line joining the $\alpha$ -particle to the proton (see Fig. 4.1). The variation with distance $x$ of the electric field strength $E_{\alpha}$ due to the $\alpha$ -particle alone is shown in Fig. 4.2.
For Examiner's Use
Fig. 4.2
The variation with distance $x$ of the electric field strength $E_p$ due to the proton alone is also shown in Fig. 4.2.
1. Explain why the two separate electric fields have opposite signs.
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5 (a) An incomplete diagram for the magnetic flux pattern due to a current-carrying solenoid is illustrated in Fig. 5.1.
<div style="text-align: center;">
</div>
Fig. 5.1
(i) On Fig. 5.1, draw arrows on the field lines to show the direction of the magnetic field. [1]
(ii) State the feature of Fig. 5.1 that indicates that the magnetic field strength at each end of the solenoid is less than that at the centre.
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(b) A Hall probe is placed near one end of the solenoid in (a), as shown in Fig. 5.2.
<div style="text-align: center;">
</div>
Fig. 5.2
The Hall probe is rotated about the axis XY. State and expla11 (c) (i) State Faraday’s law of electromagnetic induction. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... [2] (ii) The Hall probe in (b) is replaced by a small coil of wire connected to a sensitive voltmeter. State three different ways in which an e.m.f. may be induced in the coil. 1. ....................................................................................................................... ......................................................................
12 6 A charged particle of mass $m$ and charge $-q$ is travelling through a vacuum at constant speed $v$ . It enters a uniform magnetic field of flux density $B$ . The initial angle between the direction of motion of the particle and the direction of the magnetic field is $90^\circ$ . (a) Explain why the path of the particle in the magnetic field is the arc of a circle. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) The radius of the arc in (a)
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(ii) The path of the negatively-charged particle before it enters the magnetic field is shown in Fig. 6.1.
<div style="text-align: center;">
</div>
Fig. 6.1
The direction of the magnetic field is into the plane of the paper.
On Fig. 6.1, sketch the path of the particle in the magnetic field and as it emerges from the field. [2]
For Examiner's Use
© UCLES 2013 9702/42/O/N/13 [Turn over14
7 Electrons, travelling at speed $v$ in a vacuum, are incident on a very thin carbon film, as illustrated in Fig. 7.1.
<div style="display: flex; justify-content: space-between; align-items: center;">
<div>
electron,<br>speed $v$
</div>
<div>
thin carbon<br>film
</div>
<div>
fluorescent<br>screen
</div>
</div>
Fig. 7.1
The emergent electrons are incident on a fluorescent screen.
A series of concentric rings is observed on the screen.
(a) Suggest why the observed rings provide evidence for the wave nature of particles.
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(c) A proton and an electron are each accelerated from rest through the same potential difference.
Determine the ratio
$$
\frac{\text{de Broglie wavelength of the proton}}{\text{de Broglie wavelength of the electron}}
$$
ratio = .................................................. [4]
For Examiner's Use
© UCLES 2013 9702/42/O/N/13 [Turn over16
8 (a) State what is meant by *nuclear binding energy*.
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(b) The variation with nucleon number $A$ of the binding energy per nucleon $B_E$ is shown in Fig. 8.1.
Fig. 8.1
When uranium-235 ( $^{235}_{92}\text{U}$ ) absorbs a slow-moving neutron, one possible nuclear reaction is
$$
^{235}_{92}\text{U} + {}^1_0\text{n} \rightarrow {}^{95}_{42}\text{Mo} + {}^{139}_{57}\text{La} + 2{17
(iii) The masses of some particles and nuclei are given in Fig. 8.2.
<table>
<tr>
<th></th>
<th>mass/u</th>
</tr>
<tr>
<td>β-particle</td>
<td> $5.5 \times 10^{-4}$ </td>
</tr>
<tr>
<td>neutron</td>
<td>1.009</td>
</tr>
<tr>
<td>proton</td>
<td>1.007</td>
</tr>
<tr>
<td>uranium-235</td>
<td>235.123</td>
</tr>
<tr>
<td>molybdenum-95</td>
<td>94.945</td>
</tr>
<tr>
<td>lanthanum-139</td>
<td>138.955</td>
</tr>
</table>
Fig. 8.2
Calculate, for this reaction,
1. the change, in u, of the rest mass,
$$
\text{change in mass} = \underline{\hspace{4cm}} \text{u [2]}
$$
2. the energy released, in MeV, to three significant figures.
$$
\text{energy} = \underline{\hspace{4cm}} \text{MeV [3]}
$$
For Examiner'18
Section B
Answer all the questions in the spaces provided.
9 An electronic sensor may be represented by the block diagram of Fig. 9.1.
<div style="text-align: center;">
<table>
<tr>
<td>sensing device</td>
<td>→</td>
<td>processing unit</td>
<td>→</td>
<td>output device</td>
</tr>
</table>
</div>
Fig. 9.1
(a) State the function of the processing unit.
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(b)19 10 (a) Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .....................
20 (ii) An ultrasound transmitter emits a pulse. Suggest why, when the signal from the pulse is processed, any signal received later at the detector is usually amplified more than that received at an earlier time. ............................................................................................................... ............................................................................................................... ............................................................................................................... [2] For Examiner’s Use © UCLES 2013 9702/42/O/N/13
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11 The variation with time $t$ of the output $V$ produced by a microphone is shown in Fig. 11.1.
<div style="text-align: center;">
</div>
Fig. 11.1
The output is processed by a four-bit analogue-to-digital converter (ADC) that samples the output every 0.25 ms.
The first sample is taken at time $t = 0$ and is shown in Fig. 11.2.
<table>
<tr>
<td>0110</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
Fig. 11.2
(a) On Fig. 11.2, underline the most significant bit (MSB) of the sample shown. [1]
(b) Complete Fig. 11.2 for the next five samples. [2]
(c) Explain whether the sampling frequency is adequate to enable detail of the output $V$ to be reproduced.
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12 (a) Suggest why attenuation of a signal in channels of communication is usually measured on a logarithmic rather than a linear scale.
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(b) For a particular channel of communication having low attenuation, the input power is $6.5 \, \text{mW}$ and the attenuation per unit length is $1.8 \, \text{dB} \, \text{km}^{-1}$ .
(i) Suggest the name of this channel of communication.
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(ii) Calculate the d23 BLANK PAGE © UCLES 2013 9702/42/O/N/13