科目：物理 Physics (9702)
年份：2015 夏季
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, 19: Capacitance, 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.
1 (a) The Earth may be considered to be a uniform sphere of radius $6.37 \times 10^3$ km with its mass of $5.98 \times 10^{24}$ kg concentrated at its centre. The Earth spins on its axis with a period of 24.0 hours.
(i) A stone of mass 2.50 kg rests on the Earth’s surface at the Equator.
1. Calculate, using Newton’s law of gravitation, the gravitational force on the stone.
gravitational force = ………………………………………… N [2]
2. Determine the force required to maintain the stone in its circular path.
force = ………………………………………… N [2]
(ii) The stone is now hung from a newton-meter.
Use your answers in (i) to determine the reading on the meter. Give your answer to three significant figures.
reading = ………………………………………… N [2]
© UCLES 5 (b) A satellite is orbiting the Earth. For an astronaut in the satellite, his sensation of weight is caused by the contact force from his surroundings. The astronaut reports that he is ‘weightless’, despite being in the Earth’s gravitational field. Suggest what is meant by the astronaut reporting that he is ‘weightless’. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ....................................................................................
6 BLANK PAGE © UCLES 2015 9702/42/M/J/15
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2 In a sample of gas at room temperature, five atoms have the following speeds:
$$
1.32 \times 10^3 \, \text{m} \, \text{s}^{-1}
$$
$$
1.50 \times 10^3 \, \text{m} \, \text{s}^{-1}
$$
$$
1.46 \times 10^3 \, \text{m} \, \text{s}^{-1}
$$
$$
1.28 \times 10^3 \, \text{m} \, \text{s}^{-1}
$$
$$
1.64 \times 10^3 \, \text{m} \, \text{s}^{-1}.
$$
For these five atoms, calculate, to three significant figures,
(a) the mean speed,
mean speed = ………………………………………… m s $^{-1}$ [1]
(b) the mean-square speed,
mean-square speed = …………………………………… m $^2$ s $^{-2}$ [2]
(c) the root-mean-square speed.
root-mean-square speed = ………………………………… m s $^{-1}$ [1]
© UCLES 2015 9702/42/M/J/15 [Turn over8 3 (a) Define specific latent heat. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A beaker containing a liquid is placed on a balance, as shown in Fig. 3.1.  Fig. 3.1 A heater of power 110W is immersed in the liquid. The heater is switched on and, when the liquid is boiling, balance readings $m$ are taken at corresponding times $t$. A graph of the variation with time $t$ of the balance reading $m$ is shown in Fig. 3.2.
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(i) State the feature of Fig. 3.2 which suggests that the liquid is boiling at a steady rate.
...............................................................................................................................
............................................................................................................................... [1]
(ii) Use data from Fig. 3.2 to determine a value for the specific latent heat $L$ of vaporisation of the liquid.
$$
L = \underline{\hspace{5cm}} \text{ J kg}^{-1} \text{ [3]}
$$
(iii) State, with a reason, whether the value determined in (ii) is likely to be an overestimate or an underestimate of the normally accepted value for the specific latent heat of vaporisation of the liquid.
...................................................10
4 (a) State what is meant by *simple harmonic motion*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The variation with time $t$ of the displacement $x$ of two oscillators P and Q is shown in Fig. 4.1.
Fig. 4.1
The two oscillators each have the same mass.
Use Fig. 4.1 to determine
(i) the phase difference between the two oscillators,
$\text{phase difference} = \underline{\hspace{5cm}} \text{ rad [1]}$
(ii) the max11
(iii) the ratio
$$
\frac{\text{maximum kinetic energy of oscillations of Q}}{\text{maximum kinetic energy of oscillations of P}}
$$
ratio = ………………………………………… [2]
(c) Use data from (b) to sketch, on the axes of Fig. 4.2, the variation with displacement $x$ of the acceleration $a$ of oscillator Q.
<div style="text-align: center;">
<br/>
Fig. 4.2
</div>
[2]
© UCLES 2015 9702/42/M/J/15 [Turn over12 5 (a) Define *electric potential* at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two positively charged metal spheres A and B are situated in a vacuum, as shown in Fig. 5.1. sphere A sphere B P x Fig. 5.1 A point P lies on the line joining the centres of the two spheres and is a distance $x$ from the surface of sphere A. The variation with $x$ of the electric potential $V$ due to the two charged spheres is shown in Fig. 5.2.
13 (i) State how the magnitude of the electric field strength at any point P may be determined from the graph of Fig. 5.2. ............................................................................................................................... ............................................................................................................................... [1] (ii) Without any calculation, describe the force acting on a positively charged particle placed at point P for values of $x$ from $x = 0$ to $x = 10$ cm. ............................................................................................................................... ...............................................................................................................................
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6 (a) Explain what is meant by a photon.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) An X-ray photon of energy $3.06 \times 10^{-14} \, \text{J}$ is incident on an isolated stationary electron, as illustrated in Fig. 6.1.
incident photon
energy $3.06 \times 10^{-14} \, \text{J}$
$\theta$
deflected photon
wavelength $6.80 \times 10^{-12} \, \text{m}$
Fig. 6.1
The photon is deflected elastically by the electron through angle $\theta$15
(c) Explain why the magnitude of the final momentum of the electron is not equal to the change in magnitude of the momentum of the photon.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
7 (a) A solenoid is connected in series with a resistor, as shown in Fig. 7.1.
<div style="display: flex; align-items: center; gap: 20px;">
<div>
</div>
<div>
<table>
<tr>
<td>N</td>
<td>S</td>
</tr>
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8 The power for a space probe is to be supplied by the energy released when plutonium-236 decays by the emission of $\alpha$ -particles.
The $\alpha$ -particles, each of energy 5.75 MeV, are captured and their energy is converted into electrical energy with an efficiency of 24%.
(a) Calculate
(i) the energy, in joules, equal to 5.75 MeV,
$$
\text{energy} = \underline{\hspace{5cm}} \text{ J [1]}
$$
(ii) the number of $\alpha$ -particles per second required to generate 1.9 kW of electrical power.
$$
\text{number per second} = \underline{\hspace{5cm}} \text{ s}^{-1} \text{ [2]}
$$
(b) Each plutonium-236 nucleus, on disintegration, produces one $\alpha$ -particle. Plutonium-236 has a half-life of 2.8 years.
(i) Calculate the decay constant, in s $^{-1}$ , of plutonium-236.
$$
\tex17 (ii) Use your answers in (a)(ii) and (b)(i) to determine the mass of plutonium-236 required for the generation of 1.9 kW of electrical power. mass = ………………………………………… g [4] (c) The minimum electrical power required for the space probe is 0.84 kW. Calculate the time, in years, for which the sample of plutonium-236 in (b)(ii) will provide sufficient power. time = ………………………………………… years [2] © UCLES 2015 9702/42/M/J/15 [Turn over
18 Section B Answer all the questions in the spaces provided. 9 (a) The strain in a beam is to be monitored using a strain gauge. The strain gauge is included in the potential divider circuit shown in Fig. 9.1. Fig. 9.1 The strain gauge has a resistance of $120.0\,\Omega$ when it is not strained. The resistance increases to $121.5\,\Omega$ when the strain is $\varepsilon$ . Calculate the potential difference between points A and B on Fig. 9.1 when the strain in the gauge is $\varepsilon$ . potential difference = ………………………………………… mV [3] © UCLES 2015 9702/42/M/J/15
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(b) An inverting amplifier, incorporating an operational amplifier (op-amp), uses a high-resistance voltmeter to display the output. A partially completed circuit for the amplifier is shown in Fig. 9.2.
Fig. 9.2
The voltmeter is to indicate a full-scale deflection of +6.0 V for an input potential $V_{IN}$ of 0.15 V.
(i) On Fig. 9.2,
1. complete the circuit for the inverting amplifier, [2]
2. mark, with the letter P, the positive terminal of the voltmeter. [1]
(ii) Suggest appropriate values for the resistors you have shown in Fig. 9.2. Label the resistors in Fig. 9.2 with these values. [2]
© UCLES 2015 9702/42/M/J/15 [Turn over20
10 (a) State what is meant by the specific acoustic impedance of a medium.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The specific acoustic impedances $Z$ of some media are given in Fig. 10.1.
<table>
<tr>
<th></th>
<th> $Z/\text{kg m}^{-2}\text{s}^{-1}$ </th>
</tr>
<tr>
<td>air</td>
<td> $4.3 \times 10^2$ </td>
</tr>
<tr>
<td>gel</td>
<td> $1.5 \times 10^6$ </td>
</tr>
<tr>
<td>soft tissue</td>
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(ii) Ultrasound of intensity $I$ is incident normally on the boundary between two media of specific acoustic impedances $Z_1$ and $Z_2$ , as shown in Fig. 10.2.
<div style="text-align: center;">
</div>
Fig. 10.2
The intensity of the ultrasound reflected from the boundary is $I_R$ .
The ratio $\frac{I_R}{I}$ is given by the expression
$$
\frac{I_R}{I} = \frac{(Z_1 - Z_2)^2}{(Z_1 + Z_2)^2}.
$$
By making reference to the data for air, gel and soft tissue, explain quantitatively why, during medical diagnosis using ultrasound, a gel is usually put on the skin.
...............................................................................................................................
..........................................................................22 11 One channel of communication is by the use of a coaxial cable. Such a cable is illustrated in Fig. 11.1. <!-- Image description: A coaxial cable with labeled parts: "inner copper wire", "plastic insulation", "A", and "protective covering". --> Fig. 11.1 (a) (i) Suggest the material from which the component labelled A on Fig.11.1 is made. ............................................................................................................................... [1] (ii) Suggest two functions of the component labelled A. 1. ............................................................................................................................... 2. ............................................................................................................................
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(c) A television aerial is connected to a receiver using a coaxial cable of length 11 m. The attenuation per unit length of the cable is $190 \, \text{dB} \, \text{km}^{-1}$ .
Calculate the ratio
$$
\frac{\text{output signal from coaxial cable}}{\text{input signal to coaxial cable}}
$$
ratio = …………………………………………[3]
Please turn over for Question 12.
© UCLES 2015 9702/42/M/J/15 [Turn over