科目：物理 Physics (9702)
年份：2019 冬季
试卷：Paper 42
总页数：24
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
4
Answer all the questions in the spaces provided.
1 (a) State Newton’s law of gravitation.
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............................................................................................................................... [2]
(b) The astronomer Johannes Kepler showed that the period $T$ of rotation of a planet about the Sun is related to its mean distance $R$ from the centre of the Sun by the expression
$$
\frac{R^3}{T^2} = k
$$
where $k$ is a constant.
Use Newton’s law to show that, for planets in circular orbits about the Sun of 5 2 (a) Smoke particles are suspended in still air. Brownian motion of the smoke particles is seen through a microscope. Describe: (i) what is seen through the microscope ............................................................................................................................... ............................................................................................................................... [1] (ii) how Brownian motion provides evidence for the nature of the movement of gas molecules. ............................................................................................................................ ............................................................................................................................ ..................
6 (ii) the thermal energy transfer during the change. energy transfer = ………………………………………… J [2] (c) For the change in the gas in (b), state: (i) the quantity of external work done on the gas work done = ………………………………………… J [1] (ii) the change in internal energy, with the direction of this change. change = ………………………………………… J direction ………………………………………… 2 © UCLES 2019 9702/42/O/N/19
7
3 (a) State what is meant by *specific latent heat*.
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............................................................................................................................... [2]
(b) A student uses the apparatus illustrated in Fig. 3.1 to determine a value for the specific latent heat of fusion of ice.
Fig. 3.1
The balance reading measures the mass of the beaker and the melted ice (water) in the beaker.
The heater is switched on and pieces of ice at $0^\circ \text{C}$ are added continuously to the funnel so that the heater8
The variation with time of the balance reading is shown in Fig. 3.2.
Fig. 3.2
The readings of the ammeter and of the voltmeter are shown in Fig. 3.3.
<table>
<tr>
<th></th>
<th>ammeter reading /A</th>
<th>voltmeter reading /V</th>
</tr>
<tr>
<td>from time 0 to time 10 minutes<br>after time 10 minutes</td>
<td>1.8<br>3.6</td>
<td>7.3<br>15.1</td>
</tr>
</table>
Fig. 3.3
© UCLES 2019
9702/42/O/N/199
(i) From time 0 to time 10.0 minutes, 65g of ice is melted.
Use Fig. 3.2 to determine the mass of ice melted from time 12.0 minutes to time 22.0 minutes.
mass = ………………………………………… g [1]
(ii) Explain why, although the power of the heater is changed, the rate at which thermal energy is transferred from the surroundings to the ice is constant.
…………………………………………………………………………………………………………
……………………………………………………………………………………………………… [1]
(iii) Determine a value for the specific latent heat of fusion $L$ of ice.
$L = \text{……………………………………… Jg}^{-1}$ [4]
(iv) Calculate the rate at which thermal energy is transferred from the surroundings to the ice.
rate = ………………………………………… W 2
© UCLES 2019 9702/42/O/N/19 [Turn over10
4 A ball of mass $M$ is held on a horizontal surface by two identical extended springs, as illustrated in Fig. 4.1.
<div style="text-align: center;">
</div>
Fig. 4.1
One spring is attached to a fixed point. The other spring is attached to an oscillator.
The oscillator is switched off. The ball is displaced sideways along the axis of the springs and is then released. The variation with time $t$ of the displacement $x$ of the ball is shown in Fig. 4.2.
<div style="text-align: center;">
</div>
Fig. 4.2
(a) State:
(i) what is meant by *damping*
........................................................................................................................... [1]
(ii) the evidence provided by Fig. 4.2 that the motion of t11
(b) The acceleration $a$ and the displacement $x$ of the ball are related by the expression
$$
a = -\left(\frac{2k}{M}\right)x
$$
where $k$ is the spring constant of one of the springs.
The mass $M$ of the ball is 1.2 kg.
(i) Use data from Fig. 4.2 to determine the angular frequency $\omega$ of the oscillations of the ball.
$\omega = \underline{\hspace{5cm}} \text{ rad s}^{-1} \ [2]$
(ii) Use your answer in (i) to determine the value of $k$ .
$k = \underline{\hspace{5cm}} \text{ N m}^{-1} \ [2]$
© UCLES 2019 9702/42/O/N/19 [Turn over12
(c) The oscillator is switched on. The amplitude of oscillation of the oscillator is constant.
The angular frequency of the oscillations is gradually increased from $0.7\omega$ to $1.3\omega$ , where $\omega$ is the angular frequency calculated in (b)(i).
(i) On the axes of Fig. 4.3, show the variation with angular frequency of the amplitude $A$ of oscillation of the ball.
<div style="text-align: center;">
</div>
Fig. 4.3
[2]
(ii) Some sand is now sprinkled on the horizontal surface.
The angular frequency of the oscillations is again gradually increased from $0.7\omega$ to $1.3\omega$ .
State two changes that occur to the line you have drawn on Fig. 4.3.
1. ...............................................................................................13
5 (a) (i) State what is meant by the *specific acoustic impedance* of a medium.
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(ii) The density of a sample of bone is $1.8 \, \text{g} \, \text{cm}^{-3}$ and the speed of ultrasound in the bone is $4.1 \times 10^3 \, \text{m} \, \text{s}^{-1}$ .
Calculate the specific acoustic impedance $Z_B$ of the sample of bone.
$$
Z_B = \underline{\hspace{5cm}} \, \text{kg} \, \text{m}^{-2} \, \text{s}^{-1} \q14
(b) A parallel beam of ultrasound passes normally through a layer of fat and of muscle, as illustrated in Fig. 5.1.
<div style="text-align: center;">
</div>
Fig. 5.1 (not to scale)
The fat has thickness 0.45 cm and the muscle has thickness 2.1 cm.
Data for fat and for muscle are given in Fig. 5.2.
<table>
<thead>
<tr>
<th></th>
<th>specific acoustic impedance $Z/10^6 \, \text{kg} \, \text{m}^{-2} \, \text{s}^{-1}$ </th>
<th>linear attenuation (absorption) coefficient $\mu/\text{cm}^{-1}$ </th>
</tr>
</thead>
<tbody>
<tr>
<td>fat</td>
<td>1.3</td>
<td>0.24</td>
</tr>
<tr>
<td>muscle</td>
<td>1.7</td>
<td>0.23</td>
</tr>
</tbody>
</table>
Fig. 5.2
The intensity reflection 15
(c) (i) State what is meant by *attenuation* of an ultrasound wave.
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............................................................................................................................... [2]
(ii) Data for linear attenuation coefficients are given in Fig. 5.2.
Determine the ratio
$\frac{\text{intensity of ultrasound transmitted through the medium}}{\text{intensity of ultrasound entering the medium}}$
for:
1. the layer of fat of thickness 0.45 cm
ratio = .................................................................16 6 The variation with time of the displacement of an amplitude-modulated (AM) wave is shown in Fig. 6.1.  Fig. 6.1 The sinusoidal information signal has frequency 10 kHz. (a) Determine the frequency of the carrier wave. frequency = ………………………………………… Hz [1] (b) On the axes of Fig. 6.2, sketch the frequency spectrum of the modulated wave.  Fig. 6.2 3 © UCLES 2019 9702/42/O/N/19
17 7 Describe the principles of computed tomography (CT) scanning. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ......................................................................................
18
8 Electrons enter a rectangular slice PQRSEFGH of a semiconductor material at right-angles to face PQFE, as shown in Fig. 8.1.
<div style="text-align: center;">
</div>
Fig. 8.1
A uniform magnetic field of flux density $B$ is directed into the slice, at right-angles to face PQRS.
(a) The electrons each have charge $-q$ and drift speed $v$ in the slice.
State the magnitude and the direction of the force due to the magnetic field on each electron as it enters the slice.
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..................................19
(c) Aluminium ( $^{27}_{13}\text{Al}$ ) has a density of $2.7\,\text{g cm}^{-3}$ . Assume that there is one free electron available to carry charge per atom of aluminium.
(i) Show that the number of charge carriers per unit volume in aluminium is $6.0 \times 10^{28}\,\text{m}^{-3}$ .
[2]
(ii) A sample of aluminium foil has a thickness of $0.090\,\text{mm}$ . The current in the foil is $4.6\,\text{A}$ .
A uniform magnetic field of flux density $0.15\,\text{T}$ acts at right-angles to the foil.
Use the value in (i) to calculate the voltage $V_H$ that is generated.
$$
V_H = \underline{\hspace{8cm}}\,\text{V} [2]
$$
[Total: 8]
© UCLES 2019 9702/42/O/N/19 [Turn over20
9 (a) Define what is meant by *electric potential* at a point.
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............................................................................................................................... [2]
(b) In an $\alpha$ -particle scattering experiment, $\alpha$ -particles are directed towards a thin film of gold, as illustrated in Fig. 9.1.
<div style="text-align: center;">
<div style="display: inline-block; vertical-align: top;">
beam of<br>
$\alpha$ -particles
</div>
<div style="display: inline-block; vert21
(ii) the distance $d$ of closest approach of an $\alpha$ -particle to a gold nucleus.
$d = \underline{\hspace{5cm}} \text{ m [4]}$
(c) Use your answer in (b)(ii) to comment on the possible diameter of a gold nucleus.
$\underline{\hspace{10cm}}$ [1]
[Total: 8]
© UCLES 2019 9702/42/O/N/19 [Turn over22 BLANK PAGE © UCLES 2019 9702/42/O/N/19
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10 (a) The upper electron energy bands in an intrinsic semiconductor material are illustrated in Fig. 10.1.
<div style="display: flex; align-items: center;">
<div style="width: 200px; height: 50px; background-color: #e6e6e6; margin-right: 20px;"></div>
<div style="margin-left: 20px;">
<div>conduction band</div>
<div>forbidden band</div>
</div>
</div>
<div style="display: flex; align-items: center;">
<div style="width: 200px; height: 50px; background-color: #e6e6e6; margin-right: 20px;"></div>
<div style="margin-left: 20px;">
<div>valence band</div>
</div>
</div>
Fig. 10.1
Use band theory to explain why the resistance of an intrinsic semiconductor material decreases as its temperature increases.
...............................................................24 (b) A comparator circuit incorporating an ideal operational amplifier (op-amp) is shown in Fig. 10.2. Fig. 10.2 The variation with temperature $\theta$ of the resistance $R_T$ of the thermistor is shown in Fig. 10.3. Fig. 10.3 © UCLES 2019 9702/42/O/N/19
25 (i) Determine the temperature at which the light-emitting diode (LED) in Fig. 10.2 switches on or off. temperature = ………………………………………… °C [4] (ii) State and explain whether the thermistor is above or below the temperature calculated in (i) for the LED to emit light. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 3 © UCLES 2019 9702/42/O/N/19 [Turn over
26 11 (a) State Faraday’s law of electromagnetic induction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A solenoid S has a small coil C placed near to one of its ends, as shown in Fig. 11.1.  Fig. 11.1 © UCLES 2019 9702/42/O/N/19
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The coil C has a circular cross-section of diameter $3.6 \times 10^{-2} \, \text{m}$ and contains 63 turns of wire.
The solenoid S produces a uniform magnetic field of flux density $B$ , in tesla, in the region of coil C given by the expression
$$
B = 9.4 \times 10^{-4} I
$$
where $I$ is the current, in ampere, in the solenoid S.
The variation with time $t$ of the current $I$ in solenoid S is shown in Fig. 11.2.
Fig. 11.2
State two times at which:
(i) there is no electromotive force (e.m.f.) induced in coil C
time …………………………… and time …………………………… [1]
(ii) the induced e.m.f. in coil C is a maximum but with opposite polarities.
time …………………………… and time …………………………… [1]
(c) The alternating current in the solenoid S in (b) is replaced by a constant current