科目：物理 Physics (9702)
年份：2018 春季
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) (i) State what is meant by a line of force in a gravitational field. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [1] (ii) By reference to the pattern of the lines of gravitational force near to the surface of the Earth, explain why the acceleration of free fall near to the Earth’s surface is approximately constant. ...............................................................................
5
2 A cylinder contains 5.12 mol of an ideal gas at pressure of $5.60 \times 10^5$ Pa and volume $3.80 \times 10^4$ cm³.
(a) Determine the temperature of the gas.
temperature = ………………………………………… K [2]
(b) The average kinetic energy $E_K$ of a molecule of the gas is given by the expression
$$
E_K = \frac{3}{2} kT
$$
where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
The gas is heated at constant pressure so that its temperature rises by 125 K.
(i) Use your answer in (a) to determine the new volume of the gas.
volume = ………………………………………… cm³ [2]
(ii) Calculate the increase in internal energy of the gas. Explain your working.
increase in internal energy = ………………………………………… J [3]
© UCLES 2018 9702/42/F/M/18 [Turn over6 (c) (i) Use your answer in (b)(i) to determine the external work done during the expansion of the gas. work done = ………………………………………… J [2] (ii) Calculate the total thermal energy required to heat the gas in (b). energy = ………………………………………… J 1 © UCLES 2018 9702/42/F/M/18
7
3 (a) A mass is undergoing simple harmonic motion with amplitude $x_0$ . The maximum velocity of the mass has magnitude $v_0$ .
On Fig. 3.1, show the variation with displacement $x$ of the velocity $v$ of the mass.
<table>
<tr>
<td rowspan="2">v</td>
<td rowspan="2"> $v_0$ </td>
<td rowspan="2"></td>
<td rowspan="2"></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td> $-x_0$ </td>
<td>0</td>
<td> $x_0$ </td>
<td>x</td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
<td></8 (c) A sinusoidal supply has frequency 250 Hz and r.m.s. potential difference 2.8 V. On the axes of Fig. 3.3, show quantitatively the variation with time $t$ of the voltage $V$ for one cycle of the varying voltage. <div style="text-align: center;">  <br/> Fig. 3.3 <br/> [2] </div> © UCLES 2018 9702/42/F/M/18
9
(d) One particular fission reaction may be represented by the equation
$$
{}^{235}_{92}\text{U} + {}^1_0\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3{}^1_0\text{n}
$$
The variation with nucleon number $A$ of the binding energy per nucleon $B_E$ is shown in Fig. 3.4.
Fig. 3.4
On Fig. 3.4, mark on the line the position of
(i) the nucleus ${}^{235}_{92}\text{U}$ (label this point U),
(ii) the nucleus ${}^{141}_{56}\text{Ba}$ (label this point Ba),
(iii) the nucleus ${}^{92}_{36}\text{Kr}$ (label this point Kr).
2
© UCLES 2018 9702/42/F/M/18 [Turn over10 4 (a) Explain what is meant by the *natural frequency of vibration* of a system. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [1] (b) A block of metal is fixed to one end of a vertical spring. The other end of the spring is attached to an oscillator, as shown in Fig. 4.1.  Fig. 4.1 The amplitude of oscillation of the oscillator is constant. The variation of the amplitude $x_0$ of the oscillations of the block with frequency
11 (i) Name the effect shown in Fig. 4.2. ...........................................................................................................................[1] (ii) State and explain whether the block is undergoing damped oscillations. ........................................................................................................................... ........................................................................................................................... ...........................................................................................................................[2] (c) State one example in which the effect shown in Fig. 4.2 is useful. .....................................................................................................
12 BLANK PAGE © UCLES 2018 9702/42/F/M/18
13 5 (a) Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ......................
14 6 The digital transmission of speech may be represented using the block diagram of Fig. 6.1. <!-- Image: Block diagram with components labeled ADC, DAC, P, and a microphone --> Fig. 6.1 (a) Part of the signal at point P on Fig. 6.1 is shown in Fig. 6.2. <!-- Image: Graph with signal (mV) on y-axis and time (ms) on x-axis, showing a curve peaking around 1.00 ms --> Fig. 6.2 The analogue-to-digital converter (ADC) samples the signal at time intervals of 0.25 ms. Each sample is converted into a four-bit number with the smallest bit representing 1.0 mV. Use Fig. 6.2 to determine the four-bit number produced by the ADC at time (i) 0.25 ms, number _________________________________________________________ (ii) 1.25 ms. number ______________________________________________________
15
(b) The digital number is transmitted and then converted to an analogue form by the digital-to-analogue converter (DAC).
Use data from Fig. 6.2 to draw, on the axes of Fig. 6.3, the output level of the DAC for time $t = 0$ to time $t = 1.50\,\text{ms}$ .
Assume that there is no time delay of the transmission of the signal between point P and the output of the DAC.
Fig. 6.3
4
© UCLES 2018 9702/42/F/M/18 [Turn over16 7 (a) State what is meant by *electric potential* at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) The centres of two charged metal spheres A and B are separated by a distance of 44.0 cm, as shown in Fig. 7.1. <div style="text-align: center;">  </div> Fig. 7.1 (not to scale) A moveable point P lies on the line joining the centres of the two spheres. Point P is a distance $x$ from the centre of sphere A. The
17
(i) Use Fig. 7.2 to state and explain whether the two spheres have charges of the same, or opposite, sign.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [1]
(ii) A positively-charged particle is at rest on the surface of sphere A.
The particle moves freely from the surface of sphere A to the surface of sphere B.
1. Describe qualitatively the variation, if any, with distance $x$ of the speed of the particle as it
moves from $x = 12 \text{ cm}$ t18 8 (a) Two properties of an ideal operational amplifier (op-amp) are infinite bandwidth and infinite slew rate. Explain what is meant by (i) infinite bandwidth, ............................................................................................................................... ............................................................................................................................... [1] (ii) infinite slew rate. ............................................................................................................................... ............................................................................................................................... [1] (b) An ideal op-amp is incorporated into the circuit of Fig. 8.1. Fig. 8.1 (i) De
19
(ii) The temperature of the thermistor is gradually increased so that its resistance decreases from $1.5R_T$ to $0.5R_T$.
On Fig. 8.2, draw a line to show the variation of the output potential difference $V_{OUT}$ with the thermistor resistance.
Fig. 8.2
[2]
(iii) On Fig. 8.1, draw the symbol for a light-emitting diode (LED), connected at the output of the circuit, such that it emits light when the resistance of the thermistor is less than $R_T$.
2
© UCLES 2018 9702/42/F/M/18 [Turn over20 9 A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density $B$, as shown in Fig. 9.1.  Fig. 9.1 Electrons enter the slice at right-angles to face SRXY. A potential difference, the Hall voltage $V_H$, is developed between two faces of the slice. (a) (i) Use letters from Fig. 9.1 to name the two faces between which the Hall voltage is developed. ........................................................................................................ and ........................................................................................................ [1] (ii) State and explain which of the two faces named in (a)(i) is the more positive. .............................................................
21
(b) The Hall voltage $V_H$ is given by the expression
$$
V_H = \frac{BI}{ntq}
$$
(i) Use the letters in Fig. 9.1 to identify the distance $t$ .
...........................................................................................................................[1]
(ii) State the meaning of the symbol $n$ .
...........................................................................................................................
...........................................................................................................................[1]
(iii) State and explain the effect, if any, on the polarity of the Hall voltage when negative charge carriers (electrons) are replaced with positive charge carriers, moving in the same direction towards the slice.
.........22 10 (a) (i) Define magnetic flux. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) State Faraday’s law of electromagnetic induction. ............................................................................................................................... ............................................................................................................................... .........................................................
23 Calculate the average electromotive force (e.m.f.) induced in coil C when a current of 3.5A is reversed in the solenoid in a time of 2.4ms. e.m.f. = ………………………………………… V [2] (c) The d.c. supply in Fig. 10.1 is now replaced with a sinusoidal alternating supply. Describe qualitatively the e.m.f. that is now induced in coil C. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 © UCLES 2018 9702/42/F/M/18 [Turn over
24
11 Some electron energy bands in a solid are shown in Fig. 11.1.
<div style="display: flex; align-items: center; gap: 10px;">
<div style="width: 150px; height: 50px; background-color: #e0e0e0;"></div>
<div style="border-left: 1px solid black; padding-left: 10px;">
conduction band
</div>
</div>
<div style="display: flex; align-items: center; gap: 10px;">
<div style="width: 150px; height: 50px; background-color: #808080;"></div>
<div style="border-left: 1px solid black; padding-left: 10px;">
gap between conduction band<br>and valence band (forbidden band)
</div>
</div>
<div style="display: flex; align-items: center; gap: 10px;">
<div style="width: 150px; height: 50px; background-color: #808080;"></div>
<div style="border-left: 1px solid black; padding-left: 10p25 12 (a) Suggest two causes of lack of sharpness of an X-ray image. 1. ............................................................................................................................... 2. ............................................................................................................................... ............................................................................................................................... [2] (b) The thickness of a sheet of metal is examined using a parallel X-ray beam, as illustrated in Fig. 12.1.  Fig. 12.1 (not to scale) Part of the beam passes normally through the metal of thickness 3.2 mm. Another part of the beam passes normally through the metal of thickness $x$ mm. The linear attenuatio
26 (ii) The ratio of the intensities is also the ratio of the powers of the X-ray beams. Calculate this ratio in decibels. ratio = ........................................... dB 2 © UCLES 2018 9702/42/F/M/18
27
13 (a) (i) Define radioactive decay constant.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(ii) Show that the decay constant $\lambda$ is related to the half-life $t_1$ of a radioactive isotope by the expression
$$
\lambda t_1 = \ln 2
$$
[2]
(b) A small volume of solution containing the radioactive isotope sodium-24 ( $^{24}_{11}\text{Na}$ ) has an initial activity of $3.8 \times 10^4$ Bq. Sodium-24, of half-life 15 hours, decays to form a st