科目：物理 Physics (9702)
年份：2023 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, 19: Capacitance, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
4 1 (a) State Newton’s law of gravitation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A satellite is in a circular orbit around a planet. The radius of the orbit is $R$ and the period of the orbit is $T$ . The planet is a uniform sphere. Use Newton’s law of gravitation to show that $R$ and $T$ are related by $$ 4\pi^2 R^3 = GMT^2 $$ where $M$ is the mass of the planet and $G$ is the gravitational constant. [2] (c) The Earth may be consid
5 (d) Another satellite is in a circular orbit around the Earth with the same orbital radius and period as the satellite in (c). (i) Calculate the angular speed of the satellite in this orbit. Give a unit with your answer. angular speed = ………………………………………… unit …………… [2] (ii) Despite having the same orbital period, the orbit of this satellite is not geostationary. Suggest two ways in which the orbit of this satellite could be different from the orbit of the satellite in (c). 1 ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 © UCLES 2023 9702/42/M/J/23 [Turn over
6
2 (a) (i) State what is meant by an ideal gas.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
[2]
(ii) State the temperature, in degrees Celsius, of absolute zero.
temperature = ........................................... °C [1]
(b) A sealed vessel contains a mass of 0.0424 kg of an ideal gas at 227 °C.
The pressure of the gas is $1.37 \times 10^5$ Pa and the volume of the gas is $0.640 \, \text{m}^3$ .
Calculate:
(i) the number of molecules of 7 (c) The gas in (b) is now cooled gradually to absolute zero. On Fig. 2.1, sketch the variation with thermodynamic temperature $T$ of the r.m.s. speed of the molecules of the gas. r.m.s. speed $\nu$ 0 500 $T/K$ Fig. 2.1 2 © UCLES 2023 9702/42/M/J/23 [Turn over
8 3 (a) State the first law of thermodynamics. Identify the meaning of any symbols that you use. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) The state of an ideal gas is continuously changed according to the cycle ABCDA shown in Fig. 3.1. pressure ↑ C ────→ ──── D │ │ B ────←─── A │ │ └───────┘ volume → Fig. 3.1 (i) Complete Table 3.1 for the changes A to B and B to C by placing two ticks (√) in each row. Table 3.1 <table> <
9 (ii) Use the first law of thermodynamics to describe and explain the energy transfers associated with one complete cycle ABCDA. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... 3 © UCLES 2023 9702/42/M/J/23 [Turn over
10
4 A small steel sphere is oscillating vertically on the end of a spring, as shown in Fig. 4.1.
<div style="text-align: center;">
</div>
Fig. 4.1
The velocity $v$ of the sphere varies with displacement $x$ from its equilibrium position according to
$$
v = \pm 9.7 \sqrt{(11.6 - x^2)}
$$
where $v$ is in cm s $^{-1}$ and $x$ is in cm.
(a) (i) Calculate the frequency of the oscillations.
frequency = ………………………………………… Hz [2]
(ii) Show that the amplitude of the oscillations is 3.4 cm.
[1]
(iii) Calculate the maximum acceleration $a_0$ of the sphere.
$a_0$ = ………………………………………… m s $^{-2}$ [2]
© UCLES 2023 9702/42/M/J/2311 (b) On Fig. 4.2, sketch the variation with $x$ of the acceleration $a$ of the sphere. Fig. 4.2 [3] (c) Describe, without calculation, the interchange between the potential energy and the kinetic energy of the oscillations. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .....................................................
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5 Two capacitors A and B are connected into the circuit shown in Fig. 5.1.
Fig. 5.1
Capacitor A has capacitance C and capacitor B has capacitance 3C.
The electromotive force (e.m.f.) of the cell is V.
The two-way switch S is initially at position X, and capacitor B is initially uncharged.
(a) State, in terms of V and C, expressions for:
(i) the initial charge $Q_A$ on the plates of capacitor A
$$
Q_A = \text{..................................................} \quad [1]
$$
(ii) the initial energy $E_A$ stored in capacitor A.
$$
E_A = \text{..................................................} \quad [1]
$$
(b) The two-way switch S is now moved to position Y.
(i) State and explain what happens to the charge that was initially on the plates of capacitor A.
.....................13
(ii) Show that the final potential difference (p.d.) $V_B$ across capacitor B is given by
$$
V_B = \frac{V}{4}.
$$
Explain your reasoning.
[3]
(iii) Determine an expression, in terms of $V$ and $C$ , for the decrease $\Delta E$ in the total energy that is stored in the capacitors as a result of the change of the position of the switch.
$\Delta E = \underline{\hspace{5cm}}$ [2]
[Total: 9]
© UCLES 2023 9702/42/M/J/23 [Turn over14 6 A heavy aluminium disc has a radius of 0.36 m. The disc rotates with the wheels of a vehicle and forms part of an electromagnetic braking system on the vehicle. In order to activate the braking system, a uniform magnetic field of flux density 0.17 T is switched on. This magnetic field is perpendicular to the plane of rotation of the disc, as shown in Fig. 6.1. <!-- Image: Fig. 6.1 --> Fig. 6.1 (a) (i) Define magnetic flux. ............................................................................................................................... ............................................................................................................................... ........................................................................................................
15 (b) The disc is rotating at a rate of 25 revolutions per second. Calculate the magnitude of the electromotive force (e.m.f.) induced between the axle and the rim of the disc. e.m.f. = ………………………………………… V [3] (c) The axle and the rim are connected into an external circuit that enables the energy of the rotation of the disc to be stored for future use. The direction of rotation is shown in Fig. 6.1. Use Lenz’s law of electromagnetic induction to determine whether the current in the disc is from the rim to the axle or from the axle to the rim. Explain your reasoning. ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………… ………………………………………………………
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7 Four diodes are used in a bridge rectifier circuit to produce rectification of a sinusoidal a.c. input voltage $V_{IN}$ . Fig. 7.1 shows part of the circuit, but three of the diodes are missing.
Fig. 7.1
The p.d. across the load resistor R is the output p.d. $V_{OUT}$ of the bridge rectifier.
(a) (i) State the name of the type of rectification produced by a bridge rectifier. [1]
(ii) Complete Fig. 7.1 by drawing the three missing diodes, correctly connected. [2]
(iii) On Fig. 7.1, draw an arrow to indicate the direction of the current in resistor R. [1]
(b) $V_{IN}$ has amplitude $V_0$ and period $T$ . Fig. 7.2 shows the variation with time $t$ of $V_{IN}$ .
Fig. 7.2
© UCLES 2023 9702/42/M/J/2317
(i) On Fig. 7.3, sketch the variation of $V_{OUT}$ with $t$ between $t = 0$ and $t = 2.0T$ .
<div style="text-align: center;">
<br>
Fig. 7.3
<br>
[3]
</div>
(ii) The power dissipated in the resistor is $P$ .
On Fig. 7.4, sketch the variation of $P$ with $t$ between $t = 0$ and $t = 2.0T$ .
<div style="text-align: center;">
<br>
Fig. 7.4
<br>
[2]
</div>
(iii) Suggest, with a reason, how the root-mean-square (r.m.s.) value of $V_{OUT}$ compares with the r.m.s. value of $V_{IN}$ .
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8 Fig. 8.1 shows the lowest four energy levels of an electron in an isolated atom.
$\begin{array}{c}
\text{increasing} \\
\text{energy} \\
\uparrow
\end{array}$
$\begin{array}{c}
n = 4 \\
n = 3 \\
n = 2 \\
n = 1
\end{array}$
Fig. 8.1
Fig. 8.2 shows the lines in the emission spectrum of the atom that correspond to the transitions of the electron from $n = 3$ to $n = 1$ and from $n = 4$ to $n = 1$ .
$\begin{array}{c}
\text{increasing frequency} \\
\longrightarrow
\end{array}$
Fig. 8.2
(a) Explain, with reference to photons, why there is a single frequency of electromagnetic radiation that corresponds to each of these transitions.
...............................................................................................................................
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(c) The frequency of radiation represented by line A is $f_A$ .
The frequency of radiation represented by line B is $f_B$ .
The energy of the ground state ( $n = 1$ ) is $E_1$ .
Determine an expression, in terms of $f_A$ , $f_B$ , $E_1$ and the Planck constant $h$ , for the energy $E_3$ of the energy level $n = 3$ .
$$
E_3 = \text{..................................................} \quad [2]
$$
[Total: 8]
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9 (a) Define mass defect.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) Table 9.1 shows the mass defects of three nuclei.
Table 9.1
<table>
<tr>
<th>nucleus</th>
<th>mass defect/u</th>
</tr>
<tr>
<td> $_{1}^{2}\text{H}$ </td>
<td>0.002388</td>
</tr>
<tr>
<td> $_{1}^{3}\text{H}$ </td>
<td>0.009105</td>
</tr>
<tr>
<td> $_{2}^{4}\text{He}$ </td>
<td>0.030377</td>
</tr>
</table>
The nuclear fusio21
(c) The star in (b) has a radius of $2.3 \times 10^9$ m and a luminosity of $1.4 \times 10^{28}$ W.
All the energy released from the formation of $_2^4$ He is radiated away from the star.
All the energy that is radiated from the star has been released in the formation of $_2^4$ He.
Determine:
(i) the mass of $_2^4$ He produced per unit time by the fusion process
mass per unit time = ………………………………………… kg s $^{-1}$ [3]
(ii) the surface temperature of the star.
temperature = ………………………………………… K 2
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23 10 (a) X-rays for use in medical diagnosis are produced in an X-ray tube. In the X-ray tube, charged particles are accelerated towards a metal target by an applied potential difference (p.d.). (i) State the name of the charged particles that are accelerated by the applied p.d. ................................................................................................................... [1] (ii) Explain how X-rays are produced at the metal target. ................................................................................................................... ................................................................................................................... ......................................................................................................