科目：物理 Physics (9702)
年份：2022 冬季
试卷：Paper 41
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, 25: Astronomy and cosmology
4
1 (a) State the equation for the gravitational force $F$ between two point masses $m_1$ and $m_2$ that are separated by a distance $r$ . State the meaning of any other symbols you use.
[2]
(b) A satellite is in a circular orbit of radius $R$ around a planet of mass $M$ .
Show that the period $T$ of the orbit is given by
$$
T^2 = kR^3
$$
where $k$ is a constant that depends on the value of $M$ . Explain your reasoning.
[3]
(c) A satellite is in a circular orbit around the Earth with a period of 24 hours. The mass of the Earth is $6.0 \times 10^{24}$ kg.
(i) Calculate the radius of the orbit.
radius = ………………………………………… m [2]
© UCLES 2022 9702/41/O/N/225 (ii) State the two other conditions that must be met for the orbit to be geostationary. 1 ....................................................................................................................... .................................................................................................................... 2 ....................................................................................................................... .................................................................................................................... 2 [Total: 9] © UCLES 2022 9702/41/O/N/22 [Turn over
6 2 Fig. 2.1 shows a laboratory thermometer that is calibrated to measure temperature in degrees Celsius.  Fig. 2.1 The thermometer makes use of the fact that the density of mercury varies with temperature. (a) State two other physical properties of materials, apart from the density of a liquid, that can be used for measuring temperature. 1 ............................................................................................................................... 2 ............................................................................................................................... [2] (b) The thermometer is initially at 23.0 °C, as shown in Fig. 2.1. It is used to measure the temperature of an insulated beaker of water that is at 37.4 °C. The bulb
7 (ii) Suggest one change that could be made to the design of the thermometer that would enable it to give a more accurate measurement of temperature. ............................................................................................................................... ............................................................................................................................... [1] (c) (i) Explain why the thermometer in Fig. 2.1 does not provide a direct measurement of thermodynamic temperature. ............................................................................................................................ ............................................................................................................................... .............
8
3 An object is suspended from a spring that is attached to a fixed point as shown in Fig. 3.1.
<div style="text-align: center;">
</div>
Fig. 3.1
The object oscillates vertically with simple harmonic motion about its equilibrium position.
(a) State the defining equation for simple harmonic motion. Identify the meaning of each of the symbols used to represent physical quantities.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................9
The variation with $x$ of the potential energy $E_p$ of the oscillations of the object is shown in Fig. 3.3.
Fig. 3.3
Use Fig. 3.2 and Fig. 3.3 to:
(i) determine the amplitude $x_0$ of the oscillations
$$
x_0 = \underline{\hspace{5cm}} \text{ m [1]}
$$
(ii) show that the angular frequency of the oscillations is $1.7 \text{ rad s}^{-1}$
[2]
(iii) determine the mass $M$ of the object.
$$
M = \underline{\hspace{5cm}} \text{ kg [2]}
$$
© UCLES 2022 9702/41/O/N/22 [Turn over10 (c) The oscillations of the object are now lightly damped. (i) State what is meant by damping. ............................................................................................................... ............................................................................................................... ................................................................................................................... [2] (ii) Assume that the damping does not change the angular frequency of the oscillations. On Fig. 3.2, sketch the variation with $x$ of $\nu$ when the amplitude of the oscillations is 0.060 m. 2 © UCLES 2022 9702/41/O/N/22
11 BLANK PAGE © UCLES 2022 9702/41/O/N/22 [Turn over
12 4 (a) State what is indicated by the direction of an electric field line. ............................................................................................................................ [2] (b) Fig. 4.1 shows a pair of parallel metal plates with a potential difference (p.d.) of 2400 V between them. <div style="text-align: center;">  </div> Fig. 4.1 The plates are separated by a distance of 4.6 cm. The plates are in a vacuum. (i) On Fig. 4.1, draw five lines to represent the electric field in the region between the plates. [3] (ii) Calculate the strength of the electric field between the plates. electric field strength = ................................................... N C⁻¹ [2] © UCLES 2022 9702/41/O/N/22
13
(c) A moving proton enters the region between the plates from the left, as shown in Fig. 4.2.
<div style="text-align: center;">
</div>
Fig. 4.2
(i) The proton is deflected by the electric field.
On Fig. 4.2, draw a line to show the path of the proton as it moves through and out of the region of the electric field. [2]
(ii) A helium nucleus ( $^4_2\text{He}$ ) now enters the region of the electric field along the same initial path as the proton and travelling at the same initial speed.
State and explain how the final speed of the helium nucleus compares with the final speed of the proton after leaving the region of the electric field.
...........................................................................................................................14
5 A capacitor of capacitance $470\,\mu\mathrm{F}$ is connected to a battery of electromotive force (e.m.f.) $24\,\mathrm{V}$ in the circuit of Fig. 5.1.
Fig. 5.1
The two-way switch S is initially at position X.
P and Q are identical long straight wires, each with a resistance of $5.6\,\mathrm{k}\Omega$ . These wires are placed near to, and parallel to, each other. Wire Q is connected to a voltmeter.
At time $t = 0$ , switch S is moved to position Y so that the capacitor discharges through wire P.
(a) (i) Calculate the charge $Q_0$ on the capacitor at time $t = 0$ .
$$
Q_0 = \underline{\hspace{5cm}}\,\mathrm{C}\,[2]
$$
(ii) Calculate the current $I_0$ in wire P at time $t = 0$ .
$$
I_0 = \underline{\hspace{5cm}}\,\mathrm{A}\,[1]
$$
© UCLES 2022 9702/41/O/N/2215
(iii) Calculate the time constant $\tau$ of the discharge circuit.
$\tau = \underline{\hspace{6cm}} \text{ s [2]}$
(iv) On Fig. 5.2, sketch a line to show the variation with $t$ of the current $I$ in wire P as the capacitor discharges.
<div style="text-align: center;">
</div>
Fig. 5.2
[2]
(b) (i) Explain why there is an induced e.m.f. across wire Q during the discharge of the capacitor.
...............................................................................................................................
...............................................................................................................................
...................................................................................................................16
6 Fig. 6.1 shows a thin slice of semiconducting material used in a Hall probe.
<div style="text-align: center;">
</div>
Fig. 6.1 (not to scale)
Current $I$ passes through the slice in the direction shown.
The slice is placed in a uniform magnetic field of flux density $B$, so that two of its faces are perpendicular to the magnetic field.
A steady Hall voltage $V_H$ is developed between face PQXW and face SRYZ.
(a) (i) Use the letters in Fig. 6.1 to identify the faces that are perpendicular to the magnetic field.
................................................... and ................................................... [1]
(ii) Explain how the steady Hall voltage $V_H$ is developed between faces PQXW and SRYZ.
..........................................17
(b) The magnitude of $V_H$ is given by the equation
$$
V_H = \frac{BI}{ntq}.
$$
(i) State the meaning of the symbols $n$ , $t$ and $q$ . You may refer to the letters in Fig. 6.1.
$n$ : .......................................................................................................................
$t$ : .......................................................................................................................
$q$ : ....................................................................................................................... [3]
(ii) Suggest, with reference to the equation, why the slice of the material used in a Hall probe is thin.
.......................................................................................................................
.18 7 (a) A sinusoidal alternating voltage has a root-mean-square (r.m.s.) potential difference (p.d.) of 4.2 V and a frequency of 50 kHz. (i) The alternating voltage is applied across a resistor of resistance 760 Ω. By considering the peak voltage, show that the maximum power dissipated by the resistor is 46 mW. [2] (ii) On Fig. 7.1, draw a smooth curve to show how the power $P$ dissipated in the resistor varies with time $t$ between $t = 0$ and $t = 40 \mu s$ . Assume that $P = 0$ when $t = 0$ .  Fig. 7.1 [3] (iii) Use your line in (a)(ii) to explain why the mean power dissipated in the resistor is 23 mW. ............................................................................................................................... ..........................
19 (b) The alternating voltage in (a) is now applied to a piezoelectric crystal in air. (i) Explain what happens to the air surrounding the crystal. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) A second piezoelectric crystal is placed in the air near to the first crystal. Explain the effect of the surrounding air i
20
8 (a) State what is meant by the work function energy of a metal.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) Ultraviolet radiation of frequency $1.36 \times 10^{15} \text{Hz}$ is incident, in a vacuum, on a metal surface. The power of the radiation incident on the surface is 8.36 mW. Photoelectrons are emitted with a maximum kinetic energy of $3.09 \times 10^{-19} \text{J}$ .
(i) Determine the number of photons incident on the surface per21
9 (a) State what is meant by the luminosity of a star.
................................................................................................................... [1]
(b) A star in the constellation Canis Major is a distance of $8.14 \times 10^{16}$ m from the Earth and has a luminosity of $9.86 \times 10^{27}$ W. The surface temperature of the star is 9830 K.
(i) Calculate the radiant flux intensity of the radiation from the star observed from the Earth. Give a unit with your answer.
radiant flux intensity = ........................................... unit ................ [2]
(ii) Determine the radius of the star.
radius = ................................................... m [2]
(c) Explain how the surface temperature of a distant star may be determined from the wavel22
10 Carbon-15 ($^{15}_{6}\text{C}$) is an isotope of carbon that undergoes radioactive decay to nitrogen-15 ($^{15}_{7}\text{N}$), which is a stable isotope of nitrogen.
Radioactive decay is both a random and a spontaneous process.
(a) State what is meant by:
(i) random
...............................................................................................................................
............................................................................................................................... [1]
(ii) spontaneous.
...............................................................................................................................
................................................................................................................23
(iii) Show that the decay constant $\lambda$ of carbon-15 is given by the magnitude of the gradient of your line in (b)(ii).
[1]
(iv) Use your line in (b)(ii) to determine $\lambda$ . Give a unit with your answer.
$\lambda = \underline{\hspace{3cm}} \text{ unit} \quad \underline{\hspace{3cm}}$ [2]
(v) Use your answer in (b)(iv) to calculate the half-life of carbon-15.
$\text{half-life} = \underline{\hspace{3cm}} \text{ s} \quad \underline{\hspace{3cm}}$ [1]
(c) The equation for the decay of carbon-15 can be written as
$$
{}^{15}_{6}\text{C} \rightarrow {}^{15}_{7}\text{N} + {}_{-1}\beta + {}_{0}\bar{\nu}.
$$
State and explain how the mass of the products of the decay must compare with the mass of the carbon-15 nucleus.
$\underline{\hspace{8cm}}$
$\underline{\hspace{8cm}}$
$\