科目：物理 Physics (9702)
年份：2023 春季
试卷：Paper 42
总页数：28
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
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1 (a) Define gravitational potential at a point.
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(b) Artemis is a spherical planet that may be assumed to be isolated in space. The variation with distance $x$ from the centre of Artemis of the gravitational potential $\phi$ is shown in Fig. 1.1.
$\phi/10^7 \text{J kg}^{-1}$
$\begin{array}{c}
0 \\
-0.5 \\
-1.0 \\
-1.5 \\
-2.0 \\
-2.5 \\
-3.0 \\
-3.5 \\
-4.0 \\
\end{array}$
$\begin{array}{cccc}
0 & 15
(i) The radius of Artemis is 4800 km.
Determine the value of $\phi$ on the surface of Artemis.
$\phi = \underline{\hspace{5cm}} \text{ Jkg}^{-1} \text{ [1]}$
(ii) Show that the mass of Artemis is $2.55 \times 10^{24}$ kg.
[1]
(iii) Calculate the gravitational field strength $g$ on the surface of Artemis.
$g = \underline{\hspace{5cm}} \text{ Nkg}^{-1} \text{ [2]}$
(iv) A satellite is in an orbit at a fixed position above a point on the surface of Artemis. The satellite is located above the equator of Artemis at a height above the surface where the gravitational potential is $-0.65 \times 10^7 \text{ Jkg}^{-1}$ .
Calculate the period, in hours, of rotation of Artemis.
$\text{period} = \underline{\hspace{5cm}} \text{ hours [4]}$
© UCLES 2023 9702/42/F/M/23 [Turn over6 (c) State one similarity and one difference between gravitational potential due to a point mass and electric potential due to a point charge. similarity ....................................................................................................................... ....................................................................................................................... difference ................................................................................................................... ....................................................................................................................... 2 © UCLES 2023 9702/42/F/M/23
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2 (a) State what is meant by an ideal gas.
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(b) A fixed amount of helium gas is sealed in a container. The helium gas has a pressure of $1.10 \times 10^5$ Pa, and a volume of $540 \, \text{cm}^3$ at a temperature of $27^\circ \text{C}$ .
The volume of the container is rapidly decreased to $30.0 \, \text{cm}^3$ . The pressure of the helium gas increases to $6.70 \times 10^6$ Pa and its temperature incre9
(iii) The average translational kinetic energy $E_K$ of a molecule of an ideal gas is given by
$$
E_K = \frac{3}{2} kT
$$
where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
Calculate the change in the total kinetic energy of the molecules of the helium gas.
change in kinetic energy = ………………………………………… J [3]
(c) The mass of nitrogen gas in another container is 24.0 g at a temperature of 27 °C. The gas is cooled to its boiling point of –196 °C. Assume all the gas condenses to a liquid.
For this change the specific heat capacity of nitrogen gas is 1.04 kJ kg⁻¹ K⁻¹.
The specific latent heat of vaporisation of nitrogen is 199 kJ kg⁻¹.
Determine the thermal energy, in kJ, removed from the nitrogen gas.
energy = ………………………………………… kJ 3
© UCLES 2023 9702/42/F/M10 3 An object is suspended from a vertical spring as shown in Fig. 3.1.  Fig. 3.1 The object is displaced vertically and then released so that it oscillates, undergoing simple harmonic motion. Fig. 3.2 shows the variation with displacement $x$ of the energy $E$ of the oscillations.  Fig. 3.2 © UCLES 2023 9702/42/F/M/23
11 The kinetic energy, the potential energy and the total energy of the oscillations are each represented by one of the lines P, Q and R. (a) State the energy that is represented by each of the lines P, Q and R. P ....................................................................................................................... Q ....................................................................................................................... R ....................................................................................................................... [2] (b) The object has a mass of 130 g. Determine the period of the oscillations. period = ................................................ s [4] (c) (i) State the cause of damping. ............................
12 (iii) State, with a reason, the type of damping that the card introduces into the system. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 1 © UCLES 2023 9702/42/F/M/23
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14 4 (a) State Coulomb’s law. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A charged sphere X is supported on an insulating stand. A second charged sphere Y is suspended by an insulating thread so that sphere Y is in equilibrium at the position shown in Fig. 4.1. <div style="text-align: center;">  On Fig. 4.2, draw and label all the forces acting on sphere Y. Fig. 4.2 [1] (ii) Determine the mass of sphere Y. mass = ………………………………………… kg [4] (iii) Calculate the total electric potential energy stored between X and Y. energy = ………………………………………… J [1] © UCLES 2023 9702/42/F/M/23 [Turn over
16 (c) An electron enters the region between two parallel plates P and Q, that are separated by a distance of 18 mm, as shown in Fig. 4.3. <div style="text-align: center;">  <br/> Fig. 4.3 </div> The space between the plates is a vacuum. The potential difference between the plates is 250 V. The electric field may be assumed to be uniform in the region between the plates and zero outside this region. (i) State the direction of the electric force on the electron when between the plates. ................................................................................................................... [1] (ii) Determine the magnitude of the force acting on the electron due to the electric field. force = ................................................... N
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18 5 A capacitor, a battery of electromotive force (e.m.f.) 12V, a resistor R and a two-way switch are connected in the circuit shown in Fig. 5.1. Fig. 5.1 The switch is initially in position S. When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time $t$ after the switch is moved the charge on the capacitor is $Q$ . The variation with $t$ of $\ln(Q/\mu C)$ is shown in Fig. 5.2. Fig. 5.2 (a) Show that the capacitance of the capacitor is $1.5\mu F$ . [3] © UCLES 2023 9702/42/F/M/23
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(b) Determine the resistance of R.
$$
\text{resistance} = \underline{\hspace{5cm}} \ \Omega \ [3]
$$
(c) Calculate the energy stored in the capacitor at time $t = 0$ .
$$
\text{energy} = \underline{\hspace{5cm}} \ J \ [2]
$$
(d) A second identical resistor is now connected in parallel with R.
The switch is initially in position S. When the capacitor is fully charged, the switch is moved to position T so that the capacitor discharges. At time $t$ after the switch is moved the charge on the capacitor is $Q$ .
On Fig. 5.2, sketch a line to show the variation of $\ln(Q/\mu C)$ with $t$ between time $t = 0$ and time $t = 5.0\,\text{s}$ .
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6 (a) A Hall probe is placed in a magnetic field. The Hall voltage is zero. The Hall probe is rotated to a new position in the magnetic field. The Hall voltage is now maximum.
Explain these observations.
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(b) The formula for calculating the Hall voltage $V_H$ as measured by a Hall probe is
$$
V_H = \frac{BI}{ntq}
$$
Table 6.1 shows the value of $n$ for two materials.
**Table 6.1**
<table>
<tr>
21 (c) A Hall probe gives a maximum reading of 24 mV when placed in a uniform magnetic field of flux density 32 mT. The same Hall probe is then placed in a magnetic field of fixed direction and varying flux density. The Hall probe is in a fixed position so that the angle between the Hall probe and the magnetic field is the same as when the Hall voltage was 24 mV. The variation of the reading $V_H$ on the Hall probe with time $t$ from time $t = 0$ to time $t = 8.6$ s is shown in Fig. 6.1.  Fig. 6.1 A coil with 780 turns and a diameter of 3.6 cm is placed in this varying magnetic field. The plane of the coil is perpendicular to the field lines. Calculate the magnitude of the maximum electromotive force (e.m.f.) induced in the coil in the time between $t = 0$ and $
22 7 (a) A beam of white light passes through a cloud of cool gas. The spectrum of the transmitted light is viewed and contains a number of dark lines. Explain why these dark lines occur. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .............................................................................................
23 Calculate the energy, in J, of energy level $n = 3$. energy = __________________________ J 3 © UCLES 2023 9702/42/F/M/23 [Turn over
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8 Plutonium-238 ( $^{238}_{94}\text{Pu}$ ) is unstable and undergoes alpha decay.
(a) Complete the equation to show the decay of plutonium-238.
$$
^{238}_{94}\text{Pu} \rightarrow \cdots\cdots\cdots\text{U} + \cdots\cdots\cdots\alpha
$$
[2]
(b) The power source in a space probe contains 0.874 kg of plutonium-238. Each nucleus of plutonium-238 that decays emits 5.59 MeV of energy. The half-life of plutonium-238 is 87.7 years.
(i) Calculate the initial number $N_0$ of nuclei of plutonium-238 in the power source.
$$
N_0 = \text{...................................................} \quad [1]
$$
(ii) Determine the initial activity of the source. Give a unit with your answer.
$$
\text{activity} = \text{........................................ unit ..................} \quad [2]
$$
(ii25 (iv) The space probe will continue to function until the power output from the plutonium in the source decreases to 65.3% of its initial value. Calculate the time, in years, for which the space probe will function. time = ………………………………………… years [2] (c) An alternative power source uses energy generated from the radioactive decay of polonium-210. This isotope has a half-life of 0.378 years. The mass of the isotope needed for the same initial power output as in (b) is 3.37 g. Suggest one advantage and one disadvantage of using polonium-210 as the source of energy. advantage ………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… disadvantage …………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… 2 © UCLES 2023 9702/42/
26 9 Ultrasound is used to produce diagnostic information about internal body structures. (a) Explain how ultrasound waves are detected. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) An alternating voltage $V$ varies with time $t$ according to $$ V = V_o \sin \omega t. $$ The voltage is applied to an ultrasound prob
27 (ii) Calculate the density of soft tissue. density = ………………………………………… kg m⁻³ [1] (iii) Use data from Table 9.1 to explain why ultrasound cannot be used to produce an image inside an air-filled cavity such as the lungs. ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………… 2 © UCLES 2023 9702/42/F/M/23 [Turn over
28 10 (a) A student observes different stars from the Earth. Give two reasons why some stars appear brighter than others. 1 .................................................................................................................... .................................................................................................................... 2 .................................................................................................................... .................................................................................................................... [2] (b) State what is meant by a standard candle. .................................................................................................................... .....................
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