科目：物理 Physics (9702)
年份：2015 冬季
试卷：Paper 42
总页数：20
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 19: Capacitance, 20: Magnetic fields, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Section A
Answer all the questions in the spaces provided.
1 A satellite of mass $m_S$ is in a circular orbit of radius $x$ about the Earth.
The Earth may be considered to be an isolated uniform sphere with its mass $M$ concentrated at its centre.
(a) (i) Show that the kinetic energy $E_K$ of the satellite is given by the expression
$$
E_K = \frac{GMm_S}{2x}
$$
where $G$ is the gravitational constant. Explain your working.
[3]
(ii) State an expression, in terms of $G$ , $M$ , $m_S$ and $x$ , for the potential energy $E_P$ of the satellite.
...........................................................................................................................[1]
(iii) Using answers from (i) and (ii), derive an expression for the total energy $E_T$ of the satellite.
$$
E_T =5 (b) Small resistive forces acting on the satellite cause the radius of its circular orbit to change. Use your answers in (a) to state, for the satellite, whether each of the following quantities increases, decreases or remains constant. (i) total energy ...................................................................................................................[1] (ii) radius of orbit ...................................................................................................................[1] (iii) potential energy ...................................................................................................................[1] (iv) kinetic energy .............................................................................................................
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2 (a) State what is meant by an *ideal gas*.
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(b) The mean-square speed of the atoms of a fixed mass of an ideal gas at $32^\circ \text{C}$ is $1.9 \times 10^6 \, \text{m}^2 \, \text{s}^{-2}$ .
The gas is heated at constant volume to a temperature of $80^\circ \text{C}$ .
Determine
(i) the rise, in kelvin, of the temperature of the gas,
temperature rise = ............................................7 3 (a) State an expression, in terms of work done and heating, that is used to calculate the increase in internal energy of a system. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) State and explain, in terms of your expression in (a), the change, if any, in the internal energy (i) of the water in an ice cube when the ice melts, at atmospheric pressure, to form a liquid without any change of temperature, .......................................
8 4 (a) Distinguish between free oscillations and forced oscillations. free oscillations: ............................................................................................................... ............................................................................................................ forced oscillations: ............................................................................................................... ............................................................................................................ [2] (b) A trolley is held on a horizontal surface by means of two stretched springs, as shown in Fig. 4.1. <!-- Image: Fig. 4.1 --> Fig. 4.1 One spring is attached to a fixed point. The other spring is attached to an oscillator that caus
9 Use Fig. 4.2 to state and explain (i) the value of the natural frequency of vibration of the trolley, ............................................................................................................... ............................................................................................................... ............................................................................................................... ................................................................................................................... [3] (ii) whether there are any frictional forces acting on the trolley. ............................................................................................................... ...................................................
10 5 A charged particle P is situated in a vacuum at a distance $x$ from the centre of a charged conducting sphere of radius $r$ , as illustrated in Fig. 5.1. Fig. 5.1 For the particle P outside the conducting sphere, the charge on the sphere may be assumed to be a point charge at its centre. (a) (i) State Coulomb’s law. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) The sphere and the particle P are both charged positively. 1. State the dir
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(b) When the charge on the sphere is $6.0 \times 10^{-7} \, \text{C}$ , the electric field strength at the surface of the sphere is $1.5 \times 10^6 \, \text{V m}^{-1}$ .
Electrical breakdown (a spark) occurs when the electric field strength at the surface of the sphere exceeds $2.0 \times 10^6 \, \text{V m}^{-1}$ .
Determine the additional charge that may be added to the sphere before breakdown occurs.
charge = ………………………………………… C [3]
© UCLES 2015 9702/42/O/N/15 [Turn over12 6 (a) A particle has mass $m$, charge $+q$ and speed $v$. State the magnitude and direction of the force, if any, on the particle when the particle is travelling along the direction of (i) a uniform gravitational field of field strength $g$, ............................................................................................................................... ............................................................................................................................... [2] (ii) a uniform magnetic field of flux density $B$. ............................................................................................................................... ............................................................................................................
13 (ii) Derive, with explanation, the relation between the speed $v$ and the magnitudes of the electric field strength $E$ and the magnetic flux density $B$. [3] (c) A second particle has the same mass $m$ and charge $+q$ as that in (b) but its speed is $2v$. This particle enters the region between the plates along the same direction as the particle in (b). On Fig. 6.1, sketch the path of this particle in the region between the plates. [2] © UCLES 2015 9702/42/O/N/15 [Turn over
14 7 (a) By reference to the photoelectric effect, state what is meant by the *threshold frequency*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Electrons are emitted from a metal surface when light of a particular wavelength is incident on the surface. Explain why the emitted electrons have a range of values of kinetic energy below a maximum value. ............................................................................................
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(i) Use Fig. 7.1 to determine, without reference to the work function energy, the threshold frequency $f_0$ .
$$
f_0 = \underline{\hspace{5cm}} \text{ Hz [2]}
$$
(ii) Use your answer in (i) to calculate the work function energy $\Phi$ .
$$
\Phi = \underline{\hspace{5cm}} \text{ J [2]}
$$
(d) Caesium metal has a work function energy of $2.2 \times 10^{-19}$ J.
On the axes of Fig. 7.1, sketch a graph to show the variation with $1/\lambda$ of $E_{\text{MAX}}$ for caesium metal. [2]
© UCLES 2015 9702/42/O/N/15 [Turn over16
8 (a) Distinguish, for an atom, between a nucleus and a nucleon.
nucleus: ...............................................................................................................
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nucleon: .............................................................................................................
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[3]
(b) Radon gas is a naturally occurring radioactive gas with a half-life of 3.8 days.
The activity of radon gas in a room is found to be $97\,\text{Bq}$ in each $1.0\,\text{m}^3$ of air.
(i) Calculate
1. the decay constant, in $\text{s}^{-17
(ii) A volume of $2.5 \times 10^{-2} \, \text{m}^3$ of air in the room contains 1.0 mol of molecules.
Determine the ratio, for $1.0 \, \text{m}^3$ of air,
$$
\frac{\text{number of radon atoms}}{\text{number of air molecules}}.
$$
ratio = ………………………………………… [2]
© UCLES 2015 9702/42/O/N/15 [Turn over18 Section B Answer all the questions in the spaces provided. 9 A battery of e.m.f. 6.0V and negligible internal resistance is connected to three resistors, each of resistance 2.0kΩ, and a thermistor, as shown in Fig. 9.1. Fig. 9.1 The thermistor has resistance 2.8kΩ at 10°C and resistance 1.8kΩ at 20°C. (a) Calculate the potential (i) at point A, potential = ………………………………………… V [1] (ii) at point B for the thermistor at 10°C, potential = ………………………………………… V [2] © UCLES 2015 9702/42/O/N/15
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(iii) at point B for the thermistor at $20^\circ \text{C}$ .
potential = ………………………………………… V [1]
(b) The points A and B in Fig. 9.1 are connected to the inputs of an ideal operational amplifier (op-amp), as shown in Fig. 9.2.
Fig. 9.2
The thermistor is warmed from $10^\circ \text{C}$ to $20^\circ \text{C}$ .
State and explain the change in the output potential $V_{\text{OUT}}$ of the op-amp as the thermistor is warmed.
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© UCLES 2015 9702/42/O/N/15 [Turn over20
10 (a) Explain what is meant by the *sharpness* and by the *contrast* of an X-ray image.
sharpness: ...............................................................................................................
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contrast: ...............................................................................................................
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[2]
(b) A parallel X-ray beam of intensity $I$ is incident on a medium of thickness $x$ , as illustrated in Fig. 10.1.
<div style="text-align: center;">
</div>
Fig. 10.1
The transmitted intensity is $I_T21 (ii) Calculate the ratio $I_T/I$ for 80 keV X-rays passing through a thickness of 1.4 cm of bone. ratio = ………………………………………… [2] (c) An X-ray image of the upper leg of a student is produced. Part of the X-ray beam passes through a comparatively large thickness of muscle and part through some muscle and the leg bone. Use data from Fig. 10.2 to suggest whether the image has good contrast. ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… [3] © UCLES 2015 9702/42/O/N/15 [Turn over
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11 A carrier wave is frequency modulated.
(a) Describe what is meant by *frequency modulation*.
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(b) The sinusoidal carrier wave has a frequency of 750 kHz and an amplitude of 5.0 V.
The carrier wave is frequency modulated by a sinusoidal signal of frequency 7.5 kHz and amplitude 1.5 V.
The frequency deviation of the carrier wave is $20 \, \text{kHz} \, \text{V}^{-1}$ .
Determine, for the frequen23 12 (a) When infra-red radiation passes along an optic fibre, it is attenuated. (i) State what is meant by attenuation. ............................................................................................................................... ............................................................................................................................... [1] (ii) The infra-red radiation is transmitted as a series of pulses. State and explain two advantages of the digital, rather than the analogue, transmission of information. 1. ............................................................................................................................... ............................................................................................................