科目：物理 Physics (9702)
年份：2016 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, 20: Magnetic fields, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Answer all the questions in the spaces provided.
1 A satellite is in a circular orbit of radius $r$ about the Earth of mass $M$ , as illustrated in Fig. 1.1.
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Fig. 1.1
The mass of the Earth may be assumed to be concentrated at its centre.
(a) Show that the period $T$ of the orbit of the satellite is given by the expression
$$
T^2 = \frac{4\pi^2 r^3}{GM}
$$
where $G$ is the gravitational constant. Explain your working.
[3]
(b) (i) A satellite in geostationary orbit appears to remain above the same point on the Earth and has a period of 24 hours.
State two other features of a geostationary orbit.
1. ..................................................................................................................5
(ii) The mass $M$ of the Earth is $6.0 \times 10^{24}$ kg.
Use the expression in (a) to determine the radius of a geostationary orbit.
radius = ………………………………………… m [2]
(c) A global positioning system (GPS) satellite orbits the Earth at a height of $2.0 \times 10^4$ km above the Earth’s surface.
The radius of the Earth is $6.4 \times 10^3$ km.
Use your answer in (b)(ii) and the expression
$$
T^2 \propto r^3
$$
to calculate, in hours, the period of the orbit of this satellite.
period = ………………………………………… hours 2
© UCLES 2016 9702/41/O/N/16 [Turn over6
2 An ideal gas initially has pressure $1.0 \times 10^5$ Pa, volume $4.0 \times 10^{-4}$ m³ and temperature 300 K, as illustrated in Fig. 2.1.
<table>
<tr>
<th>initial state</th>
<th>final state</th>
</tr>
<tr>
<td>
$1.0 \times 10^5$ Pa<br>
$4.0 \times 10^{-4}$ m³<br>
300 K
</td>
<td>
$5.0 \times 10^5$ Pa<br>
$4.0 \times 10^{-4}$ m³<br>
$T$
</td>
</tr>
</table>
Fig. 2.1
A change in energy of the gas of 240 J results in an increase of pressure to a final value of $5.0 \times 10^5$ Pa at constant volume.
The thermodynamic temperature becomes $T$ .
(a) Calculate
(i) the temperature $T$ ,
$$
T = \underline{\hspace{8cm}} \text{ K [2]}
$$
(ii) the amount of gas.
$$
\text{amount} = \underline{\hspace{8cm}} \text{ mol 7 (b) The increase in internal energy $\Delta U$ of a system may be represented by the expression $$ \Delta U = q + w. $$ (i) State what is meant by the symbol 1. $+q$ , 2. $+w$ . [2] (ii) State, for the gas in (a), the value of 1. $\Delta U$ , $\Delta U =$ ………………………………………… J 2. $+q$ , $+q =$ ………………………………………… J 3. $+w$ . $+w =$ ………………………………………… J 3 © UCLES 2016 9702/41/O/N/16 [Turn over
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3 To demonstrate simple harmonic motion, a student attaches a trolley to two similar stretched springs, as shown in Fig. 3.1.
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Fig. 3.1
The trolley has mass $m$ of 810g.
The trolley is displaced along the line of the two springs and then released. The subsequent acceleration $a$ of the trolley is given by the expression
$$
a = -\frac{2kx}{m}
$$
where the spring constant $k$ for each of the springs is 64 N m⁻¹ and $x$ is the displacement of the trolley.
(a) Show that the frequency of oscillation of the trolley is 2.0 Hz.
[3]
(b) The maximum displacement of the trolley is 1.6 cm.
Calculate the maximum speed of the trolley.
speed = ………………………………………… m s⁻¹ [2]
© UCLES 2016 9702/41/O/N/169 (c) The mass of the trolley is increased. The initial displacement of the trolley remains unchanged. Suggest the change, if any, that occurs in the frequency and in the maximum speed of the oscillations of the trolley. frequency: ............................................................................................................... maximum speed: ............................................................................................................... 2 © UCLES 2016 9702/41/O/N/16 [Turn over
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11 4 (a) Signals may be transmitted in either analogue or digital form. One advantage of digital transmission is that the signal can be regenerated. Explain (i) what is meant by *regeneration*, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) why an analogue signal cannot be regenerated. ............................................................................................................................... ..............................
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5 Two small solid metal spheres A and B have equal radii and are in a vacuum. Their centres are 15 cm apart.
Sphere A has charge +3.0 pC and sphere B has charge +12 pC. The arrangement is illustrated in Fig. 5.1.
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Fig. 5.1
Point P lies on the line joining the centres of the spheres and is a distance of 5.0 cm from the centre of sphere A.
(a) Suggest why the electric field strength in both spheres is zero.
...............................................................................................................................
...............................................................................................................................
.........................................................13
(d) A silver-107 nucleus ($^{107}_{47}\text{Ag}$) has speed $v$ when it is a long distance from point P.
Use your answer in (c) to calculate the minimum value of speed $v$ such that the nucleus can reach point P.
speed = ………………………………………… m s⁻¹ 3
© UCLES 2016 9702/41/O/N/16 [Turn over14
6 (a) The slew rate of an ideal operational amplifier (op-amp) is said to be infinite.
Explain what is meant by *infinite slew rate*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The circuit of Fig. 6.1 is designed to indicate whether the temperature of the thermistor is above or below $24^\circ \text{C}$ .
Fig. 6.1
The operational amplifier (op-amp) is assumed to be ideal.
At $24^\circ \text{C}$ , the resistance of the thermistor is $1.15
(ii) On Fig. 6.1,
1. draw two light-emitting diodes (LEDs) connected so as to indicate whether the output $V_{OUT}$ of the op-amp is either +5 V or –5 V, [2]
2. label with the letter G the LED that will be emitting light when the temperature is below 24 °C. Explain your working.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... 3
© UCLES 2016 9702/41/O/N/16 [Turn over16 7 (a) Explain what is meant by a *field of force*. ............................................................................................................................... ............................................................................................................................... [1] (b) State the type of field, or fields, that will give rise to a force acting on (i) a moving uncharged particle, ............................................................................................................................... [1] (ii) a stationary charged particle, ............................................................................................................................... [1] (iii) a charged particle moving at an angle to the field or fie
17 (ii) Derive an expression, in terms of the radius $r$ of the path, for the linear momentum of the electron. Show your working. 2 8 Explain the main principles behind the use of nuclear magnetic resonance imaging (NMRI) to obtain diagnostic information about internal body structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ..........................................................................................................................
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9 (a) State Faraday’s law of electromagnetic induction.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The diameter of the cross-section of a long solenoid is 3.2 cm, as shown in Fig. 9.1.
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Fig. 9.1
A coil C, with 85 turns of wire, is wound tightly 19
(c) The current $I$ in the solenoid in (b) is reversed in 0.30 s.
Calculate the mean e.m.f. induced in coil C.
$$
\text{e.m.f.} = \underline{\hspace{5cm}} \text{ mV [2]}
$$
(d) The current $I$ in the solenoid in (b) is now varied with time $t$ as shown in Fig. 9.2.
Fig. 9.2
Use your answer to (c) to show, on Fig. 9.3, the variation with time $t$ of the e.m.f. $E$ induced in coil C.
Fig. 9.3
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© UCLES 2016 9702/41/O/N/16 [Turn over20 10 (a) Explain what is meant by the photoelectric effect. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) One wavelength of electromagnetic radiation emitted from a mercury vapour lamp is 436 nm. Calculate the photon energy corresponding to this wavelength. energy = ................................................... J [2] (c) Light from the lamp in (b) is incident, separately, on the surfaces of caesium and tungsten metal. Data for the work
21 (ii) tungsten. threshold wavelength = ……………………………………… nm [1] (d) Use your answers in (c) to state and explain whether the radiation from the mercury lamp of wavelength 436 nm will give rise to photoelectric emission from each of the metals. caesium: ………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… tungsten: ……………………………………………………………………………………………………… ……………………………………………………………………………………………………………… 2 © UCLES 2016 9702/41/O/N/16 [Turn over
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11 Some of the electron energy bands in a solid are illustrated in Fig. 11.1.
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conduction band<br>(partially filled)
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forbidden band
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valenc23
12 Radon-222 ( $^{222}_{86}\text{Rn}$ ) is a radioactive element found in atmospheric air.
The decay constant of radon-222 is $2.1 \times 10^{-6} \, \text{s}^{-1}$ .
(a) (i) Define radioactive *half-life*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(ii) Show that the half-life $t_{\frac{1}{2}}$ is related to the decay constant $\lambda$ by the expression
$$
\lambda t_{\frac{1}{2}} = 0.693.
$$
[2]
(b) Radon-222 is considered to be an unac