科目：物理 Physics (9702)
年份：2019 夏季
试卷：Paper 43
总页数：24
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
4 Answer all the questions in the spaces provided. 1 (a) Two point masses are isolated in space and are separated by a distance $x$ . State an expression relating the gravitational force $F$ between the two masses to the magnitudes $M$ and $m$ of the masses. State the name of any other symbol used. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [1] (b) A spacecraft is to be put into a circular orbit about a spherical planet. The planet may be consider
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(ii) One possible path of the spacecraft as it approaches the planet is shown in Fig. 1.1.
<div style="text-align: center;">
</div>
Fig. 1.1 (not to scale)
The spacecraft enters the orbit at point A with speed $3.7 \times 10^3 \, \text{m} \, \text{s}^{-1}$ .
At point B, a distance of $5.00 \times 10^7 \, \text{m}$ from the centre of the planet, the spacecraft has a speed of $4.1 \times 10^3 \, \text{m} \, \text{s}^{-1}$ . The mass of the spacecraft is 650 kg.
For the spacecraft moving from point B to point A, show that the change in gravitational potential energy of the spacecraft is $8.3 \times 10^9 \, \text{J}$ .
[3]
(c) By considering changes in gravitational potential energy and in kinetic energy of the spacecraft, determine whether the total energy of6
2 A fixed mass of an ideal gas has volume $210 \, \text{cm}^3$ at pressure $3.0 \times 10^5 \, \text{Pa}$ and temperature $270 \, \text{K}$ . The volume of the gas is reduced at constant pressure to $140 \, \text{cm}^3$ , as shown in Fig. 2.1.
<table>
<tr>
<td>210 cm³<br>3.0 × 10⁵ Pa<br>270 K</td>
<td>→</td>
<td>140 cm³<br>3.0 × 10⁵ Pa<br>T</td>
</tr>
</table>
Fig. 2.1
The final temperature of the gas is $T$ .
(a) Determine:
(i) the amount of gas
amount = ………………………………………… mol [3]
(ii) the final temperature $T$ of the gas
$T$ = ………………………………………… K [2]
(iii) the external work done on the gas.
work done = ………………………………………… J [2]
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(b) For this change in volume and temperature of the gas, the thermal energy transferred is 53 J.
Determine $\Delta U$ , the change in internal energy of the gas.
$\Delta U = \underline{\hspace{5cm}} \text{ J [3]}$
[Total: 10]
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9702/43/M/J/19
[Turn over8
3 A hollow tube, sealed at one end, has a cross-sectional area $A$ of $24 \, \text{cm}^2$ . The tube contains sand so that the total mass $M$ of the tube and sand is $0.23 \, \text{kg}$ .
The tube floats upright in a liquid of density $\rho$ , as illustrated in Fig. 3.1.
Fig. 3.1
The depth of the bottom of the tube below the liquid surface is $h$ .
The tube is displaced vertically and then released. The variation with time $t$ of the depth $h$ is shown in Fig. 3.2.
Fig. 3.2
(a) Determine:
(i) the amplitude, in metres, of the oscillations
$$
\text{amplitude} = \underline{\hspace{5cm}} \, \text{m} \, [1]
$$
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(ii) the frequency of oscillation of the tube in the liquid
frequency = ………………………………………… Hz [2]
(iii) the acceleration of the tube when $h$ is a maximum.
acceleration = ………………………………………… m s $^{-2}$ [2]
(b) The frequency $f$ of oscillation of the tube is given by the expression
$$
f = \frac{1}{2\pi} \sqrt{\left( \frac{A \rho g}{M} \right)}
$$
where $g$ is the acceleration of free fall.
Calculate the density $\rho$ of the liquid in which the tube is floating.
$\rho$ = ………………………………………… kg m $^{-3}$ [2]
(c) The oscillations illustrated in Fig. 3.2 are undamped. In practice, the liquid does cause light damping.
On Fig. 3.2, draw a line to show light damping of the oscillations for time $t = 0$ to time $t = 1.4$ s. 3
© UCLES 2019 9702/43/M/J/19 [Turn over10 4 (a) During the transmission of a signal, attenuation occurs and noise is picked up. State what is meant by: (i) attenuation ............................................................................................................................ [1] (ii) noise. ............................................................................................................................ [2] (b) By reference to (a)(ii), explain the advantage of the transmission of the signal in digital form rather than in analogue form. ............................................................................................................................ [1] (c) Part of an analogue signal is shown in Fig. 4.1.  Fig. 4.1 © UCLES 2019 9702/43/M/J/19
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The signal is to be transmitted in digital form.
The analogue signal is sampled at a frequency of $1.0 \times 10^3 \text{Hz}$ using an analogue-to-digital converter (ADC). The ADC produces 4-bit numbers.
The times $t$ at which the analogue signal is sampled are shown in Fig. 4.2.
<table>
<tr>
<th>time $t/\text{ms}$ </th>
<td>0</td>
<td>1.0</td>
<td>2.0</td>
<td>3.0</td>
<td>4.0</td>
<td>5.0</td>
<td>6.0</td>
</tr>
<tr>
<th>digital number</th>
<td>0010</td>
<td>0110</td>
<td>0100</td>
<td>0101</td>
<td>........</td>
<td>........</td>
<td>........</td>
</tr>
</table>
Fig. 4.2
On Fig. 4.2:
(i) for the digital number at time $t = 3.0 \text{ms}$ , underline the least significant bit (LSB) [1]
(ii) state the digit12 5 (a) State what is meant by *electric field strength*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two point charges A and B are situated a distance 15 cm apart in a vacuum, as illustrated in Fig. 5.1. <div style="text-align: center;">  <br/> Fig. 5.1 </div> Point P lies on the line joining the charges and is a distance $x$ from charge A. The variation with distance $x$ of the electric field strength $E$ at po
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(i) By reference to the direction of the electric field, state and explain whether the charges A and B have the same, or opposite, signs.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(ii) State why, although charge A is a point charge, the electric field strength between $x = 3 \text{ cm}$ and $x = 7 \text{ cm}$ does not obey an inverse-square law.
.................................................................................................14
6 (a) State two different functions of capacitors in electrical circuits.
1. ...............................................................................................................................
2. ...............................................................................................................................
[2]
(b) Three uncharged capacitors of capacitances $C_1$ , $C_2$ and $C_3$ are connected in series with a battery of electromotive force (e.m.f.) $E$ and a switch, as shown in Fig. 6.1.
Fig. 6.1
When the switch is closed, there is a charge $+q$ on plate P of the capacitor of capacitance $C_1$ .
Show that the combined capacitance $C$ of the three capacitors is given by the expression
$$
\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C15
(c) A student has available four capacitors, each of capacitance $20\,\mu\text{F}$ .
Draw circuit diagrams, one in each case, to show how the student may connect some or all of the capacitors to produce a combined capacitance of:
(i) $60\,\mu\text{F}$
[1]
(ii) $15\,\mu\text{F}$
1
[Total: 7]
© UCLES 2019 9702/43/M/J/19 [Turn over16 7 The circuit for an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in Fig. 7.1. Fig. 7.1 (a) For the circuit of Fig. 7.1: (i) explain why point P is known as a virtual earth ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) calculate the gain of the amplifier. gain = ...........
17 (b) When the op-amp is saturated, the potential difference across the LED is 2.3 V. Calculate the minimum resistance of resistor R so that the current in the LED is limited to 30 mA. resistance = ………………………………………… Ω 3 © UCLES 2019 9702/43/M/J/19 [Turn over
18 8 A solenoid is connected in series with a battery and a switch, as illustrated in Fig. 8.1.  Fig. 8.1 A small coil, connected to a sensitive ammeter, is situated near one end of the solenoid. As the current in the solenoid is switched on, there is a changing magnetic field inside the solenoid. (a) (i) State what is meant by a *magnetic field*. ............................................................................................................................ [1] (ii) On Fig. 8.1, draw an arrow on the axis of the solenoid to show the direction of the magnetic field inside the solenoid. Label this arrow P. [1] (b) As the current in the solenoid is switched on, there is a current induced in the small coil. This induced current gives rise to a magnetic
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(ii) Use Lenz’s law to state and explain the direction of the magnetic field due to the induced current in the small coil. On Fig. 8.1, mark this direction with an arrow inside the small coil.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [3]
(c) The small coil has an area of cross-section $7.0 \times 10^{-4} \, \text{m}^2$20 BLANK PAGE © UCLES 2019 9702/43/M/J/19
21 9 Nuclear magnetic resonance imaging (NMRI) is used to obtain diagnostic information about internal body structures. State, during the use of NMRI, the function of: (a) the large constant magnetic field ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ..........................................................................
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10 A bridge rectifier contains four diodes. The output of the rectifier is connected to a resistor R, as shown in Fig. 10.1.
<div style="text-align: center;">
<br/>
Fig. 10.1
</div>
The variation with time $t$ of the input e.m.f. $E$ to the rectifier is given by the expression
$$
E = 15 \cos(210t)
$$
where $t$ is measured in seconds and $E$ in volts.
The variation with time $t$ of the potential difference $V$ across resistor R is shown in Fig. 10.2.
<div style="text-align: center;">
<br/>
Fig. 10.2
</div>
Determine:
(a) the maximum potential difference $V_{\text{MAX}}$ across resistor R
$$
V_{\text{MAX}} = \underline{\hspace{5cm}} \text{V [1]}
$$
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Note: The images referenced in the original do23 (b) the time interval, to two significant figures, between time $t_1$ and time $t_2$. time = ………………………………………… s 3 © UCLES 2019 9702/43/M/J/19 [Turn over
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11 (a) State three pieces of evidence provided by the photoelectric effect for a particulate nature of electromagnetic radiation.
1. ...............................................................................................................................
2. ...............................................................................................................................
3. ...............................................................................................................................
...............................................................................................................................
[3]
(b) The work function energies of some metals are shown in Fig. 11.1.
<table>
<tr>
<th></th>
<th>work function energy/eV</th25
(c) Photons of wavelength 380 nm are incident normally on a metal surface at a rate of $7.6 \times 10^{14} \, \text{s}^{-1}$ .
All the photons are absorbed in the surface and no photoelectrons are emitted.
Calculate the force exerted on the metal surface by the incident photons.
force = ………………………………………… N 3
© UCLES 2019 9702/43/M/J/19 [Turn over26 12 (a) A sample of a radioactive isotope contains $N$ nuclei of the isotope at time $T$ . At time $(T + \Delta T)$ , the sample contains $(N - \Delta N)$ nuclei of the isotope. The time interval $\Delta T$ is short. Use the symbols $N$ , $\Delta N$ , $T$ and $\Delta T$ to give expressions for: (i) the average activity of the sample during the time $\Delta T$ ................................................................................................................... [1] (ii) the probability of decay of a nucleus in the time $\Delta T$ ................................................................................................................... [1] (iii) the decay constant $\lambda$ of the isotope. ....................................................................
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2. the total energy, in pJ, released.
energy = ………………………………………… pJ [3]
(ii) The polonium-208 nucleus is initially stationary. The initial kinetic energy of the $\frac{4}{2}$ He nucleus ( $\alpha$ -particle) is found to be less than the energy calculated in (i) part 2.
Suggest two possible reasons for this difference.
1. ……………………………………………………………………………………………………………
2. ……………………………………………………………………………………………………………
…………………………………………………………………………………………………………
2
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