科目：物理 Physics (9702)
年份：2018 冬季
试卷：Paper 41
总页数：24
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
4 BLANK PAGE © UCLES 2018 9702/41/O/N/18
5 Answer all the questions in the spaces provided. 1 (a) (i) State what is meant by *gravitational potential* at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. ............................................................................................................................... ...............................
6
2 (a) State what is meant by the *internal energy* of a system.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) An ideal gas undergoes a cycle of changes as shown in Fig. 2.1.
Fig. 2.1
At point P, the gas has volume $950 \text{cm}^3$ , pressure $2.10 \times 10^5 \text{Pa}$ and temperature $280 7
Some energy changes that take place during the cycle PQRP are shown in Fig. 2.2.
<table>
<tr>
<th></th>
<th>change P → Q</th>
<th>change Q → R</th>
<th>change R → P</th>
</tr>
<tr>
<td>thermal energy transferred to gas/J</td>
<td>+97.0</td>
<td>0</td>
<td>.......................</td>
</tr>
<tr>
<td>work done on gas/J</td>
<td>.......................</td>
<td>−42.5</td>
<td>+37.0</td>
</tr>
<tr>
<td>increase in internal energy of gas/J</td>
<td>.......................</td>
<td>.......................</td>
<td>.......................</td>
</tr>
</table>
Fig. 2.2
(i) State the total change in internal energy of the gas during the complete cycle PQRP. Explain your answer.
....................................8
3 A U-tube contains liquid, as shown in Fig. 3.1.
<div style="display: flex; justify-content: space-between;">
<div style="text-align: center;">
Fig. 3.1<br>
</div>
<div style="text-align: center;">
Fig. 3.2<br>
</div>
</div>
The total length of the column of liquid in the tube is $L$ .
The column of liquid is displaced so that the change in height of the liquid in each arm of the U-tube is $x$ , as shown in Fig. 3.2.
The liquid in the U-tube then oscillates with simple harmonic motion such that the acceleration $a$ of the column is given by the expression
$$
a = -\left(\frac{2g}{L}\right)x
$$
where $g$ is the acceleration of free fall.
(a) Calculate the period $T$ of oscillation of the liquid column for a column length $L$ of 19.0 c9 (b) The variation with time $t$ of the displacement $x$ is shown in Fig. 3.3.  Fig. 3.3 The period of oscillation of the liquid column of mass 18.0 g is $T$ . The oscillations are damped. (i) Suggest one cause of the damping. ............................................................................................................................... ............................................................................................................................... [1] (ii) Calculate the loss in total energy of the oscillations during the first 2.5 periods of the oscillations. energy loss = ................................................... J 3 © UCLES 2018 9702/41/O/N/18 [Turn over
10 4 (a) Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ......................
11 (b) (i) Define specific acoustic impedance. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) The fraction of the incident intensity of an ultrasound beam that is reflected at a boundary between two media depends on the specific acoustic impedances $Z_1$ and $Z_2$ of the media. Discuss qualitatively how the relative magnitudes of the two specific acoustic impedances affect the reflected intensity. ..............................................
12 5 (a) State two advantages of the transmission of data in digital form, compared with the transmission in analogue form. 1. ............................................................................................................................... ............................................................................................................................ 2. ............................................................................................................................... ............................................................................................................................ [2] (b) The digital numbers shown in Fig. 5.1 are transmitted at a sampling rate of 500 Hz. 0111 1011 1001 0100 1110 0101 0010 ``` end o
13 (c) State the effect on the transmitted analogue signal when (i) the sampling rate of the analogue-to-digital converter (ADC) and of the DAC is increased, ............................................................................................................................... ............................................................................................................................... [1] (ii) the number of bits in each sample is increased. ............................................................................................................................ ............................................................................................................................... 1 © UCLES 2018 9702/41/O/N/18 [Turn over
14 6 (a) (i) Define *electric potential* at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) State the relationship between electric potential and electric field strength at a point. ............................................................................................................................... ...............................................................................................................................
15
(ii) As the helium nucleus ( $^4_2\text{He}$ ) moves from plate A towards plate B, its distance $x$ from plate A increases.
Calculate the speed of the nucleus after it has moved a distance $x = 0.40\,\text{cm}$ from plate A.
speed = ………………………………………… m s $^{-1}$ 3
© UCLES 2018 9702/41/O/N/18 [Turn over16 7 (a) An ideal operational amplifier (op-amp) has infinite bandwidth and infinite slew rate. State what is meant by (i) *infinite bandwidth*, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) *infinite slew rate*. ............................................................................................................................... .......................................................................................................
17
(c) The completed amplifier of Fig. 7.1 has a voltage gain of 10.
State the output voltage $V_{OUT}$ for an input voltage $V_{IN}$ of
(i) $-0.36\,V$,
$\quad V_{OUT} = \underline{\hspace{5cm}}\,V\,[1]$
(ii) $0.56\,V$.
$\quad V_{OUT} = \underline{\hspace{5cm}}\,V\,[1]$
[Total: 8]
© UCLES 2018
9702/41/O/N/18
[Turn over18 8 (a) Explain what is meant by a *magnetic field*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A particle has mass $m$, charge $+q$ and speed $v$. The particle enters a uniform magnetic field of flux density $B$ such that, on entry, it is moving normal to the magnetic field, as shown in Fig. 8.1. path of particle mass $m$ → charge $+q$ speed $v$ region of magnetic field Fig. 8.1 The direction of the magnetic field is perpendicu
19 (c) The particle in (b) loses an electron so that its charge becomes $+2q$. Its change in mass is negligible. Determine, in terms of $v$, the initial speed of the particle such that its path through the magnetic field is unchanged. Explain your working. speed = ................................................... 3 © UCLES 2018 9702/41/O/N/18 [Turn over
20
9 (a) State Faraday’s law of electromagnetic induction.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) A solenoid S is wound on a soft-iron core, as shown in Fig. 9.1.
Fig. 9.1
A coil C having 120 turns of wire is wound on to one end of the core. The area of cross-section of coil C is $1.5 \text{cm}^2$ .
A Hall probe is close to the other end of the core.
When there is a constant current in solenoid S, the flux densi21
(ii) Complete Fig. 9.2 for the voltmeter readings for the times before, during and after the direction of the current is reversed.
<table>
<tr>
<th></th>
<th>before current changes</th>
<th>during current change when current is zero</th>
<th>after current changes</th>
</tr>
<tr>
<td>reading on voltmeter connected to coil C/V</td>
<td>...........................</td>
<td>...........................</td>
<td>...........................</td>
</tr>
<tr>
<td>reading on voltmeter connected to Hall probe/V</td>
<td>0.20</td>
<td>...........................</td>
<td>...........................</td>
</tr>
</table>
Fig. 9.2
4
© UCLES 2018 9702/41/O/N/18 [Turn over22 BLANK PAGE © UCLES 2018 9702/41/O/N/18
23 10 Some of the electron energy bands in a semiconductor material at the absolute zero of temperature are shown in Fig. 10.1. <div style="text-align: center;">  </div> Fig. 10.1 Use band theory to explain why, as the temperature of the semiconductor material rises, the electrical resistance of the sample of material decreases. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ......................................................
24
11 A stationary isolated nucleus emits a $\gamma$ -ray photon of energy $0.51\,\text{MeV}$ .
(a) State what is meant by a *photon*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) For the $\gamma$ -ray photon, calculate
(i) its wavelength,
wavelength = ................................................... m [2]
(ii) its momentum.
momentum = ................................................... Ns [2]
© UCLES 2018 9702/41/O/N/1825
(c) (i) For this nucleus, determine the change in mass $\Delta m$ during the decay that gives rise to the energy of the $\gamma$ -ray photon.
$\Delta m = \underline{\hspace{6cm}} \text{ kg [2]}$
(ii) Explain why, after the decay, the nucleus is no longer stationary.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [1]
[Total: 9]
© UCLES 2018 9702/41/O/N/18 [Turn over26 12 (a) State what is meant by *radioactive decay*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) The variation with time $t$ of the number $N$ of undecayed nuclei in a sample of a radioactive isotope is shown in Fig. 12.1.  Fig. 12.1 © UCLES 2018 9702/41/O/N/18
27
(i) Use the gradient of the line in Fig. 12.1 to determine the activity, in Bq, of the sample at time $t = 4.0$ hours. Show your working.
$$
\text{activity} = \underline{\hspace{5cm}} \text{Bq [3]}
$$
(ii) Use your answer in (i) to show that the decay constant $\lambda$ of the isotope is approximately $4 \times 10^{-5} \, \text{s}^{-1}$ .
[2]
(c) A sample of a different radioactive isotope has an initial activity of $4.6 \times 10^3 \, \text{Bq}$ . The sample must be stored safely until its activity is reduced to $1.0 \times 10^3 \, \text{Bq}$ .
The decay constant of the isotope is $5.5 \times 10^{-7} \, \text{s}^{-1}$ . The decay products are not radioactive.
Calculate the minimum time, in days, for which the sample must be stored.
$$
\text{time} = \underline{\hspace{5cm}} \tex