科目：物理 Physics (9702)
年份：2016 春季
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, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
4 Answer all the questions in the spaces provided. 1 (a) State Newton’s law of gravitation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A satellite of mass $m$ has a circular orbit of radius $r$ about a planet of mass $M$ . It may be assumed that the planet and the satellite are uniform spheres that are isolated in
5
(i) Determine the ratio
1. $\frac{v_A}{v_B}$
ratio = ………………………………………… [2]
2. $\frac{T_A}{T_B}$
ratio = ………………………………………… [3]
(ii) The planet spins about its own axis with angular speed $1.7 \times 10^{-4} \, \text{rad} \, \text{s}^{-1}$ .
Moon A is always above the same point on the planet’s surface.
Determine the orbital period $T_B$ of moon B.
$T_B = \text{……………………………………… s [2]}$
[Total: 11]
© UCLES 2016 9702/42/F/M/16 [Turn over6 2 (a) State (i) what is meant by *internal energy*, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) the basic assumption of the kinetic theory of gases that leads to the conclusion that there is zero potential energy between the molecules of an ideal gas. ............................................................................................................................... .............................................................
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(c) A cylinder contains 17 g of oxygen gas at a temperature of 12°C. The mass of 1.0 mol of oxygen gas is 32 g. It may be assumed that the oxygen behaves as an ideal gas.
Calculate, for the oxygen gas in the cylinder,
(i) the mean kinetic energy of a molecule,
$$
\text{mean kinetic energy} = \underline{\hspace{5cm}} \text{J [2]}
$$
(ii) the number of molecules,
$$
\text{number} = \underline{\hspace{5cm}} \text{[2]}
$$
(iii) the total internal energy.
$$
\text{internal energy} = \underline{\hspace{5cm}} \text{J [1]}
$$
[Total: 11]
© UCLES 2016 9702/42/F/M/16 [Turn over8
3 (a) Define specific heat capacity.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................[2]
(b) A student carries out an experiment to determine the specific heat capacity of a liquid using the apparatus illustrated in Fig. 3.1.
Fig. 3.1
Liquid enters the tube at a constant temperature of $19.5^\circ\text{C}$ and leaves the tube at a temperature of $25.5^\circ\text{C}$ . The mass of liquid flowing through the tube per unit time is $9 (ii) Calculate the specific heat capacity of the liquid. Show your working. specific heat capacity = ……………………………… J kg⁻¹ K⁻¹ [3] (c) When the heating coil in (b) dissipates 33.3 W of power, the potential difference $V$ across the coil is given by the expression $$ V = 27.0 \sin(395t). $$ The potential difference is measured in volts and the time $t$ is measured in seconds. Determine the resistance of the coil. resistance = ………………………………………… Ω 3 © UCLES 2016 9702/42/F/M/16 [Turn over
10 4 An object of mass 80g oscillates with simple harmonic motion. The variation with time $t$ of the displacement $x$ of the object is shown in Fig. 4.1. Fig. 4.1 (a) Use Fig. 4.1 to determine the amplitude and the period of the oscillations. amplitude = ………………………………………… cm period = ………………………………………… s [1] (b) Use Fig. 4.1 and your answers in (a) to calculate the kinetic energy of the object at time $t = 0.19$ s. kinetic energy = ………………………………………… J 3 © UCLES 2016 9702/42/F/M/16
11 5 (a) A digital signal is produced by sampling an analogue signal and passing the samples through an analogue-to-digital converter (ADC). (i) State what is meant by a *digital signal*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) State one change to the sampling or to the ADC that will improve the accuracy of reproduction of the original analogue signal. .....................................................................................
12
6 A parallel beam of ultrasound is incident normally on the surface of a layer of fat of thickness 1.1 cm, as shown in Fig. 6.1.
Fig. 6.1
For the ultrasound,
$I_1$ is the intensity just after entering the surface of the fat layer,
$I_2$ is the intensity incident on the fat-muscle boundary,
$I_3$ is the intensity reflected from the fat-muscle boundary,
$I_4$ is the intensity received back at the surface of the fat layer.
Some data for the fat are given in Fig. 6.2.
<table>
<tr>
<td>specific acoustic impedance $Z$ </td>
<td> $1.4 \times 10^6 \, \text{kg} \, \text{m}^{-2} \, \text{s}^{-1}$ </td>
</tr>
<tr>
<td>density $\rho$ </td>
<td> $940 \, \text{kg} \, \text{m}^{-3}$ </td>
</tr>
<tr>
<td>absorption (attenuation) coefficient 13
(b) Calculate the ratio $\frac{I_2}{I_1}$
ratio = …………………………………………[2]
(c) Intensity $I_4$ is 0.33% of intensity $I_1$ .
Determine the ratio $\frac{I_3}{I_2}$
ratio = …………………………………………[2]
(d) The specific acoustic impedance of the muscle is greater than that of the fat.
State the effect, if any, on the value of the ratio $\frac{I_3}{I_2}$ of an increase in the difference between the specific acoustic impedance of the muscle and that of the fat.
………………………………………………………………………………………………………[1]
[Total: 8]
© UCLES 2016 9702/42/F/M/16 [Turn over14
7 (a) Define capacitance.
...............................................................................................................................
............................................................................................................................... [1]
(b) Three capacitors of capacitances $C_1$ , $C_2$ and $C_3$ are initially uncharged. They are then connected in series to a battery, as shown in Fig. 7.1.
Fig. 7.1
The battery applies a potential difference $V$ across the three capacitors.
Show that the combined capacitance $C$ of the capacitors is given by
$$
\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}.
$$
[2]
(c) A battery of e.m.f. 12V and negligible internal resistance is connected to a network of two capacitors and a resisto15 (i) The switch is moved to position A. Calculate 1. the combined capacitance of the two capacitors, combined capacitance = ………………………………………… $\mu$ F [1] 2. the charge on the $600\mu$ F capacitor, charge = ………………………………………… C [1] 3. the potential difference across the $600\mu$ F capacitor. potential difference = ………………………………………… V [1] (ii) The switch is now moved from position A to position B. Calculate the potential difference across the $600\mu$ F capacitor when it has discharged 50% of its initial energy. potential difference = ………………………………………… V 3 © UCLES 2016 9702/42/F/M/16 [Turn over
16 8 (a) State two effects of negative feedback on the gain of an amplifier incorporating an operational amplifier (op-amp). 1. ............................................................................................................................... 2. ............................................................................................................................... ............................................................................................................................... [2] (b) An incomplete diagram of an amplifier circuit incorporating an ideal operational amplifier is shown in Fig. 8.1. Fig. 8.1 The amplifier has a voltage gain of +5.0. (i) Complete the circuit diagram of Fig. 8.1. [2] (ii) Calculate the resistance of any additional resis
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(iii) Fig. 8.2 shows the variation with time of the input potential $V_{IN}$.
Fig. 8.2
On Fig. 8.2, draw the variation with time of the output potential $V_{OUT}$. 2
© UCLES 2016 9702/42/F/M/16 [Turn over18
9 A particle of charge $+q$ and mass $m$ is travelling with a constant speed of $1.6 \times 10^5 \, \text{m} \, \text{s}^{-1}$ in a vacuum. The particle enters a uniform magnetic field of flux density $9.7 \times 10^{-2} \, \text{T}$ , as shown in Fig. 9.1.
<div style="text-align: center;">
</div>
Fig. 9.1
The magnetic field direction is perpendicular to the initial velocity of the particle and perpendicular to, and out of, the plane of the paper.
A uniform electric field is applied in the same region as the magnetic field so that the particle passes undeviated through the fields.
(a) State and explain the direction of the electric field.
.......................................................................................................................19
(c) The electric field is now removed so that the positively-charged particle follows a curved path in the magnetic field. This path is an arc of a circle of radius 4.0 cm.
Calculate, for the particle, the ratio $\frac{q}{m}$ .
ratio = ………………………………………… C kg⁻¹ [3]
(d) The particle has a charge of $3e$ where $e$ is the elementary charge.
(i) Use your answer in (c) to determine the mass, in $u$ , of the particle.
mass = ………………………………………… u [2]
(ii) The particle is the nucleus of an atom. State the number of protons and the number of neutrons in this nucleus.
number of protons = …………………………………………
number of neutrons = ………………………………………… 1
© UCLES 2016 9702/42/F/M/16 [Turn over20
10 A small coil of wire is situated in a non-uniform magnetic field, as shown in Fig. 10.1.
<div style="text-align: center;">
</div>
Fig. 10.1
The coil consists of 40 turns of wire and moves with a constant speed in a straight line. The coil has displacement $x$ from a fixed point P.
The variation with $x$ of the magnetic flux $\phi$ in the coil is shown in Fig. 10.2.
<div style="text-align: center;">
</div>
Fig. 10.2
(a) The coil is moved at constant speed between point P and the point where $x = 3.0 \text{cm}$ .
(i) Calculate the change in magnetic flux linkage of the coil.
change in flux linkage = ………………………………………… Wb [1]
© UCLES 2016 9702/42/F/M/16
Note: The images referenced in the original document are represented here wit21
(ii) The e.m.f. induced in the coil is $5.0 \times 10^{-4} \text{V}$ . Determine the speed of the coil.
speed = ………………………………………… m s⁻¹ [2]
(b) On Fig. 10.3, sketch the variation with $x$ of the e.m.f. $E$ induced in the coil for values of $x$ from $x = 0$ to $x = 6.0 \text{cm}$ .
<div style="text-align: center;">
<br/>
Fig. 10.3
</div>
2
© UCLES 2016 9702/42/F/M/16 [Turn over22
11 (a) With reference to the photoelectric effect, state what is meant by the *threshold frequency*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) Electromagnetic radiation of wavelength $\lambda$ is incident on a metal surface. Electrons of maximum kinetic energy $E_{\text{MAX}}$ are emitted.
(i) On Fig. 11.1, sketch the variation with $1/\lambda$ of $E_{\text{MAX}}$ .
$\begin{array}{c}
E_{\text{MAX}} \\
\uparrow \\
0 \quad \longrightarrow23 (iv) Light of a particular wavelength is incident on a metal surface and gives rise to a photoelectric current. The wavelength is reduced. The intensity of the light is kept constant. State and explain the effect, if any, on the photoelectric current. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .........................