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A digital voltmeter with a three-digit display is used to measure the potential difference across a resistor. The manufacturers of the meter state that its accuracy is ±1% and ±1 digit. The reading on the voltmeter is 2.05 V.
(a) For this reading, calculate, to the nearest digit,
(i) a change of 1% in the voltmeter reading, [1]
(ii) the maximum possible value of the potential difference across the resistor. [1]
(b) The reading on the voltmeter has high precision. State and explain why the reading may not be accurate. [2]
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(a) State the two conditions that must be satisfied for a body to be in equilibrium. [2]
(b) Three co-planar forces act on a body that is in equilibrium.
(i) Describe how to draw a vector triangle to represent these forces. [3]
(ii) State how the triangle confirms that the forces are in equilibrium. [1]
(c) A weight of 7.0 N hangs vertically by two strings AB and AC, as shown in figure.
For the weight to be in equilibrium, the tension in string AB is $T_1$ and in string AC it is $T_2$.
On figure, draw a vector triangle to determine the magnitudes of $T_1$ and $T_2$. [3]
(d) By reference to Fig. 2.1, suggest why the weight could not be supported with the strings AB and AC both horizontal. [2]
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A cyclist is moving up a slope that has a constant gradient. The cyclist takes 8.0 s to climb the slope.
The variation with time $t$ of the speed $v$ of the cyclist is shown in Fig. 3.1.
(a) Use Fig. 3.1 to determine the total distance moved up the slope. [3]
(b) The bicycle and cyclist have a combined mass of 92 kg. The vertical height through which the cyclist moves is 1.3 m.
(i) For the movement of the bicycle and cyclist between $t = 0$ and $t = 8.0$ s,
1. use Fig. 3.1 to calculate the change in kinetic energy, [2]
2. calculate the change in gravitational potential energy. [2]
(ii) The cyclist pedals continuously so that the useful power delivered to the bicycle is 75 W. Calculate the useful work done by the cyclist climbing up the slope. [2]
(c) Some energy is used in overcoming frictional forces.
(i) Use your answers in (b) to show that the total energy converted in overcoming frictional forces is approximately 670 J. [1]
(ii) Determine the average magnitude of the frictional forces. [1]
(d) Suggest why the magnitude of the total resistive force would not be constant. [2]
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(a) State the evidence for the assumption that
(i) there are significant forces of attraction between molecules in the solid state, [1]
(ii) the forces of attraction between molecules in a gas are negligible. [1]
(b) Explain, on the basis of the kinetic model of gases, the pressure exerted by a gas. [4]
(c) Liquid nitrogen has a density of $810\text{kg m}^{-3}$. The density of nitrogen gas at room temperature and pressure is approximately $1.2\text{kg m}^{-3}$.
Suggest how these densities relate to the spacing of nitrogen molecules in the liquid and in the gaseous states. [2]
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(a) A source of sound has frequency $f$. Sound of wavelength $\lambda$ is produced by the source.
(i) State
what is meant by the frequency of the source, [1]
the distance moved, in terms of $\lambda$, by a wavefront during $n$ oscillations of the source. [1]
(ii) Use your answers in (i) to deduce an expression for the speed $v$ of the wave in terms of $f$ and $\lambda$.
(b) The waveform of a sound wave produced on the screen of a cathode-ray oscilloscope (c.r.o.) is shown in Fig. 5.1.
The time-base setting of the c.r.o. is 2.0 ms cm$^{-1}$.
(i) Determine the frequency of the sound wave. [2]
(ii) A second sound wave has the same frequency as that calculated in (i). The amplitude of the two waves is the same but the phase difference between them is 90°.
On Fig. 5.1, draw the waveform of this second wave. [1]
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(a) (i) State what is meant by an $electric \ current$.
..........................................................................................................
..........................................................................................................[1]
(ii) Define $electric \ potential \ difference$.
..........................................................................................................
..........................................................................................................[1]
(b) The variation with potential difference $V$ of the current $I$ in a component Y and in a resistor R are shown in Fig. 6.1.
Use Fig. 6.1 to explain how it can be deduced that resistor R has a constant resistance of $20\Omega$.
..........................................................................................................
..........................................................................................................
..........................................................................................................[2]
(c) The component Y and the resistor R in (b) are connected in parallel as shown in Fig. 6.2.
A battery of $e.m.f. \ E$ and negligible internal resistance is connected across the parallel combination.
Use data from Fig. 6.1 to determine
(i) the current in the battery for an $e.m.f. \ E$ of $6.0 V$,
current = ..................................................A [1]
(ii) the total resistance of the circuit for an $e.m.f. \ E$ of $8.0 V$.
resistance = .................................................. $\Omega$ [2]
(d) The circuit of Fig. 6.2 is now re-arranged as shown in Fig. 6.3.
The current in the circuit is $0.20 A$.
(i) Use Fig. 6.1 to determine the $e.m.f. \ E$ of the battery.
$E$ = ..................................................V [1]
(ii) Calculate the total power dissipated in component Y and resistor R.
power = ..................................................W [2]
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One property of \( \alpha \)-particles is that they produce a high density of ionisation of air at atmospheric pressure. In this ionisation process, a neutral atom becomes an ion pair. The ion pair is a positively-charged particle and an electron.
(a) State
(i) what is meant by an \( \alpha \)-particle,
\( \text{..........................................................................................................................} \)
\( \text{..........................................................................................................................[1]} \)
(ii) an approximate value for the range of \( \alpha \)-particles in air at atmospheric pressure.
range = \( \text{............................................} \) cm [1]
(b) The energy required to produce an ion pair in air at atmospheric pressure is 31 eV.
An \( \alpha \)-particle has an initial kinetic energy of \( 8.5 \times 10^{-13} \) J.
(i) Show that \( 8.5 \times 10^{-13} \) J is equivalent to 5.3 MeV.
[1]
(ii) Calculate, to two significant figures, the number of ion pairs produced as the \( \alpha \)-particle is stopped in air at atmospheric pressure.
number = \( \text{.................................................} \) [2]
(iii) Using your answer in (a)(ii), estimate the average number of ion pairs produced per unit length of the track of the \( \alpha \)-particle as it is brought to rest in air.
number per unit length = \( \text{.................................................} \) [2]
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