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A metal wheel consists of an axle A, eight spokes and a rim, as shown in Fig. 1.1.
Point X is on the rim at the end of one of the spokes.
The rim has a radius of 0.85 m.
The wheel is rotating clockwise with an angular speed of 140 rad s⁻¹.
(a) For point X, determine:
(i) the speed [2]
(ii) the centripetal acceleration. [2]
(b) There is a uniform magnetic field of flux density 0.18 T into the plane of the page.
(i) State Lenz's law of electromagnetic induction. [2]
(ii) Show that the time taken for point X to complete one revolution is 45 ms. [1]
(iii) Calculate the magnetic flux cut by spoke AX during one revolution of the wheel. Give a unit with your answer. [3]
(iv) Determine the magnitude of the electromotive force (e.m.f.) induced across spoke AX. [2]
(v) Use Lenz's law to explain whether the potential is higher at end A or end X of the spoke. [1]
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The Sun may be considered as a uniform sphere with a mass of $1.99 \times 10^{30} \text{kg} $ and a surface temperature of 5780K.
A probe with a mass of $2.63 \text{kg} $ moves in a straight line towards the Sun. When it is at a distance $x$ from the centre of the Sun, the probe measures the gravitational field strength $g$ due to the Sun and the radiant flux intensity $F$ of radiation from the Sun.
For the position of the probe where $x = 1.47 \times 10^{11} \text{m}$
(a) Calculate g. [2]
(b) Determine the gravitational potential energy $E_p$ of the probe. [2]
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(a) Define specific latent heat. [2]
(b) A dish containing $7.2 \times 10^{-5} \text{ m}^3$ of a substance rests on a laboratory bench. The substance is initially a liquid of density $710 \text{ kg m}^{-3}$. Atmospheric pressure is $1.0 \times 10^5 \text{ Pa}$.
The liquid is heated at its boiling point so that it completely vaporises. The increase in the internal energy of the substance during this process is $17.6$ kJ. The final volume of the vapour is $0.017 \text{ m}^3$.
(i) Show that the magnitude of the work done on the substance when it vaporises is $1.7$ kJ. [2]
(ii) Use the information in (b)(i) to calculate the thermal energy $Q$, in kJ, supplied to the substance to cause it to vaporise. [2]
(iii) Use your answer in (b)(ii) to determine a value for the specific latent heat of vaporisation $L_V$, in $\text{kJ kg}^{-1}$, of the substance. [2]
(c) The substance in (b) has a specific latent heat of fusion $L_F$.
Suggest and explain whether $L_F$ is likely to be less than, the same as, or greater than the answer in (b)(iii). [3]
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(a) State three of the basic assumptions of the kinetic theory of gases. [3]
(b) Explain how molecular movement causes the pressure exerted by a gas. [3]
(c) Fig. 4.1 shows the variation with thermodynamic temperature $T$ of the mean-square speeds $\langle c^2 \rangle$ for two gases X and Y.
Fig. 4.2 shows the variation with $T$ of the product $pV$ for samples of the two gases, where $p$ is the pressure of the gas and $V$ is the volume of the gas.
State three conclusions about the gases and their samples that may be drawn from Fig. 4.1 and Fig. 4.2. The conclusions may be qualitative or quantitative. Use the space below for any working that you need. [3]
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Fig. 5.1 shows a pendulum consisting of a metal sphere suspended by a thin string.
The sphere undergoes small oscillations about its equilibrium position. The oscillations may be considered to be simple harmonic.
Fig. 5.2 shows the variation with time t of the displacement x of the sphere from its equilibrium position.
(a) On Fig. 5.1, draw an arrow, from the centre of the sphere, to represent the direction of the resultant force acting on the sphere when it is in the position shown. [1]
(b) The mass of the sphere is 0.15 kg.
(i) State the amplitude of the oscillations. [1]
(ii) Determine the angular frequency of the oscillations. [2]
(iii) Calculate the total energy of the oscillations. [2]
(c) On Fig. 5.3, sketch the variation with x of the kinetic energy E_{K} of the sphere. [3]
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(a) State Coulomb’s law.
............................................................................................................................. ............................................................................................................................. [2]
(b) Fig. 6.1 shows an isolated hollow conducting sphere that is positively charged.
On Fig. 6.1, draw field lines to represent the electric field outside the sphere. [3]
(c) Fig. 6.2 shows the variation of the electric field strength $E$ with distance $x$ from the centre of the sphere in (b).
(i) Determine the radius, in cm, of the sphere.
radius = .................................................. cm [1]
(ii) Calculate the charge on the sphere.
charge = .................................................. C [3]
(iii) Suggest an explanation for the fact that the electric field inside the sphere is zero.
................................................................................................................................. ................................................................................................................................. [1]
[Total: 10]
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(a) Define the capacitance of a parallel-plate capacitor. ........................................................................................................................................... [2]
(b) An initially uncharged capacitor X, of capacitance C, is gradually charged so that the final potential difference (p.d.) between its plates is V and the final charge is Q.
(i) On Fig. 7.1, sketch the variation of charge with p.d. for capacitor X as the p.d. increases from 0 to V.
[2]
(ii) Determine an expression, in terms of Q and V, for the work $W$ done on capacitor X during the charging process. Explain your reasoning.
$W = \text{..........................................................}$ [2]
(c) Another capacitor Y is initially uncharged. The fully charged capacitor X in (b) is now connected to capacitor Y, as shown in Fig. 7.2.
The capacitance of capacitor Y is 3C.
(i) Complete Table 7.1 to show expressions, in terms of Q and V, for the final p.d.s across, and the final charges on, the two capacitors. Use the space below for any working that you need.
[Table_1]
[3]
(ii) State whether the total energy stored in the two capacitors is less than, the same as, or greater than the energy initially stored in capacitor X.
................................................................................................................................................. [1]
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(a) State what is meant by the frequency of an alternating current.
.................................................................................................................... [1]
(b) An alternating current I in a resistor of resistance 680\,\Omega varies with time t according to
\( I = 3.5 \sin(40\pi t) \)
where I is in A and t is in s.
(i) Show that the period of the alternating current is 50\,ms.
[1]
(ii) On Fig. 8.1, sketch the variation of I with t between t = 0 and t = 100\,ms.
[3]
(iii) Determine the root-mean-square (r.m.s.) current in the resistor.
r.m.s. current = ........................................A [1]
(c) Use data from (b), including your answer in (b)(iii), to show by calculation that the mean power in the 680\,\Omega resistor is half of the peak power.
[3]
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Electrons in a vacuum are accelerated from rest through a potential difference (p.d.) $V$ to form a beam. The electrons each have mass $m$ and charge $q$.
The beam is incident on a graphite crystal that acts as a diffraction grating. After passing through the crystal, the beam reaches a fluorescent screen. An interference pattern is observed on this screen.
(a) Explain what this observation shows about the nature of electrons.
........................................................................................................................................................ [1]
(b) Determine an expression, in terms of $m$, $q$ and $V$, for the momentum $p$ of an electron in the beam.
$p$ = ........................................................... [3]
(c) The p.d. through which the electrons are accelerated is now increased to a greater value.
Describe and explain the effect of this change on the interference pattern observed.
........................................................................................................................................................ [2]
(d) The electrons are now accelerated through different values of $V$, resulting in pairs of corresponding values for $p$ and the de Broglie wavelength $\lambda$.
(i) On Fig. 9.1, sketch the variation of $p$ with $\frac{1}{\lambda}$.
[Image_1: Fig. 9.1]
[2]
(ii) State the name of the quantity represented by the gradient of the line in Fig. 9.1.
........................................................................................................................................................ [1]
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(a) Radioactive decay is both random and spontaneous.
(i) State what is meant by random.
.............................................................................................................................................. [1]
(ii) State what is meant by spontaneous.
.............................................................................................................................................. [1]
(iii) State one piece of evidence for the random nature of decay.
.............................................................................................................................................. [1]
(b)
(i) Describe the differences between nuclear fission and nuclear fusion.
.............................................................................................................................................. [3]
(ii) Explain, with reference to the variation of binding energy per nucleon with nucleon number, why the processes of nuclear fission and nuclear fusion both result in a release of energy.
.............................................................................................................................................. [2]
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