1.
The figure below shows the London Eye. capsule
It has 32 capsules equally spaced around the edge of a large vertical wheel of radius
60 m. The wheel rotates about a horizontal axis such that each capsule has a constant speed of 0.26 m s
–1
.
(i) Calculate the time taken for the wheel to make one complete rotation. time = ...................................................... s
[1]
(ii) Each capsule has a mass of 9.7 × 10 3
kg. Calculate the centripetal force which must act on the capsule to make it rotate with the wheel. centripetal force = ..................................................... N
[2]
[Total 3 marks]
Ambrose College 1

2.
The figure below shows a mass suspended from a spring.
(a) The mass is in equilibrium. By referring to the forces acting on the mass, explain what is meant by equilibrium .
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[2]
(b) The mass in (a) is pulled down a vertical distance of 12 mm from its equilibrium position. It is then released and oscillates with simple harmonic motion.
(i) Explain what is meant by simple harmonic motion .
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(ii) The displacement x , in mm, at a time t seconds after release is given by x = 12 cos (7.85 t ).
Use this equation to show that the frequency of oscillation is 1.25 Hz.
[2]
[2]
Ambrose College 2

(iii) Calculate the maximum speed V max
of the mass.
V max
= ............................................... m s
–1
[2]
(c) Fig. 1 shows how the displacement x of the mass varies with time t .
15
10
5
0
0
–5
–10
–15
0.2
0.4
0.6
0.8
1.0
Fig. 1
Put a suitable scale on the velocity axis.
1.2
Sketch on Fig. 2 the graph of velocity against time for the oscillating mass. t / s
1.4
velocity / ms
–1
0
0 0.2
0.4
0.6
0.8
1.0
1.2
t / s
1.4
Fig. 2
[3]
[Total 11 marks]
3.
A satellite of mass 1500 kg is launched from the surface of the Earth into a circular orbit around the Earth at a height of 6800 km above the Earth’s surface. At this height
Ambrose College 3

the satellit e has an orbital period of 8.5 × 10 3
s. The radius of the Earth is 6400 km.
(i) A student uses the equation gain in potential energy = mgh to determine the increase in the potential energy of the satellite. Suggest why this equation cannot be used and s tate whether the student’s answer would be less than, equal to, or greater than the actual value.
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[2]
(ii) Calculate the kinetic energy of the satellite. kinetic energy = ......................................... J
[3]
Ambrose College 4

(iii) State a benefit of having a satellite in a geostationary orbit round the Earth.
Explain whether or not a satellite orbiting at a height of 6800 km above the
Earth’s surface is in a geostationary orbit.
In your answer, you should use appropriate technical terms, spelled correctly.
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[3]
[Total 8 marks]
4.
Define simple harmonic motion .
In your answer, you should use appropriate technical terms, spelled correctly.
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[Total 2 marks]
Ambrose College 5

5.
The electric motor in a washing machine rotates the drum containing the clothes by means of a rubber belt stretched around two pulleys, one on the motor shaft and the other on the drum shaft, as shown in Fig. 1.
X motor machine casing belt drum
Fig. 1
(a) The motor pulley of radius 15 mm rotates at 50 revolutions per second. Calculate
(i) the speed of the belt speed = ................... m s
–1
[2]
(ii) the centripetal acceleration of the belt at point X . acceleration = ................... m s
–2
[2]
Ambrose College 6

(iii) When the motor speed is increased, the belt can start to slip on the motor pulley. Explain why the belt slips.
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[2]
(b) When the drum is rotated at one particular speed, a metal side panel of the machine casing vibrates loudly. Explain why this happens.
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(c) A fault develops in the motor, causing the coil to stop rotating. Magnetic flux from the electromagnet of the motor still links with the now stationary coil. Fig. 2 shows how the flux linkage of the coil varies with time.
3 flux linkage /
Wb turns
2
1
0
0
–1
–2
–3
5 10 15 20 25 time/ms
30
Fig. 2
[2]
Ambrose College 7

(i) Using Fig. 2 state a time at which the e.m.f. induced across the ends of the coil is
1 zero
2 a maximum.
.................................... ms
.................................... ms
[2]
(ii) Use the graph of Fig. 2 to calculate the peak value of the e.m.f. across the ends of the coil. peak e.m.f. = ............................... V
[2]
[Total 12 marks]
6.
The student next designs a loop-the-loop stunt shown in the diagram below. The cyclist must enter the circular runway at the same 15 m s
–1
speed in order to exit from it smoothly.
T
A
15 m s
–1
B
E
Ambrose College 8

•
•
•
•
In order to calculate the maximum diameter of loop in which the cyclist can safely execute the manoeuvre, the student makes the following assumptions the cyclist stops pedalling once he enters the loop at the normal reaction of the runway on the tyre just becomes zero at the top of the loop T
E therefore the centripetal force at the top T is provided by the force of gravity only air resistance and runway friction can be ignored.
As a result, the student calculates the diameter of the track to be 9.17 m.
(i) Show that the speed of the cyclist at the top T of the loop should be 6.7 m s
–1
.
[3]
(ii) The total mass of the cyclist and bike is 86 kg. Calculate
1 the kinetic energy of the cyclist at the top T kinetic energy = .............................................. J
[2]
Ambrose College 9

2 the gravitational potential energy of the cyclist at the top T . Take the gravitational potential energy at E to be zero. potential energy = ............................................. J
(iii) Show that the sum of the kinetic and potential energies at the top T of the loop is equal to the kinetic energy of the cyclist as he enters the loop at E .
[2]
[2]
(iv) The cyclist suggests that removing the top half or semicircle of the loop from A to
B would allow him to fly in a semi-circular arc through the air and thus make a more spectacular stunt. How should the student should respond to this suggestion? Explain your reasoning.
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[2]
[Total 11 marks]
Ambrose College 10

7.
(a) (i) State the equation that represents Newton’s law of gravitation, defining all symbols.
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[1]
(ii) Why did Newton believe that the Universe must be infinitely large?
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[1]
(b) The period and average orbital radius of two Earth-orbiting research satellites are given in the table below. satellite
A
B period
/h
1.63
48.1 orbital radius
/km
7010
67100
(i) Satellite B has the larger orbital radius. Using Newton’s law of gravitation, explain why the satellites have such different periods.
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[2]
Ambrose College 11

(ii) Using data from the table, calculate the average orbital radius for a satellite with a period of 57.2 hours. radius = ..................km
[3]
(c) Suggest three advantages that land
–based telescopes have over those which are on satellites orbiting the Earth.
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[3]
[Total 10 marks]
Ambrose College 12

8.
The figure below shows a diagram of the Earth and the path of a geostationary satellite around it.
For the satellite to be in a geostationary orbit, three conditions must be satisfied regarding the period, the plane of the orbit and the direction of rotation. State and explain why each of these conditions is necessary. period ......................................................................................................................
................................................................................................................................. plane .......................................................................................................................
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................................................................................................................................. direction ...................................................................................................................
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[Total 5 marks]
Ambrose College 13