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## Practice

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Q1.
Which graph shows how the gravitational potential energy Ep of a simple pendulum varies
with displacement s from the equilibrium position?

A

B

C

D

(Total 1 mark)

Q2.
An object of mass 0.15 kg performs simple harmonic motion. It oscillates with amplitude
55 mm and frequency 0.80 Hz

What is the maximum value of its kinetic energy?

A 5.7 × 10–3 J

B 11 × 10–3 J

Page 1 of 14
C 0.57 J

D 11 J

(Total 1 mark)

Q3.
A helicopter circles continuously at a constant speed around a horizontal path of diameter
800 m, taking 5.0 minutes to complete each orbit of the path.

What are the speed v and the centripetal acceleration a of the helicopter?

v / m s−1 a / m s−2
A 0.021 0.18

B 8.4 0.088

C 8.4 0.18

D 17 0.35
(Total 1 mark)

Q4.
A body performs simple harmonic motion.

What is the phase difference between the variation of displacement with time and the
variation of acceleration with time for the body?

A 0

B

C

(Total 1 mark)

Q5.
A simple pendulum and a mass−spring system perform simple harmonic oscillations on
Earth with the same period T. Both systems are moved to a region where the gravitational
field strength is four times that at the surface of Earth.

What is the period of each system when oscillating at this new location?

Pendulum Mass−spring

Page 2 of 14
A T

B T

C 4T 2T

D 2T 2T
(Total 1 mark)

Q6.
A string passes through a smooth thin tube. Masses m and M are attached to the ends of
the string. The tube is moved so that the mass m travels in a horizontal circle of constant
radius r and at constant speed v.

Which of the following expressions is equal to M ?

A

B mv2rg

C

D

(Total 1 mark)

Q7.
A particle oscillates with undamped simple harmonic motion.

The acceleration of the particle

is always in the opposite direction to its
A
velocity.

B decreases as the potential energy increases.

Page 3 of 14
C is proportional to the frequency.

D is least when the speed is greatest.
(Total 1 mark)

Q8.
The diagram shows a string XY supporting a heavy pendulum P and four pendulums A, B,
C and D of smaller mass.

Pendulum P is set in oscillation perpendicular to the plane of the diagram.

Which one of the pendulums, A to D, then oscillates with the largest amplitude?
(Total 1 mark)

Q9.
A ball of mass 0.30 kg is attached to a string and moves in a vertical circle of radius 0.60
m at a constant speed of 5.0 m s–1.

Which line, A to D, in the table gives the correct values of the minimum and maximum
tension in the string?

Minimum tension / Maximum tension /
N N
A 2.5 5.4
B 6.7 9.6
C 13 13
D 9.6 15
(Total 1 mark)

Q10.
Which one of the following graphs shows how the acceleration, a, of a body moving with
simple harmonic motion varies with its displacement, x?

Page 4 of 14
(Total 1 mark)

Q11.
(a) (i) Name the two types of potential energy involved when a mass–spring system
performs vertical simple harmonic oscillations.
(1)

(ii) Describe the energy changes which take place during one complete oscillation
of a vertical mass-spring system, starting when the mass is at its lowest point.
(2)

(b) Figure 1 shows how the total potential energy due to the simple harmonic motion
varies with time when a mass-spring system oscillates vertically.

Figure 1

time / s

(i) State the time period of the simple harmonic oscillations that produces the
energy–time graph shown in Figure 1, explaining how you arrive at your
(2)

(ii) Sketch a graph on Figure 2 to show how the acceleration of the mass varies
with time over a period of 1.2 s, starting with the mass at the highest point of
its oscillations. On your graph, upwards acceleration should be shown as
positive and downwards acceleration as negative. Values are not required on
the acceleration axis.

Figure 2

Page 5 of 14
(2)

(c) (i) The mass of the object suspended from the spring in part (b) is 0.35 kg.
Calculate the spring constant of the spring used to obtain Figure 1. State an
(3)

(ii) The maximum kinetic energy of the oscillating object is 2.0 × 10–2 J. Show that
the amplitude of the oscillations of the object is about 40 mm.
(4)
(Total 14 marks)

Q12.
A simple pendulum was made by attaching a small mass to a 1.20 m length of thin string.
The pendulum was displaced 10.0 cm sideways and released to swing in a vertical plane.
The amplitude of the motion was then observed and recorded after each oscillation.
Figure 1 shows some of the results from the experiment.

Figure 1

Oscillation 0 1 2 3 4 5 6

Amplitude/cm 10.0 8.4 7.1 5.9 5.0 4.2 3.5

(a) The time for 6 oscillations was 13.2 s. Calculate the periodic time of the
oscillations.
(1)

(b) On the axes in Figure 2, carefully sketch a graph of displacement against time for
the first two oscillations of the pendulum. Mark the scale on each axis.

Figure 2

Page 6 of 14
(4)

(c) State the effect on the motion of the pendulum when

(i) a shorter string is used,

(ii) a greater mass of the same size is used.
(2)
(Total 7 marks)

Q13.
(a) Figure 1 and Figure 2 each show a car travelling in a horizontal circular path.

(i) Draw and label on Figure 1 and Figure 2 arrows to indicate the other forces
acting on the cars.

Figure 1

Page 7 of 14
Figure 2
(2)

(ii) State the possible origins of the centripetal force on the car in Figure 2.
(4)

(b) Figure 3 shows a motorcycle stunt rider travelling around a track in a vertical circle
of radius 5.2 m. At position Q, when the speed is the minimum necessary to keep
the motorcycle in contact with the track, the centripetal force is supplied by the
weight of the motorcycle and rider. The combined mass of the motorcycle and rider
is 220 kg.

Figure 3

Calculate the minimum speed which will keep the motorcycle in contact with the
track at position Q. The acceleration due to gravity, g, is 9.8 m s–2.
...

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