Periodic motionAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Periodic motion topic test

Total 54 marks

Name

Class

Date

1
A model train of mass 0.80 kg runs at a constant speed round a circular track of radius 1.5 m. It completes one lap in 4.0 s.
(a)
Which statement about the acceleration of the train is correct?
[1 mark]
AIt is zero because the speed is constant.
BIt is directed along the tangent to the track, in the direction of motion.
CIt is directed towards the centre of the track.
DIt is directed away from the centre of the track.
(b)
What is the angular speed of the train?
[1 mark]
A0.25 rad s⁻¹
B0.64 rad s⁻¹
C1.6 rad s⁻¹
D2.4 rad s⁻¹
(c)
Calculate the magnitude of the resultant force on the train.
[2 marks]
Total for question 1: 4 marks
2
A sewing-machine needle moves vertically with simple harmonic motion of amplitude 8.0 mm at a frequency of 20 Hz.
(a)
What is the maximum speed of the needle?
[1 mark]
A1.0 m s⁻¹
B0.50 m s⁻¹
C0.16 m s⁻¹
D2.0 m s⁻¹
(b)
What is the maximum acceleration of the needle?
[1 mark]
A1.0 m s⁻²
B1.3 × 10² m s⁻²
C3.2 m s⁻²
D1.3 × 10⁵ m s⁻²
(c)
Calculate the displacement of the needle from its equilibrium position at the instant when its speed is half of its maximum speed.
[2 marks]
Total for question 2: 4 marks
3
A vibration-testing rig has a block of mass 0.50 kg on a smooth horizontal surface, joined to a fixed support by a light spring of spring constant 80 N m⁻¹. The block is pulled 15 mm from its equilibrium position, released from rest, and then oscillates with simple harmonic motion.
(a)
Calculate the time period and the frequency of the oscillation.
[3 marks]
(b)
Calculate the maximum kinetic energy of the block and hence its maximum speed.
[4 marks]
Total for question 3: 7 marks
4
A small ball is fixed to the rim of a vertical disc of radius 0.15 m that rotates at a steady 2.0 revolutions per second. A lamp casts the shadow of the ball onto a screen beside the disc, and the shadow moves up and down along a vertical line with simple harmonic motion.
(a)
Calculate the speed of the ball and its centripetal acceleration. State and explain how the maximum speed and the maximum acceleration of the shadow compare with these values.
[6 marks]
(b)
A student wants a 0.20 kg mass on a vertical spring to oscillate with the same time period and amplitude as the shadow. Calculate the spring constant needed and the maximum kinetic energy of the mass.
[6 marks]
Total for question 4: 12 marks
5
A physics teacher clamps a hacksaw blade at one end and drives its free end with a vibration generator whose frequency can be varied. The blade has a natural frequency of 12 Hz.
(a)
The generator is set to a steady frequency of 8 Hz. Which statement describes the motion of the blade once it has settled?
[1 mark]
AIt vibrates at 12 Hz with a small amplitude.
BIt vibrates at 8 Hz with a smaller amplitude than at resonance.
CIt vibrates at 8 Hz, with the same amplitude as at resonance.
DIt vibrates at 20 Hz, the sum of the two frequencies.
(b)
The teacher repeats the experiment with the blade vibrating inside a tank of thick oil. Which row describes the effect on the resonance of the blade?
[1 mark]
AAmplitude at resonance is greater and the peak is sharper.
BAmplitude at resonance is unchanged and the peak is sharper.
CAmplitude at resonance is greater and the peak is broader.
DAmplitude at resonance is smaller and the peak is broader.
(c)
The driving frequency is increased slowly from 6 Hz to 18 Hz with the driving amplitude kept constant. Describe how the amplitude of the blade changes, and explain the change.
[2 marks]
Total for question 5: 4 marks
6
On a distant planet an astronaut times a simple pendulum of length 0.90 m. For small oscillations the time period is 2.8 s. The bob has a mass of 0.25 kg and its maximum kinetic energy during an oscillation is 0.020 J.
(a)
What is the gravitational field strength on the planet?
[1 mark]
A12.7 N kg⁻¹
B4.5 N kg⁻¹
C1.1 N kg⁻¹
D2.3 N kg⁻¹
(b)
What is the kinetic energy of the bob when its displacement from equilibrium is half of the amplitude?
[1 mark]
A0.015 J
B0.0050 J
C0.010 J
D0.020 J
(c)
Calculate the maximum speed of the bob.
[2 marks]
Total for question 6: 4 marks
7
A hammer thrower whirls a hammer head of mass 7.26 kg, attached to a light wire, in a horizontal circle of radius 1.7 m before releasing it. The hammer head completes one revolution in 0.50 s. Treat the wire as horizontal and ignore the weight of the hammer head.
(a)
Calculate the tension in the wire.
[3 marks]
(b)
The wire can withstand a maximum tension of 3.5 kN. Calculate the shortest time period of rotation possible without the wire breaking, and the speed of the hammer head at this limit.
[4 marks]
Total for question 7: 7 marks
8
A washing machine of total suspended mass 40 kg rests on mountings that behave as a single spring of spring constant 3.6 × 10⁵ N m⁻¹. During the spin cycle a badly distributed load makes the drum exert a periodic vertical force on the machine at the same frequency as the rotation of the drum, which is 900 revolutions per minute.
(a)
Show that the natural frequency of vertical oscillation of the machine is about 15 Hz. Explain why the machine shakes violently during the spin cycle, and explain how fitting dampers to the mountings would change this.
[6 marks]
(b)
When the machine is loaded with wet washing its total suspended mass rises to 50 kg. Calculate the new natural frequency and explain the effect on the vibration when the drum is at 900 revolutions per minute. Explain also why the machine will still shake strongly for a short time as the drum speeds up from rest to 900 revolutions per minute.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).