Page 319 - Physics Coursebook 2015 (A level)

Chapter 19: Oscillations
7 Figure 19.41 shows the piston of a small car engine which oscillates in the cylinder with a motion which approximates simple harmonic motion at 4200 revs per minute (1 rev = 1 cycle). The mass of the piston is 0.24 kg.
a Explain what is meant by simple harmonic motion.
b Calculate the frequency of the oscillation.
c The amplitude of the oscillation is 12.5 cm. Calculate:
i the maximum speed at which the piston moves
ii the maximum acceleration of the piston
iii theforcerequiredonthepistontoproducethe
piston cylinder
maximum acceleration.
8 Figure 19.42 shows a turntable with a rod attached to it a distance 15 cm from the centre. The turntable is
illuminated from the side so that a shadow is cast on a screen.
View from front
screen pendulum
rod turntable
lamp to illuminate the setup
View from front
[2] [1]
connecting rod
[2] [2]
[1]
screen
pendulum rod
Figure19.41 ForEnd-of-chapter7. turntable
15 cm
View from above
screen
pendulum rod
turntable
Figure 19.42 For End-of-chapter Question 8.
View from above
screen
15 cm
A simple pendulum is placed behind the turntable and is set oscillating so that it has an amplitude equal
pendulum
to the distance of the rod from the centre of the turntable.
The speed of rotation of the turntable is adjusted. When it is rotating at 1.5 revolutions per second the shadow
of the pendulum and the rod are found to move back and forth across the screen exactly in phase.
a Explain what is meant by the term in phase. [1]
rod
turntable
b Write down an equation to describe the displacement x of the pendulum from its equilibrium position and
the angular frequency of the oscillation of the pendulum. [1]
c Theturntablerotatesthroulagmhp60to°firlolumtihneatpeotshietiosentuopfmaximumdisplacementshowninthediagram.
i Calculate the displacement (from its equilibrium position) of the pendulum at this point. [3]
ii Calculate its speed at this point. [2]
iii Through what further angle must the turntable rotate before it has this speed again? [2]
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