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GCSE Questions: Moments and Centre of Gravity

Q9. A drum is hit by a beater attached to a drumstick lever. The drumstick lever is attached to a foot-pedal by a chain, as shown in the diagram.

(a) When the toe is pushed down the force creates a moment on the foot-pedal.

(i) State what is meant by the moment of a force.

The moment is the turning effect of the force - it is equal to the force multiplied by perpendicular distance from the line of action of the force to the pivot.

[1 mark]

(ii) The foot-pedal is pushed halfway down and held stationary.

The toe and the chain both exert a force on the foot-pedal.

Compare the sizes and directions of the moments caused by the force of the toe and the force of the chain on the foot-pedal.

Moments are equal (in size) and opposite (in direction), that means that the clockwise moment is equal to the anticlockwise moment.

[1 mark]

(iii) The drummer's toe pushes with a 1.5 N force on the foot-pedal. The perpendicular distance from the pivot to the force is 0.12 m. The perpendicular distance from the pivot to the chain is 0.20 m. Calculate the force of the chain acting on the foot-pedal.

Σ clockwise moments = Σ anticlockwise moments

1.5 x 0.12 = F x 0.20

F = 0.18 ÷ 0.20

F = 0.90 N

[3 marks]

(b) The foot-pedal is pushed with different forces to make the beater move at different speeds. The higher the speed at which the beater hits the drum, the louder the sound the drum makes.

The diagram shows how the length of the drumstick lever affects the speed of the beater for three different forces.

 

The drummer needs to be able to sometimes play the drum quietly and sometimes loudly.

How does the length of the drumstick lever affect the variation in loudness of the sound from the drum when applying:

(i) a force of 3 N?

A longer drumstick lever will give a quieter sound.

Remember the moment has two parts - the distance and the force - if you increase the distance you will decrease the force - making the drum be hit with a smaller force and produce a quieter sound.

Saying 'a greater force gives a louder sound' is insufficient to get the mark - you are asked about changing the length of the drumstick....

(ii) a range of forces from 3 N to 9 N?

A longer drumstick lever, combined with varying force will allow a greater range of sound volume to be achieved.

[2 marks]

[7 Marks TOTAL]