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Questions on Moments

Q2. The diagram shows a crane. The counterweight and the load are able to be moved along the crane arms.

The crane is lifting a load. The load and the counterweight are balanced.

(a) The load is moved away from the pivot, to the right.

(i) What happens to the turning moment produced by the load?

Moment = force x perpendicular distance from the pivot

So if the distance increases the moment increases

 

It increases

(1 mark)

(ii) What should happen to the counterweight to keep the arm balanced?

  • We now have to increase the moment of the counterweight. Therefore the counterweight would also have too be moved away from the pivot (to the left).
  • To increase the moment we could increase the weight itself (more force) but that is impractical and would not happen in practice.

It should be moved away from the pivot to balance

(1 mark)

(b) A load of 4,000 N is placed 10 m from the pivot.

(i) What is the turning moment of the load?

Moment = Fd = 4,000 N x 10 m

Moment = 40,000 Nm

(2 marks)

(ii) How far from the pivot must the 8,000 N counter weight be placed in order to balance the load?

5 metres

If you double the weight applied you need to halve the distance from the pivot point.

(1 mark)

(iii) The counterweight is then placed 3 m from the pivot.

What load could now be balanced 12 m from the pivot?

Anticlockwise Moment = Fd = 8,000 N x 3 m = 24,000 Nm

Clockwise Moment = 24,000 Nm if it balances

So,

24,000 Nm = load x 12 m

load = 2,000 N

(2 marks)

Total 7 marks