Figure 4.5 shows an example. The 40 N force is 2.0 m from the pivot, so:
Questions 4.1 Three different forces are shown pulling on a heavy trapdoor. Which force will have the biggest turning effect? Explain your answer.
Studyy tip p If distances are given in cm, the unit of moment will be N cm. Take care not to mix these different units (N m and N cm) in a single calculation.
F3 = 200 N
F2 = 200 N
moment of force = 40 N × 2.0 m = 80 N m
F1 = 100 N
Balancing moments hinge
trapdoor
4.2 A tall tree can survive a gentle breeze but it may be blown over by a high wind. Explain why a tall tree is more likely to blow over than a short tree.
4.2 Calculating moments We have seen that, the greater a force and the further it acts from the pivot, the greater is its moment. We can write an equation for calculating the moment of a force, as shown.
Key definition moment of a force – the turning effect of a force about a point. moment of a force = force × perpendicular distance from pivot to force
The three children in Figure 4.6 have balanced their see-saw – it is in equilibrium. The weight of the child on the left is tending to turn the see-saw anticlockwise. So the weight of the child on the left has an anticlockwise moment. The weights of the two children on the right have clockwise moments. From the data in Figure 4.6, we can calculate these moments: anticlockwise moment = 500 × 2.0 = 1000 N m clockwise moments = (300 × 2.0) + (400 × 1.0) = 600 N m + 400 N m = 1000 N m (The brackets are included as a reminder to perform the multiplications before the addition.) We can see that, in this situation: total clockwise moment = total anticlockwise moment So the see-saw in Figure 4.6 is balanced. 2m
1m
1m
Now let us consider the unit of moment. Since moment is a force (N) multiplied by a distance (m), its unit is simply the newton metre (N m). There is no special name for this unit in the SI system.
2.0 m
500 N
beam
Figure 4.5
pivot
40 N
Calculating the moment of a force.
400 N
300 N
Figure 4.6 A balanced see-saw. On her own, the child on the left would make the see-saw turn anticlockwise; her weight has an anticlockwise moment. The weight of each child on the right has a clockwise moment. Since the see-saw is balanced, the sum of the clockwise moments must equal the anticlockwise moment.
Original material © Cambridge University Press 2014
Chapter 4: Turning effects of forces
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