Page 73 - Physics Coursebook 2015 (A level)

Chapter 4: Forces – vectors and moments
WORKED EXAMPLES
2 Is the see-saw shown in Figure 4.18 in equilibrium (balanced), or will it start to rotate?
Step 2 Determine the anticlockwise moment: moment of anticlockwise force = X × 0.8
Step3 Sinceweknowthatthebeammustbebalanced, we can write:
sum of clockwise moments
= sum of anticlockwise moments
20 = X × 0.8
X= 20 =25N
20 N
pivot
40 N
2.0 m
1.0 m
Figure 4.18 Will these forces make the see-saw rotate, or are their moments balanced?
The see-saw will remain balanced, because the 20 N force is twice as far from the pivot as the 40 N force.
To prove this, we need to think about each force individually. Which direction is each force trying to turn the see-saw, clockwise or anticlockwise? The 20 N force is tending to turn the see-saw anticlockwise, while the 40 N force is tending to turn it clockwise.
Step1 Determinetheanticlockwisemoment: moment of anticlockwise force = 20 × 2.0 = 40 N m
Step2 Determinetheclockwisemoment: moment of clockwise force = 40 × 1.0 = 40 N m
Step3 Wecanseethat:
clockwise moment = anticlockwise moment
So the see-saw is balanced and therefore does not rotate. The see-saw is in equilibrium.
3 The beam shown in Figure 4.19 is in equilibrium. Determine the force X.
0.8
20 N
0.5 m 1.0 m 0.8 m
X pivot
Figure 4.19 For Worked example 3.
10 N
So a force of 25N at a distance of 0.8m from the pivot will keep the beam still and prevent it from rotating (keep it balanced).
4 Figure 4.20 shows the internal structure of a human arm holding an object. The biceps are muscles attached to one of the bones of the forearm. These muscles provide an upward force.
biceps 35 cm
4.0 cm
Figure 4.20 The human arm. For Worked example 4.
An object of weight 50 N is held in the hand with the forearm at right angles to the upper arm. Use the principle of moments to determine the muscular force F provided by the biceps, given the following data:
weight of forearm = 15 N
distance of biceps from elbow = 4.0 cm distance of centre of gravity
of forearm from elbow = 16 cm distance of object in the hand from elbow = 35 cm
Step1 Thereisalotofinformationinthisquestion.
It is best to draw a simplified diagram of the forearm that shows all the forces and the relevant distances (Figure 4.21). All distances must be from the pivot, which inthiscaseistheelbow.
The unknown force X is tending to turn the beam anticlockwise. The other two forces (10 N and 20 N) are tending to turn the beam clockwise. We will start by calculating their moments and adding them together.
Step1 Determinetheclockwisemoments: sum of moments of clockwise forces
= (10×1.0)+(20×0.5) = 10+10=20Nm
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