The diagram shows a wrench turning a nut.
(a) State the principle of moments for a body in equilibrium
(b) Explain why it is easier to turn the nut with a wrench than with your fingers.
(c) Given that the diameter of the bolt is 1.2 cm and the maximum friction between the nut and the bolt is 48.0 N, find the minimum force the hand needs to exert on the wrench. The maximum distance of the centre of the bolt to the end of the wrench is 24.0 cm. Draw a clearly labelled diagram to show the forces involved.
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Answer:
(a) For a body in equilibrium, the sum of the clockwise moments about any pivot equals the sum of the anti-clockwise moments about the same pivot.
(b) It is easier to turn the nut with a wrench than with your fingers because the distance from the centre of the bolt to where the force is exerted is larger when using the wrench than when using the fingers. Hence, for the wrench, a smaller force is required to create the same turning effect as compared to using the fingers.
(c) Using the Principle of Moments,
and taking moments about the centre of the bolt,
F * 24.0 cm = 48.0 N * 0.6 cm (radius of bolt)
Resolving,
F = 1.2 N
