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Question A mechanic applies a force of 100 N at the end of a spanner to tighten a bolt. The length of the spanner is 0.5 metres. How much torque is exerted on the bolt? If the mechanic increases the force applied by 20% but holds the spanner closer at 0.4 metres, would it result in an increase or decrease of torque?
In first case,
F1 = 100 N
r1 = 0.5 m
Torque 1 = r1 x F1 = 0.5 x 100 = 50 Nm
∴ Torque exerted on the bolt = 50 Nm
In second case,
F2 = F1 + 20% x F1 = F1 + 0.2 x F1 = 1.2 F1 = 1.2 x 100 = 120 N
r2 = 0.4 m
Torque 2 = r2 x F2 = 0.4 x 120 = 48 Nm
Here, Torque 1 > Torque 2
Torque 1 - Torque 2 = 50 Nm - 48 Nm = 2 Nm
∴ The torque will decrease by 2 Nm