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?

Answer 1

In first case,

F₁ = 100 N

r₁ = 0.5 m

Torque 1 = r₁ × F₁

= 0.5 × 100

= 50 Nm

∴ Torque exerted on the bolt = 50 Nm

In second case,

F₂ = F₁ + 20% × F₁

= F₁ + 0.2 × F₁

= 1.2 F₁

= 1.2 × 100

= 120 N

r₂ = 0.4 m

Torque 2 = r₂ × F₂

= 0.4 × 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.