Question

A 28 cm wrench applies 53 N of force to loosen a bolt when force is applied at the end in a perpendicular manner. What force is required if the same torque is applied at a 53° angle? Answers:

106 N
86 N
96 N
118 N

Answer 1

66.42 N

Step-by-step explanation:

Torque is defined as the product of force and the perpendicular distance.

`\tau =r* F* Sin\theta`

Where, r be the distance, f be the force and θ be the angle between the force vector and the distance vector

Case I :

F = 53 N, r = 28 cm = 0.28 m, θ = 90°

So,
`\tau_(1) =0.28 * 53* Sin90`

`\tau _(1)=14.84 Nm`

case II :

F = ?, r = 0.28 m, θ = 53°

Let the force be F for the same toque.

`\tau_(1) =0.28 * F* Sin53`

`14.84 Nm=0.28* F* Sin53`

F = 66.42 N

Thus, the force required is 66.42 N.