Question

A 20-centimeter wrench is used to loosen a bolt. The force is applied 0.20m from the bolt. It takes 50 newtons to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30-degree angle from perpendicular?

Answer 1

The force would be 57.8 N if it was applied at a 30-degree angle from perpendicular.

Step-by-step explanation:

We know that torque and force are represented by the following equation

τ = r x F sinθ ---- (1)

where τ is Torque, r is radius, F is force and θ is the angle between the force and lever arm.

Given data:

F = 50 N

r = 0.2 m

we have to find the force when θ = 30°

Putting these values in equation 1, we get

τ = 0.2 x 50 x sin(90°)

τ = 10 Nm

so Torque is 10 Nm

Now we will calculate the force was applied at a 30 degree angle from perpendicular, in this case the equation 1 becomes as

τ = r x F cosθ

Putting the values of τ , r, θ and F in above equation

10 = 0.2 x F x cos(30°)

Rearranging the above equation

F = 10 / (0.2 x cos (30°))

F = 10 / 0.173

F = 57.8 N