PHYSICS-Force and torque question (I am confused on these types of problems)

Question

The tune-up specifications of a car call for the spark plugs to be tightened to a torque of 34 N⋅m . You plan to tighten the plugs by pulling on the end of a 25-cm-long wrench. Because of the cramped space under the hood, you'll need to pull at an angle of 120' with respect to the wrench shaft.

1. With what force must you pull?

Answer 1

120° is 30° greater than the 90° angle providing maximum torque (for a given force).

So θ = 30° in the figure above.

τ = 34 N⋅m = (0.25 m)(Fcosθ N) = (0.25 m)(Fcos(30°) N) = (0.25 m)((√3/2)F N)

So F = (34 N⋅m)/[(0.25 m)(√3/2))] = 157 N