A technician tightens a bolt using a T-shaped hex key
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A technician tightens a bolt using a T-shaped hex key. The straight shaft of the key extends 0.18\,m from the centre of the bolt. The technician applies a 35\,N force at the end of the shaft in a vertical plane such that the force makes an angle of 25∘ above the shaft.
(a) Starting from fundamental definitions, derive a symbolic expression for the magnitude of the torque produced about the bolt in terms of the applied force F, the distance r, and the angle θ between F and the shaft.
(b) Using F=35N, r=0.18m, and θ=25∘, calculate the numerical value of the torque in newton–metres.
(c) The bolt manufacturer specifies that a minimum of 5.0\,N·m of torque is required. If the technician can only apply the force at 60∘ to the shaft, determine the minimum force that must be exerted to meet the specification. Show all steps in your calculation.