Chapter 3 Question2

Question

Question 2:  When unable to loosen the lug nut on an automobile tire a mechanic may put a piece of pipe on the handle of the tire so as to extend its length. Please explain from Physics point of view how does that help.

Answer 1

The lug nut is tightened to a certain torque value. In order to loosen the lug nut the mechanic must apply slightly more torque in the opposite direction from that used to tighten it. Torque is a force applied at a distance, or T = Fd. To achieve more torque, one can either increase the force or increase the distance that the force is applied. To increase the distance, the mechanic can put a pipe on the handle of the wrench being used to apply the force. This effectively increases the length of the handle and the distance that the force is applied.

d₁ is the length of the handle of the wrench before a pipe is put on. Let's say it is 0.25 m and lets say the the applied force is 200 N. Then the torque applied to the lug nut in this case is 200(0.25) = 50 Nm. Now, let's say we put a pipe on and double the length of the wrench (d₂) to 0.5 m and still apply the same 200 N force. Then the torque applied to the lug nut will be 200(0.5) = 100 Nm (twice as much torque).