Question

A fixed pulley carries a weightless thread with masses m₁ and m₂ at its ends. There is friction between the thread and the pulley. It is such that the thread starts slipping when the ratio m₂/m₁ = η₀. Find:

(a) the friction coefficient;

(b) the acceleration of the masses when m₂/m₁ = η >η₀.

Answer 1

Let, us consider a small element of the thread and draw free body diagram for this element.

(a) Applying Newton's second law of motion in projection form, F_n=mw_n for this element, 

(b) When m₂/m₁= η, which is greater than η₀ the blocks will move with same value of acceleration. (say w) and clearly m₂ moves downwards. From Newton's second law in projection from(downward for m₂ and upward for m₁) we get: