Hi. I've started this problem, and have managed as far as proving the result for acceleration. If someone could finish it, or explain how to finish it so that I can finish it myself, that would be great. Thanks.
A planed is inclined at an angle arctan ¾ to the horizontal and a small, smooth, light pulley P is fixed to the top of the place. A string, APB, passes over the pulley. A particle of mass m1 is attached to the string at A and tests on the inclined place with AP parallel to a line of greatest slope in the place. A particle of mass m2, where m2 > m1, is attached to the string at B and hangs freely with BP vertical. The coefficient of friction between the particle at A and the plane is ½.
The system is released from rest with the string taut. Show that the acceleration of the particles is ((m2 – m1)g)/(m2 + m1).
At a time T after release, the string breaks. Given that the particle at A does not reach the pulley at any point in its motion, find an expression in terms of T for the time after release at which the particle at A reaches its maximum height. It is found that, regardless of when the string broke, this time is equal to the time taken by the particle at A to descend from its point of maximum height to the point at which it was released. Find the ratio m1 : m2.