Question

A body P (shown in red) of mass m is at the base of a fixed rough inclined plane of inclination a to the horizontal and elevation h. A light inelastic string is attached to P and passes over a smooth pulley (shown in yellow) at the top of the plane where it is attached to a body Q (shown in white) of mass M initially adjacent to the pulley and able to move vertically downwards. Initially, the system is a rest, the body Q is next to the pulley at height h above the horizontal, and the plane has friction coefficient . The diagram below shows a snapshot of the system shortly after the body Q is released. Po a (a) Copy the diagram above, label the forces acting and formulate Newton's equations of motion for the system. (b) Show that M > m(u cos a + sin a). (c) Assuming the condition in part (b) above is satisfied, find in terms of m, M, u, h, g and a, an expression for the speed of P when Q is level with the initial position of P.

Answer 1

Ma Ma- T ma T-mgsin-g m Thee are eg of nsh as som T7 mosindtrmgco Mg7T7 mgsinLumo minltemg cas MY MLsin+ LicoR). Inital peed duslance hrauelSh ED Now acdding Mem)a Mg-mg sin-4g C LM-msin-Mucos Mtm

v2-uP+ 9as ing 2 Ot (M-msind- umos) ah V= CM-msin -umcosx) gh Mtm Thi usl be the