Mass 2 m is attached to mass m with a light cable, strung over a pulley of mass
ID: 2076732 • Letter: M
Question
Mass 2 m is attached to mass m with a light cable, strung over a pulley of mass m, and moment of inertia I = mr^2. Mass 2 m rests on an wedge of inclination theta, compressing a spring with constant k to - x past the springs equilibrium position x_0. The system starts at rest, but is not in equilibrium. Assuming - x and k are large enough to move 2m up the incline, what must the coefficient of kinetic friction mu_k between mass 2 m and the incline be so that mass 2 m travels distance d past x_0 before stopping? What must the coefficient of static friction be so that after 2m travels d, it stays at rest? Answer in terms of m, r, theta, k, d, x, x_0.Explanation / Answer
Solution :-
Mass = 2m is attached to mass m with a light cable, strung over a pulley oof mass m and moment of inertia I = mr^2
Mass 2m rests on an wedge of inclination , compressing a spring with constant k to -x past the springs equilbrium position xo.
The system starts at rest, but is not in equilbrium.
Assuming -x and k are large enough to move 2m and incline,
Coefficient of friction betwen mass 2m and incline 2m travels distance d past xo before stooping =
(2m-m) Cos/ k(x-xo)
= (m) Cos/ k(x-xo)