Question

A box (mass 25.8 kg) sits on a rough incline that makes an angle α = 28.1o with the horizontal. A massless string is tied to the box, runs parallel to the incline, passes over a massless, frictionless pulley, and is tied to mass M hanging on the other end. Assume μs = 0.455 is the coefficient of static friction between the box and the surface of the plane. Find the maximum value of M, in kg, for which this system can be in equilibrium.

part b

A box (mass 94.2 kg) sits on a rough incline that makes an angle α = 60.1o with the horizontal. A massless string is tied to the box, runs parallel to the incline, passes over a massless, frictionless pulley, and is tied to mass M hanging on the other end. Assume μs = 0.12 is the coefficient of static friction between the box and the surface of the plane. Find the minimum value of M, in kg, for which this system can be in equilibrium.

part c

A box of mass 57.6 kg is initially sliding upward (in the positive direction) on a rough incline that makes an angle α = 58.3o with the horizontal. As in the previous problem: a massless string is tied to the box, runs parallel to the incline, passes over a frictionless pulley and is tied to mass M = 37.4 kg hanging on the other end. Assume the coefficient of kinetic friction between the box and the surface of the incline is μk = 0.268. Find a, the acceleration of the masses. The direction is given by the sign of the answer: up the incline is positive, down the incline is negative.

Answer 1

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