Question

A block of mass = M (measured in kg) is supported by a massless string wound on a uniform solid cylinder, which has a mass = 3M . The radius of the cylinder = R (in units of meters) and the axle about which the cylinder turns has no friction. The system, shown in the accompanying diagram, is released from rest and the falling mass unwinds the rope without any slipping of the rope as the mass falls.

(a) How far does M fall, as a multiple of R, in the time that it takes for the 3M cylinder complete exactly one revolution?

(b) Use Work/Energy concepts to derive an expression for the linear velocity of M at the time the cylinder has completed exactly one revolution. Your answer should be expressed in terms of g, and R (as necessary) and numerical constants.

(c) Use the kinematic equations to find the linear acceleration of M. Express this acceleration in terms of g.

Answer 1

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