An Atwood’s machine with a pulley in the shape of a uniform disk of mass M and r

Question

An Atwood’s machine with a pulley in the shape of a uniform disk of mass M and radius R is in an elevator having vertical acceleration A relative to the ground. Let positive A correspond to the elevator accelerating upward. Mass mA hangs on the left side of the pulley while mass mB hangs on the right. The rope connecting masses mA and mB is massless. The pulley is suspended from the ceiling of the elevator by a spring of spring constant k and natural length l.

Determine a general expression for the length of the spring in terms of the given variables.

Explanation / Answer

As, Force in spring , F = kx

=> general expression for the length of the spring =   natural length + stretched length

                                                                           =   l + [(mA + mB + M) * g]/k

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