Question

A mass M hangs from a uniform rope of length L and mass m. Find an expression for

the rope tension as a function of the distance y measured downward from the top of
the rope.

Answer 1

The tension equals Mg from the mass plus mg from the rope, minus the amount of rope down from the top to some point, y. using the mass per unit length of the rope: m/l
T = Mg + m/L(L-y)g
= Mg + mg - m/L yg = (M + m)g - (m/L)yg

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