A uniform chain of mass M and length L is suspended vertically such that its lower end just touches a horizontal floor. The chain is then released from rest. Any portion of the chain that strikes the floor immediately comes to rest. Assuming the chain does not pile up into a heap on the floor, determine the force it exerts on the floor when a length x has reached the floor.

Step-by-step solution

Let = M L be the linear mass density of the chain. When a length x of the chain has reached the floor, the chain has fallen through a distance x . The velocity of the falling portion of the chain is v = 2gx . The force exerted by the chain on the floor consists of two components. The weight of the portion of the chain lying on the floor is given by: W = ( x)g = Mgx L The thrust force due to the continuous impact of the falling chain is equal to the rate of change of momentum. The rate at which mass strikes the floo