One end of the pile of chain falls through a hole in its support and pulls the remaining...

One end of the pile of chain falls through a hole in its support and pulls the remaining links after it in a steady flow. If the links which are initially at rest acquire the velocity of the chain suddenly and without frictional resistance or interference from the support or from adjacent links, find the velocity v of the chain as a function of x if v = 0 when x = 0. Also find the acceleration a of the falling chain and the energy Q lost from the system as the last link leaves the platform. (Hint: Apply Eq. 4/20 and treat the product xv as the variable when solving the differential equation. Also note at the appropriate step that dx = v dt.) The total length of the chain is L, and its mass per unit length is ρ.