A heavy chain with a mass per unit length `p` is pulled by the constant force `F` along a horizontal surface consisting of a smooth section and a rough section. The chain is initially at rest on the rough surface with `x = 0` . If the coefficient of kinetic friction between the chain and the rough surface is `mu_(k)` determine the velocity `v` of the chain when `x = L` . The force `F` is greater than `mu_(k) pgL` in under to initiate the motion ,

Answer

`[sqrt((2F)/(rho)-mu_(k)gL)]`