A heavy chain with a mass per unit length ispulled by the constant force P along a

Chapter 3, Problem 3/34

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A heavy chain with a mass \(\rho\) per unit length is pulled by the constant force P 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 P is greater than \(\mu_k \rho g L\) in order to initiate motion.

                                                         

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