Serway & Jewett — The Laws of Motion: Problem 42

A rope with mass \(m_r\) is attached to a block with mass \(m_b\) as in Figure P5.42. The block rests on a frictionless, horizontal surface. The rope does not stretch. The free end of the rope is pulled to the right with a horizontal force \(\vec{F}\). (a) Draw force diagrams for the rope and the block, noting that the tension in the rope is not uniform. (b) Find the acceleration of the system in terms of \(m_b\), \(m_r\), and \(F\). (c) Find the magnitude of the force the rope exerts on the block. (d) What happens to the force on the block as the rope’s mass approaches zero? What can you state about the tension in a light cord joining a pair of moving objects?