Serway & Jewett — Conservation of Energy: Problem 26

As shown in Figure P8.26, a light string that does not stretch changes from horizontal to vertical as it passes over the edge of a table. The string connects \(m_1\), a 3.50-kg block originally at rest on the horizontal table at a height \(h = 1.20\) m above the floor, to \(m_2\), a hanging 1.90-kg block originally a distance \(d = 0.900\) m above the floor. Neither the surface of the table nor its edge exerts a force of kinetic friction. The blocks start to move from rest. The sliding block \(m_1\) is projected horizontally after reaching the edge of the table. The hanging block \(m_2\) stops without bouncing when it strikes the floor. Consider the two blocks plus the Earth as the system. (a) Find the speed at which \(m_1\) leaves the edge of the table. (b) Find the impact speed of \(m_1\) on the floor. (c) What is the shortest length of the string so that it does not go taut while \(m_1\) is in flight? (d) Is the energy of the system when it is released from rest equal to the energy of the system just before \(m_1\) strikes the ground? (e) Why or why not?