Chapter 4, Problem 45P

An inventive child named Nick wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P4.45), Nick pulls on the loose end of the rope with such a force that the spring scale reads 250 N. Nick’s true weight is 320 N, and the chair weighs 160 N. Nick’s feet are not touching the ground. (a) Draw one pair of diagrams showing the forces for Nick and the chair considered as separate systems and another diagram for Nick and the chair considered as one system. (b) Show that the acceleration of the system is upward and find its magnitude. (c) Find the force Nick exerts on the chair.

Figure P4.45

Problems 45 and 46.

46. In the situation described in Problem 45 and Figure P4.45, the masses of the rope, spring balance, and pulley are negligible. Nick’s feet are not touching the ground. (a) Assume Nick is momentarily at rest when he stops pulling down on the rope and passes the end of the rope to another child, of weight 440 N, who is standing on the ground next to him. The rope does not break. Describe the ensuing motion. (b) Instead, assume Nick is momentarily at rest when he ties the end of the rope to a strong hook projecting from the tree trunk. Explain why this action can make the rope break.