An inventive child named Nick wants to reach an apple in a tree without climbing

Question

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 (see figure below), 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. The masses of the rope, spring balance, and pulley are negligible and 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.

Explanation / Answer

a)When Nick passes to the boy, the total tension in the rope exceeds 440N (it is 480N=320+160) and therefore, the boy will be lifted off his feet. and NIck would move down.

b)Tying the rope to a tree trunk will increase the tension in the rope to 480N since it would not allow any motion. Therefore, the rope may break under this increases tension.

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