An inventive child wants to reach an apple in a tree without climbing the tree.

Question

An inventive child 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), the child pulls on the loose end of the rope with such a force that the spring scale reads 268 N. The child's true weight is 302 N, and the chair weighs 160 N. The child's feet are not touching the ground.

An inventive child 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), the child pulls on the loose end of the rope with such a force that the spring scale reads 268 N. The child's true weight is 302 N, and the chair weighs 160 N. The child's feet are not touching the ground. Show that the acceleration of the system is upward. (Do this on paper. Your instructor may ask you to turn in this work.) Find its magnitude. Find the force the child exerts on the seat of the chair.

Explanation / Answer

a) 2*268-302-160 = ma

2*268-302-160 = (302+160)*a/9.81

a=1.57

b) sum forces to the chair

268 - 160 -N = (160)*1.57/9.81

N=82.4 N

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