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 310 N. Nick's true weight is 290 N, and the chair weighs 160 N. Nick's feet are not touching the ground.

(b) Find Nick's acceleration, using upward as positive.
m/s2

(c) Find the magnitude of the force Nick exerts on the chair.
N

(d*) Instead Nick hands the rope with the scale to his friend Barney, who stands on the ground. Barney pulls on the rope so that the spring scale again reads 310 N. What is Nick's acceleration now, again using upward as positive.
m/s2

Explanation / Answer

Because of the mechanical advantage of the single pulley
both sides of the pulley provides a force on the rope which
pulls (the chair and the boy) upward with 310 N.

Therefore, the total force upward: 620 N.

The total force downwards is the boy's weight and chair's weight:

290 +160 = 450 N

then the total mass: M = W/g = 450 /9.81 = 45.87 kg,

And the net force is 620 - 450 = 170 N upwards.

The acceleration: a = Fnet / M

a = 170 / 45.87 = 3.706 m/s²

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