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 320 N. Nick's true weight is 230 N, and the chair weighs 160 N. Nick's feet are not touching the ground.

(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 320 N. What is Nick's acceleration now, again using upward as positive.

I'm having trouble andswering part d, can someone help?

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 320 N. Nick's true weight is 230 N, and the chair weighs 160 N. Nick's feet are not touching the ground. 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 320 N. What is Nick's acceleration now, again using upward as positive.

Explanation / Answer

total weight = 230+160 = 390N
mass = 390/9.8 kg
F = 320 N

F - mg = ma

=> a = (F-mg)/m = F/m -g = 320/( 390/9.8) - 9.8 = -1.758974358974359 m/sec^2

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