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 270 N. Nick's true weight is 260 N, and the chair weighs 160 N. Nick's feet are not touching the ground. Find Nick's acceleration, using upward as positive. Your response differs from the correct answer by more than 10%. Double check your calculations, m/s^2 Find the magnitude of the force Nick exerts on the chair. 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 270 N. What is Nick's acceleration now, again using upward as positive.

Explanation / Answer

Weight of Nick, Wn = 260 N
Weight of Chair, = 160 N

(a)
Total Upward Force, F = 270 * 2 = 540 N

Total Downward Force = 260 + 160 = 420 N

Net Force = (540 - 420) = 120 N

Force = Mass * Acceleration
120 = (420/9.8) * a
a = 2.8 m/s^2
Acceleration, a = 2.8 m/s^2


(c)
Let the Force exerted by Nick on Chair = N newton
The chair will also exert the same force back on Nick, which is the Normal Force.

So Using Newton equation of motion,
T + N - Wn = Mn * a
270 + N - 260 = 260/9.8 * 2.8
N = 64.3 N

Force Nick exerts on the Chair, = 64.3 N

(d)

Now, Tension in the Rope = 270 N
Total Weight = 420 N
Therefore, Net Acceletion ,a = (270 - 420)/   (420/9.8)
a = - 3.5 m/s^2
( -ve sign means, acceleration is downwards )

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