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Working with a block-pulley system

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Please see the attached file for full problem description.

Please use work concepts for solution. The solution should involve integration from 2 to 0 distance block travel.

Please detail any calculus involved - if the response doesn't involve calculus, I would still like to see it, but please explain why since I am fairly certain that calculas and work concepts should be involved.

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The work-energy principle states that the net work done on an object is equal to its change in kinetic energy,

W = d(KE) ----(1)

We are releasing the block from rest. Thus the initial KE = 0 and it will acquire some KE after some time.

Thus, W = KE_final - KE_initial = Final KE

Thus we have to find the work done by the force to pull the block up the incline through a distance of 2ft.

We have, work done = force * distance moved

We have 30 lb force applied downwards on the hanging pulley therefore, tension (T) on each side of the pulley will be 30/2 = 15 lb

The force acting on the block will be ...

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