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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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Solution Preview

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 ...

Solution Summary

The solution gives all steps along with proper explanations so that you can solve similar problems yourself. All mathematical steps are clearly shown.