Question

Derive work-energy theorem. If the velocity of a body of mass 2 kg is changed from 2m/s to 5 m/s by applying a force, calculate the work done by the force on body.

Answer 1

Solution

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Work energy theorem states that the change in kinetic energy of an object 

is equal to the net-work done on it by the net force.

Let us suppose that a body is initially at rest and a force. 

is applied on the body to displace it through

ds

along the direction of the force. Then, a small amount of work done is given by

dw = F.ds = Fds

Also, according to Newton's second law of motion, we have

F = ma 

where a is acceleration produced (in the direction of force) on applying the force. Therefore, 

dw = Mada = Mdtdvds

Now, work done by the force in order to increase its velocity from u (initial velocity) to v (final velocity) is given by

W = ∫uvMvdv = M∫uvvdv

     = M∣2v2∣uv

W = 21Mv2−21Mu2

Hence, work done on a body by a force is equal to the change in its kinetic energy

Explanation:

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