state and prove work energy theorem 3 marks question
Answers
Step-by-step explanation:
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.
F
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.