initial velocity of a block is zero, prove work energy theorem in a time interval of 5 second
Answers
Answer: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
d
s
along the direction of the force. Then, a small amount of work done is given by
dw =
F
.d
s
= 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 = M
dt
dv
ds
Now, work done by the force in order to increase its velocity from u (initial velocity) to v (final velocity) is given by
W = ∫
u
v
Mvdv = M∫
u
v
vdv
= M∣
2
v
2
∣
u
v
W =
2
1
Mv
2
−
2
1
Mu
2
Hence, work done on a body by a force is equal to the change in its kinetic energy.
Explanation: