state and prove work energy theorem for constant force
Answers
Answer:
Prove Work-Energy Theorem For A Constant Force
Consider a body of mass moving under the influence of constant force F. From newton’s second law of motion
F = m * a
Where,
F is the constant force, m is the mass of the body and a is the acceleration of the body.
If due to this acceleration a, velocity of the body increases from v1 to v2 during the displacement d then from the equation of motion with constant acceleration, we get
v
2
2
–
v
2
1
=
2
a
d
a =
v
2
2
–
v
2
1
2
d
Now by using this acceleration equation in Newton’s second law of motion, we get
F =
m
∗
v
2
2
–
v
2
1
2
d
or
Fd =
m
∗
v
2
2
–
v
2
1
2
or
Fd =
1
2
m
v
2
2
–
1
2
m
v
2
1
As we know, Fd is the work done by the force F in the moving body through distance d
From the above equation,
The initial Kinetic energy of the body = \( K_{1} =\frac{1}{2} mv_{1}^{2}
\)
The final Kinetic energy of the body = \( K_{2} =\frac{1}{2} mv_{2}^{2}
\)
The change in the Kinetic energy of the body =
Δ
K
=
K
2
–
K
1
Δ
K
=
1
2
m
v
2
2
–
1
2
m
v
2
1
Thus Work done = Change in Kinetic energy (Work energy theorem).