derive mathematical expression for potential energy kinetic energy and mechanical energy
Answers
Answer:
Solution
Formula for kinetic energy:
Let a body of mass m moving with a velocity u.
After a time t due to a force F which produces acceleration a in the body and it changes the velocity of the body to v.
Thus, we have;
The initial velocity of the body = u
Final velocity of the body = v
The force applied on the body = F
Acceleration in the body = a
Let the displacement in the body is s, then,
The work done on the body = Force applied on the body
×
displacement in the body
W = F
×
s ........(1)
Using the second law of motion;
F= ma........(2)
And according to the third equation of motion;
v
2
=
u
2
+
2
a
s
Thus,
s
=
v
2
−
u
2
2
a
.........(3)
From equations (1), (2) and (3), we get;
W
=
m
a
×
v
2
−
u
2
2
a
W
=
1
2
m
(
v
2
−
u
2
)
As the body is ibn motion; the work done on the body = Kinetic energy of the body
Thus,
K
=
1
2
m
(
v
2
−
u
2
)
For initial velocity(u) = 0
We get;
K
=
1
2
m
v
2
This is the formula for the kinetic energy of a body.
The formula for Potential energy:
The energy possessed by a body due to the position of the body is called the potential energy of the body.
Let a body of mass m is brought to a height of h,
Then work done
W=
w
e
i
g
h
t
o
f
t
h
e
b
o
d
y
×
h
e
i
g
h
t
W=mgh
Since at height the body is kept therefore the work done to place the body at height h is the potential energy of the body.
Thus,
P=mgh
This is the formula for the potential energy of a