Energy
Kinetic Energy
The energy possessed by a body by virtue of its motion is called kinetic energy.
Examples for body having kinetic energy ;
(i) Flowing water possesses kinetic energy which is used to run the water mills.
(ii) Moving vehicle possesses kinetic energy.
(iii) Moving air (i.e. wind) possesses kinetic energy which is used to run wind mills.
(iv) The hammer possesses kinetic energy which is used to drive the nails in wood.
(v) A bullet fired from the gun has kinetic energy and due to this energy the bullet
Expression for kinetic energy
Let
m = mass of the body, u = Initial velocity of the body (= 0)
F = Force acting on the body, a = Acceleration of the body
s = Distance travelled by the body, v = Final velocity of the body
From \(
v^2 = u^2 + 2as
\)
\(
\begin{gathered}
\Rightarrow v^2 = 0 + 2as \hfill \\
\therefore s = \frac{{v^2 }}
{{2a}} \hfill \\
\end{gathered}
\)
Since the displacement of the body is
in the direction of the applied force, then
work done by the force is
\(
\begin{gathered}
W = F \times s = ma \times \frac{{v^2 }}
{{2a}} \hfill \\
\Rightarrow W = \frac{1}
{2}mv^2 \hfill \\
\end{gathered}
\)
This work done appears as the kinetic energy of the body \(
K.E = W = \frac{1}
{2}mv^2
\)
Examples :
(i) Flowing water possesses kinetic energy which is used to run the water mills.
(ii) Moving vehicle possesses kinetic energy.
(iii) Moving air (i.e. wind) possesses kinetic energy which is used to run wind mills.
(iv) The hammer possesses kinetic energy which is used to drive the nails in wood.
(v) A bullet fired from the gun has kinetic energy and due to this energy the bullet penetrates into a target.
This work done appears as the kinetic energy of the body \(
K.E = W = \frac{1}
{2}mv^2
\). In vector form \(
K.E = \frac{1}
{2}m(\overline v .\overline v )
\)
As m and \(
\overline v .\overline v
\) are always positive, kinetic energy is always positive scalar i.e. kinetic energy can never be negative.
¶¶ Kinetic energy depends on frame of reference :
The kinetic energy of a person of mass m, sitting in a train moving with speed v, is zero in the frame of train but \(
\frac{1}
{2}mv^2
\) in the frame of the earth .