Mechanical energy is of two types:

Þ            Kinetic Energy

Þ            Potential Energy

Kinetic energy is the energy which is possessed by a body by virtue of its motion. Kinetic energy of a body is the energy due to its motion. If a body of mass ‘m’ moves with a velocity ‘v’, its kinetic energy is given by

For an unaccelerated body, the resultant force acting on the body is zero. But for an accelerated body, the resultant force is not zero and will do some work. We can relate the work done by this force with the consequent increase in kinetic energy of the body. Consider a body being acted on by various forces

ü        The above equation states that the work done by the resultant external force on a body is equal to the change in the kinetic energy of the body. This relation is called Work-Energy Theorem.

Illustrations

1.      A 50 g bullet strikes a wooden plank and comes to rest after penetrating 10 cm into wood. If wood offers a resistance of 10000 N, what is the velocity with which the bullet strikes the plank?

Sol. Work done by the resistant force, acting on the bullet opposite in the direction of displacement of bullet, is given by

W = 10000 N * (10 * 10²) m

= 1000 J

According to Work-Energy Theorem this should be equal to the change in kinetic energy.

W = K₂K₁

i.e.,                          1000 = 0  K1

(K₂ = 0, because the final velocity of bullet is zero)

K1 = 1/2(mv²) = 1000

where v is the initial velocity of bullet

v² = (2 * 1000 J)/ (5 * 10^-3 kg)

= 4000 (m/s)²

v = 200 m/s