Work Energy And Power

When two bodies stick together after collision, then the collision is said to be perfectly inelastic.
In inelastic collision most of the kinetic energy is lost in other forms (specially as heat). Thus, in inelastic collision the kinetic energy is not conserved but total energy and momentum are conserved.
From law of conservation of momentum



Decrease in kinetic energy




Note: It is not necessary that in inelastic collision, there is always a loss of kinetic energy. If in collision, the potential energy of a body is released then the kinetic energy would increase.

The kinetic energy of a moving body is equal to half the product of the mass of the body and the square of its speed .
Kinetic energy
i.e.,
Let mass of man is and speed is and speed of boy is , then

When man speeds up by , then


Dividing E (1) by (2), we get




Note : In the formula for kinetic energy speed occurs in the second power and so has a larger effect compared to mass.

Force experienced by the surface is equal to change in momentum in one second.
From Newton's second law of motion the rate of change of momentum of a body is equal to the external force applied on the body and the change is momentum always takes place in the direction of the force.
Momentum of ball before inpact
Momentum after inpact
Change in momentum .
Change in momentum due to balls in one
second is .
Change of momentum Force experienced per second

Kinetic energy of cylinder is consumed in doing work against friction in rolling motion.
A body of mass moving with velocity , Possess kinetic energy given by

This kinetic energy is utilized in doing work against the frictional forces.

Where is coefficient of kinetic friction, is mass, is gravity and is displacement.
Equating Egs. (1) and , we get

Where

Given,

Potential energy of the mass at a height above the surface is given by
J ..(i)
Now, KE of the mass at the end of fall
KE = ..(ii)
Applying law of conservation of energy

v =

Using

As power,

As m and a are constants,

For a exploding body, linear momentum is conserved.
From conservation of linear momentum


or
or ...(i)
Thus, ratio of kinetic energies

By work-energy theorem

=500 J

Tension in the string is along the radius of circular path adopted by the bob, while displacement of the bob is along the circumference of the path. Hence, again and are at and so, .