Work and Kinetic Energy

A particle with mass m moving in a straight line under the action of a constant resultant force with magnitude F direction same along axis . the particle's acceleration is constant . Work done by resultant force F is equal to the total work Wtot done by all the force.
The kinetic energy K of the particle defined as


K= 1/2mv^2

And We can say that the work done by the resultant external force on a particle is equal to the change in kinetic energy of particle

Wtot = K2-K1 = delta K

This result is called the work-energy theorem. Kinetic energy is a scalar quantity.


Example 1. Assume the force of gravity to be constant for small distance above the surface of the earth. A body is dropped from rest at the height h a bove the earth's surface. What will its kinetic energy be just beforce it strikes the ground ?

solution
The gain in kinetic energy is equal to the work done by the resultant force, which here is the force of gravity. This force is constant and directed along the line of motion, so that the work done by gravity is



W=F.d =mgh

Initially the body has speed v0=0 and finally a speed v. The gain in kinetic energy of the body is

1/2 mv^2-1/2mv0^2 = 1/2mv^2 - 0.
Equating these two equivalent terms we obtain

K =1/2 mv^2 =mgh
as the kinetic energy of the body just before it strikes the ground.
The speed of the body is then

v=sqrt(2gh)

If the body is falled from a height h1 to a height h2 a body will increase its kinetic energy from 1/2 mv2^2 -1/2 mv1^2 = mg(h1-h2).

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