**Subject :**Elements of Mechanical Engineering

## Work and Energy

**Work and Energy:**** **Newton's law for a particle moving relative to an inertial reference is given by,

Multiplying each side of the equation by d** r** as a dot product and integrating from

*r*

_{1}to

*r*along the path of motion:

_{2}

Thus, the work done on the particle is equal to change in its kinetic energy.

If we write Newton's law in component form,

then,

or,

Taking the dot product of this equation with

Similarly,

Thus, the work done on a particle in any directions equals the change in kinetic energy associated with the component of velocity in that direction.

Instead of using Newton's law, one can use energy equation. One example is provided.