# Work, Energy and Power

The product of force and displacement (in the direction of force), during which the force is acting, is defined as **work**.

When 1 N force is applied on a particle and the resulting displacement of the particle, in the direction of the force, is 1 m, the work done is defined as 1 J (joule). The dimensional formula of work is M^{1}L^{2}T^{-2}.

The displacement may not be in the direction of the applied force in all cases. If the displacement, d, makes an angle θ with the applied force, F, then

Work, W = force × displacement in the direction of the force

**W = F (d cos θ)**

- For θ = π/2, W = 0, even if F and d are both non-zero. In uniform circular motion, the centripetal force acting on a particle is perpendicular to its displacement. Hence, the work done due to centripetal force during such a motion is zero.
- If θ < π/2, work done is positive and is said to be done on the object by the force.
- If π/2 < θ < π, work done is negative and is said to be done by the object against the force.

### Kinetic Energy

The capacity of a body to do work, by virtue of its motion, is known as the kinetic energy of the body.

More the speed of the object, more is its kinetic energy. The net force acting on a body produces acceleration or deceleration in its motion thereby changing its velocity and kinetic energy.

The work, W, done by the force, F, on a particle of mass, m, causing acceleration, a and displacement, d is given by

W = F . d

W = m x (a . d)

Using, v^{2} - u^{2} = 2ad

W = m(v^{2} - u^{2})/2

W = ½mv^{2} - ½mu^{2}

= Change in kinetic energy = ΔK

The unit of kinetic energy is the same as that of work - joule.

### Potential Energy

The capacity of a body to do work, by virtue of its position in a force field or due to its configuration is known as the potential energy of the body.

### Power

Power is defined as the work done per unit time.

Power is a scalar quantity like work and energy. Its unit is watt (W).

1 W = 1 J /s. Its dimensional formula is M^{1}L^{2}T^{-3}.