# Chapter 5: Work, Energy and Power

Doing work is the way of transferring energy from one object to another object.

The work done is defined as the product of force and distance moved in the direction of the force.

W=F ×s

Work done = energy transferred.

Force, distance and direction

The work done by the force depends on the angle between the force and the distance it moves.

Work done = Fs cosƟ

Work done by gas

Gas at pressure p inside a cylinder of cross sectional area A. The cylinder is closed by a moveable piston. The gas pushes the piston a distance s. and force f is applied.
So,
Pressure =force/area
force=pressure ×area
F= p × A
Work done,
W = p × A × s
W = pΔV

Gravitational potential energy (g.p.e.) = mgh

Kinetic Energy (Ek) = mv2

It is given by;

V2 = u2 +2as    (u=0)

V2 =2as

Multiplying both sides by ½

½ mv2 = mas

So, F= ½ mv2

Efficiency = (useful output energy)/(total input energy) ×100%

Principle of conservation of energy

Energy can neither be created nor be destroyed, it can only be transferred from one form to another.

Power

Power is defined as the rate of work done. Its unit is watt.

Power=(work done)/(time taken)
P= W/t

Suppose the body is moving with velocity v. It provides the necessary force F in time t, it travels the distance s which is equal to vt. So the work done by it is:
Work done = force × distance
W= F × v × t
P = W/t = (F ×v×t)/t
P= F × v
Power = force × velocity.