When a force acts on an object and the object actually moves in the direction of force, then the work is said to be done by the force.
Work done by the force is equal to the product of the force and the displacement of the object in the direction of force.
If under a constant force F the object displaced through a distance s, then work done by the force
Here θ is the angle between and .
Work done by a force is zero, if
(a) body is not displaced actually, i.e., s = 0
(b) body is displaced perpendicular to the direction of force, i.e.,
θ = 90°
Work done by a force is positive if angle between F and s is acute angle.
Work done by a force is negative if angle between F and s is obtuse angle.
Work done by a constant force depends only on the initial and final Positions and not on the actual path followed between initial and final positions.
The time rate of work done by a body is called its power.
Power = Rate of doing work = Work done / Time taken
If under a constant force F a body is displaced through a distance s in time t, the power
p = W / t = F * s / t
But s / t = v ; uniform velocity with which body is displaced.
∴ P = F * v = F v cos θ
where θ is the smaller angle between F and v.
power is a scalar quantity. Its S1 unit is watt and its dimensional formula is [ML2T-3].
Its other units are kilowatt and horse power,
1 kilowatt = 1000 watt
1 horse power = 746 watt
Energy of a body is its capacity of doing work.
It is a scalar quantity.
Its S1 unit is joule and CGS unit is erg. Its dimensional formula is [ML3T-3].
There are several types of energies, such as mechanical energy (kinetic energy and potential energy), chemical energy, light energy, heat energy, sound energy, nuclear energy, electric energy etc.
The sum of kinetic and potential energies at any point remains constant throughout the motion. It does not depend upon time. This is known as law of conservation of mechanical energy.
Mechanical energy is of two types:
1. Kinetic Energy
The energy possessed by any object by virtue of its motion is called its kinetic energy.
Kinetic energy of an object is given by
k = 1 / 2 mv2 = p2 / 2m
where m = mass of the object, U = velocity of the object and p = mv = momentum of the object.
2. Potential Energy (U):- Potential energy of a body is defined as, U = mgh
Here, m is the mass of the body, g is the free fall acceleration (acceleration due to gravity) and h is the height.
3. Gravitational Potential Energy:- An object’s gravitational potential energy U is its mass m times the acceleration due to gravity g times its height h above a zero level.
U = mgh