# 1.6 Energy, work and power \$

The energy of a body is its capacity of doing work.

It is a scalar quantity.

Its SI 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.

Mechanical Energy

The sum of kinetic and potential energies at any point remains constant throughout the motion. It does not depend on upon time. This is known as the law of conservation of mechanical energy.

Mechanical energy is of two types:

1. Kinetic Energy

The energy possessed by an object by virtue of its motion is called its kinetic energy.

The 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

The energy possessed by an object by virtue of its position or configuration is called its potential energy.

There are three important types of potential energies:

(i) Gravitational Potential Energy If a body of mass m is raised through a height h against gravity, then its gravitational potential energy = mgh,

((ii) Elastic Potential Energy If a spring of spring constant k is stretched through a distance x, then the elastic potential energy of the spring = 1 . 2 kx2

Potential energy is defined only for conservative forces. It does not exist for non-conservative forces.

Potential energy depends upon the frame of reference.

Mass-Energy Equivalence

According to Einstein, the mass can be transformed into energy and vice – Versa.

When Δm. mass disappears, then produced energy

E = Δmc2

where c is the speed of light in vacuum.

The principle of Conservation of Energy

The sum of all kinds of energies in an isolated system remains constant at all times.

The principle of Conservation of Mechanical Energy

For conservative forces, the sum of kinetic and potential energies of any object remains constant throughout the motion.

According to the quantum physics, mass and energy are not conserved separately but are conserved as a single entity called ‘mass-energy’.

Collisions

A collision between two or more particles is the interaction for a short interval of time in which they apply relatively strong forces on each other.

In a collision physical contact of two bodies is not necessary. There are two types of collisions:

1. Elastic collision

The collision in which both the momentum and the kinetic energy of the system remains conserved are called elastic collisions. In an elastic collision, all the involved forces are conservative forces. Total energy remains conserved.

2. Inelastic collision

The collision in which only the momentum remains conserved but kinetic energy does not remain conserved are called inelastic collisions. In an inelastic collision, some or all of the involved forces are non-conservative forces. The total energy of the system remains conserved. If after the collision two bodies stick to each other, then the collision is said to be perfectly inelastic.