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.

1. Mechanical Energy

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 theobject.

2. Potential Energy

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

There are three important types of potential energies:

Gravitational Potential Energy If a body of mass m is raised through a height h against gravity,

then its gravitational potential

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

The variation of potential energy with distance is shown in figure.

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

Potential energy depends upon frame of reference.

2. Electric Potential Energy: The electric potential energy of two point charges ql and q’l. separated by a distance r in vacuum is given by

U = 1 / 4πΣ₀ * q₁ q₂ / r

Here 1 / 4πΣ₀ = 9.0 * 10¹⁰ N-m²/ C² constant.

Work-Energy Theorem

Work done by a force in displacing a body is equal to change in its kinetic energy.  Where, Ki = initial kinetic energy.

Where, K_i = initial kinetic energy

And K_f = final kinetic energy.

Regarding the work-energy theorem it is worth noting that

1. If W _net is positive, then K_f – K_i = positive, i.e., K_f > K_i or kinetic energy will increase and

Vice-versa.

2. This theorem can be applied to non-inertial frames also. In a non-inertial frame it can be written as:

Work done by all the forces (including the Pseudo force) = change in kinetic energy in non-inertial frame.

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.

Principle of Conservation of Energy

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

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.