#### Need Help?

Get in touch with us  # Law of Conservation of Mechanical Energy – Types with Examples

## Conservation of Mechanical Energy

### Gravitational potential energy:

Gravitational potential energy can be defined as the energy possessed by the body with respect to other bodies in the gravitational field.

Gravitational potential energy is given by

U = mgh

Where,

U= gravitational potential energy

m = mass

g = acceleration due to gravity

h = heigh at which body experiencing potential energy

### Elastic potential energy:

The energy is possessed by anybody which has elastic property (spring). The potential energy created in the body before the release, or the relaxation of the body is called elastic potential energy.

The elastic potential energy is given by the magnitude of the force in the ideal spring.

F = Kx

Where,

F = magnitude of the force

K = spring constant

X = displacement of the spring

The elastic potential energy is given by

U = ½ k x2

### Mechanical energy:

Mechanical energy is the sum of kinetic energy and potential energy of the body.

M.E = K.E + P. E

#### The formula for the mechanical energy:

As we discussed that the mechanical energy is the sum of kinetic energy and potential energy,

I.e., Mechanical energy = potential energy + kinetic energy

M.E = ½ mv2+ mgh

#### Law of conservation of energy:

Law of conservation of energy states that energy is neither created nor destroyed but changes from one form to another.

#### Example:

Consider a ball that is at height h and is at rest.

To prove a law of energy conservation, we have to show that the energy in each case is equal.

#### Case 1:

Consider ball is at heigh H.

Here the balls have potential energy and kinetic energy is zero.

P.E = mgH

K.E = 0

P.E + K.E = 0 + mgH

M.E = mgH

#### Case 2:

Consider a ball falling freely from the height H.

Here the ball has both potential energy and kinetic energy.

P.E = mgh

K.E = ½ mv2

But v = √2g(H−h)

Sub v in K.E

M.E = K.E + P.E

M.E = 1/2 m(√2g(H−h))2 + mgh

M.E = mgH

#### Case 3:

Consider that a ball reached to the ground from the height H.

Here the potential energy is zero, and the ball has only kinetic energy.

P.E = 0

K.E = ½ mv2

But v =√2gH

Sub v in K.E

M.E = K.E + P.E

M.E = 1/2 m(√2gH)2 + 0

M.E = mgH

## Summary

Mechanical energy:
Mechanical energy is the sum of kinetic energy and potential energy of the body.
M.E = K.E +P.E

The formula for the mechanical energy:
As we discussed that the mechanical energy is the sum of kinetic energy and potential energy,
I.e., Mechanical energy = potential energy + kinetic energy
M.E = 1/2mv2+ mgh

Law of conservation of energy:
Law of conservation of energy states that energy is neither created nor destroyed but changes from one form to another.
K=spring constant
X = displacement of the spring
The elastic potential energy is given by
U= 1/2 k x2

#### Related topics #### Different Types of Waves and Their Examples

Introduction: We can’t directly observe many waves like light waves and sound waves. The mechanical waves on a rope, waves on the surface of the water, and a slinky are visible to us. So, these mechanical waves can serve as a model to understand the wave phenomenon. Explanation: Types of Waves: Fig:1 Types of waves […] #### Dispersion of Light and the Formation of Rainbow

Introduction: Visible Light: Visible light from the Sun comes to Earth as white light traveling through space in the form of waves. Visible light contains a mixture of wavelengths that the human eye can detect. Visible light has wavelengths between 0.7 and 0.4 millionths of a meter. The different colors you see are electromagnetic waves […] #### Force: Balanced and Unbalanced Forces

Introduction: In a tug of war, the one applying more force wins the game. In this session, we will calculate this force that makes one team win and one team lose. We will learn about it in terms of balanced force and unbalanced force. Explanation: Force Force is an external effort that may move a […]   