#### Need Help?

Get in touch with us

# Law of Conservation of Mechanical Energy – Types with Examples

## Conservation of Mechanical Energy

### Key Concepts

• Mechanical energy
• The formula of mechanical energy
• Law of conservation of 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

#### Define Position Time Graph and its Types

Key Concepts • Slope of a graph • Position time graph • Slope of s-t graph = Velocity • Types of position time graphs Introduction An object in a uniform motion covers equal distances in equal intervals of time. This also indicates that it moves at a constant velocity. When its position at different instants […]

#### Magnetic Field Lines: Definition, Explanation and Q&A

Key Concepts Magnetic Field Magnetic Field Lines properties of magnetic field lines Uniform and non uniform magnetic lines Introduction Two magnets when placed close to each other attract and stick to each other. However, if we go on increasing the distance between them, the attraction between them reduces gradually to such an extent that they […]

#### The Life Cycles of Stars: Meaning and Example

Key Concepts Stars Analysis of starlight Composition of stars Stars’ temperature Size and mass of stars Stages of life cycle of a star Introduction Stars are huge, shining balls of extremely hot gas (known as plasma) in space. The Sun is our nearest star. During the nighttime, many other stars are visible to the naked […]  