**Note**
- Enter the values of the mass ,velocity and height in the text boxes

- Click on the calculate button to get Total Energy

**Mechanical Energy Formula used**
Mechanical Energy= Kinetic Energy + potential energy
$\text{TE}=\frac {1}{2} mv^2 + mgH$

Where m -> mass

v -> velocity of the object

g -> Acceleration due to gravity( 9.8 $m/s^2$)

H -> Height of the object

### Mechanical Energy Calculator

## What is Mechanical Energy

Mechanical energy is the sum of the kinetic energy and Potential energy. It is basically the ability of the body to do work because of the motion of the body and position of the body. If the system is isolated and only forces acting are conservative forces,then mechanical energy is conserved.

Mechanical energy is given by the Formula

M.E = K.E + P.E
Now K.E as we know is given by

$K = \frac {1}{2} mv^2$

Also if only gravitational forces are acting on the system, the P.E is given as

P.E= mgH

Therefore Mechanical energy will be given by below formula

$M= \frac {1}{2} mv^2 + mgH$

Where

m -> mass of the object

v -> speed of the object

g -> Acceleration due to gravity

H -> Position of the object

**Example of Few questions where you can use this Mechanical Energy Formula**

**Question 1**

Calculate the Mechanical energy of the object have mass 10 kg and velocity 3m/s and height above the ground is 10 m

(g=10 m/s^{2})

**Solution**
Given , m=10 kg, v=3 m/s , H=10 m, g=10 m/s^{2}, M=?

Mechanical energy is given by below formula

$M= \frac {1}{2} mv^2 + mgH$

$M = \frac {1}{2} \times 10 \times 3^2 + 10 \times 10 \times 10=1030 J

**Question 2**

calculate the Kinetic Energy,Potential energy and Mechanical energy of the object have mass 1 kg and velocity 2m/s and height above the ground is 50 m

(g=10 m/s^{2})

**Solution**
Given , m=1 kg, v=2 m/s , H=50 m, g=10 m/s^{2}, M=? ,K=?, P=?

Kinetic energy is given by

$K= \frac {1}{2} mv^2= \frac {1}{2} \times 1 \times 2^2= 2 \ J$

Potential energy is given by

$P= mgH= 1 \times 10 \times 50=500 \ J$

Now

Mechanical energy is given by the Formula

M.E = K.E + P.E= 2 + 500 = 502 J

**Question 3**

calculate the Kinetic Energy,Potential energy and Mechanical energy of the object have mass 5 kg lying at rest at height 10 m above the ground

(g=10 m/s^{2})

**Solution**
Given , m=5 kg, v=0 m/s( as at rest) , H=10 m, g=10 m/s^{2}, M=? ,K=?, P=?

Kinetic energy is given by

$K= \frac {1}{2} mv^2= =0 \ J$

Potential energy is given by

$P= mgH= 5 \times 10 \times 10=500 \ J$

Now

Mechanical energy is given by the Formula

M.E = K.E + P.E= 0 + 500 = 500 J

## How to Calculate the Mechanical Energy

Given values are $m$, $v$ and $h$ and $g=10 \ m/s^2$

Kinetic energy is calculated as

$\text{KE} = \frac {1}{2} mv^2$

Potential energy is calculated as

$\text{PE} = mgH$

Total Energy or Mechanical energy is calculated as

Mechanical energy = KE + PE

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