# Mechanical Energy Formula

Mechanical energy is the sum of kinetic energy and potential energy in an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both. Potential energy is possessed by the object’s position whereas kinetic energy is possessed by the movement. When an object is moving, its potential energy is zero. When it’s at rest, the kinetic energy is zero.

The mechanical energy formula is given by,

**M.E = K. E + P.E**

**M.E = ½ mv****2**** + mgh**

Where,

**m **= mass of an object,

**v **= velocity of that object,

**g **= acceleration due to gravity and

**h ** = height of an object.

**Example 1**

A person is sitting on a building of height 10m and the mass of the person is 50kg, determine the mechanical energy.

**Solution:**

Given parameters are,

m = 50 kg

h = 10m

the person is not moving, therefore, K. E = 0

Mechanical energy formula is given by,

- E = 1 / 2mv2 + mgh

Since K.E is 0, the equation becomes,

M.E = mgh

= 50 ×9.81 ×10

= 4905 J

**Example 2**

Determine the mechanical energy of a 20 kg object which is moving with a speed of 10m/s.

**Solution:**

Given parameters are,

m = 20kg

v = 10m/s

the person is moving, therefore P. E = 0

Mechanical energy formula is given by

- E = 1 / 2 mv2 + mgh

Since P.E is 0, the equation becomes,

M.E = 1 / 2mv2

= 1 / 2 × 20 ×102

= 1000 J