# Mechanical Energy Formula: Definitions & Examples

The act of dislocating an object when a force acts upon it is said to produce work. Work involves a force through which an object can be displaced. When the work is completed, the thing will gain energy. The energy acquired by an object on which work is done is known as its mechanical energy.

In this article, we will discuss the concept and components of mechanical energy with the mechanical energy formula and examples. Let us begin learning!

## Mechanical Energy Formula

### What is mechanical energy?

Mechanical energy is generally defined as the sum of kinetic energy and potential energy in an object. It accumulates as a result of performing a particular task. In other words, we can describe the energy of an object because of its motion or position, or sometimes both.

Due to its position, the object possesses potential energy. To place an object at a certain height, some work is required. Objects possess kinetic energy in addition to the work they do to move. When an object is in motion, its potential energy is considered zero. On the other hand, if it is at rest, then its kinetic energy will be zero.

Objects have mechanical energy if they are in motion and/or if they are at some position relative to the surface. For example, a box held in a vertical position above the ground will have only potential energy. A moving vehicle generates mechanical energy due to its motion and kinetic energy. Thus we can say that a moving baseball possesses mechanical energy due to both its speed and its vertical position above the ground.

### The formula for Mechanical Energy

We can express the mechanical energy formula as:

M.E = K. E + P.E

Also, we know that

K.E. = 12×m×v2

And

P.E. = m×g×h

Hence,

M.E. = 12×m×v2+m×g×h

Where,

M.E. = Mechanical Energy

K.E. = Kinetic Energy

P.E. = Potential Energy

m = Mass of the object

g = Acceleration due to gravity

h = Height position

v = The velocity of the object

## Solved examples

In Q.1, a 100kg person sits on a 10m building. Determine the mechanical energy.

Solution:

As given parameters in the problem are,

M = 100 kg

H = 10m

Since the person is in a static state, therefore,

E. = 0

Mechanical energy formula is:

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

M.E. = 0+ m × g × h

= 100 × 9.81 × 0

M.E. = 9810 J

Therefore mechanical energy will be 9810 J.

Q.2: Find out the mechanical energy of a 10 kg object which is moving at a speed of 10 ms−1.

Solution:

Based on the values in the problem,

M = 10 kg

V = 10 ms−1

Since the person is moving, therefore

E. = 0

Now, the mechanical energy formula is:

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

M.E. = 12×m×v2+0

=12×10×102

M.E. = 500 J

Therefore mechanical energy will be 500 J.