It was said that work is done when an object whenever a force acts upon it to displace. Work involves a force through which an object can be displaced. When the work is done upon the object then it 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 is accumulated due to performing some particular work. In other words, we can describe the energy of an object because of its motion or position, or sometimes both.

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We know that potential energy is possessed by the object due to its position. It is because to place some object at some height, some work will be done. Also, kinetic energy is possessed by an object due to work done by it for its movement. When an object is moving, then its potential energy considered zero. On the other hand when 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 at a vertical position above the ground will have only potential energy. A moving vehicle possesses the mechanical energy due to its motion i.e. 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.

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**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. = \( \frac{1}{2} \times m \times v^2 \)

And

P.E. =\( m \times g \times h \)

Hence,

M.E. = \(\frac{1}{2} \times m \times v^2+ m \times g \times h\)

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**

Q.1: A person is sitting on a building of height 10m and the mass of the person is 100kg. 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 Ã— gÂ Ã— h

= 100Â Ã— 9.81 Ã— 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 with a speed of 10 \(ms^{-1}.\)

Solution:

Given values in the problem are,

m = 10 kg

v = 10 \(ms^{-1}\)

Since the person is moving, therefore

E. = 0

Now, Mechanical energy formula is:

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

M.E. = \( \frac{1}{2} \times m \times v^2 + 0 \)

=\( \frac{1}{2} \times 10 \times 10^2 \)

M.E. = 500 J

Therefore mechanical energy will be 500 J.

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