# Mechanical Energy Formula

## Mechanical Energy Formulas - Definitions & Examples

Mechanical energy refers to the total of kinetic energy and potential energy possessed by 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.

If K E and P E refers to the kinetic and potential energies of a body, its mechanical energy is given by,
M.E = K.E + P.E
For an object thrown upwards, its total mechanical energy is given by:
E = ½ mv2 + mgh
Where,is the mass of an object, , the velocity of that object, g, the acceleration due to gravity and h tells at what height the object is from the ground.

Example: The kinetic energy of a body flying at a certain height from the ground is 4500 J and its potential energy is 8000 J. Find the total mechanical energy associated with it.
Solution:
KE = 4500 J, PE = 8000 J, ME=?
ME = KE + PE = 4500 + 8000 = 12500 J

Example: An object of mass 2 kg has been projected vertically upwards with a kinetic energy of 100 J. Find the maximum height it can reach (take g = 10 m/s2 and PE of the object at the point of projection is zero).
Solution: In motion under gravity, total mechanical energy is conserved.
Total Mechanical energy at the point of projection = total mechanical energy at the maximum height.
At the point of projection: KE1 = 100 J, PE1 = 0
At the maximum height: KE2 = 0, PE2 = mgh
Now, KE1 + PE1 = KE2 + PE2
Therefore, 100 + 0 = 0 + mgh
⇒h=100mg=1002×10=5m
The object will reach upto a maximum height of 5 m.

Question: A ball thrown up with certain kinetic energy can reach a maximum height of 8 m. An identical ball thrown up with four times kinetic energy can reach a maximum height of:
Options:
(a) 8 m
(b) 32 m
(c) 64 m
(d) 128 m