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Mechanical Energy Formula

Mechanical Energy is the sum total of potential and kinetic energy. Potential energy is possessed due to its position, whereas kinetic energy is possessed due to the movement of the object. If an object is moving, potential energy should be zero. If the object is at rest, the kinetic energy should be zero. The mechanical energy formula is,
Mechanical Energy Formula

Where, m is the mass of an object and v is the velocity of that object, g is the acceleration due to gravity and h is the height of an object.

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Mechanical Energy Formula

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Problems related to mechanical energy is given below:

Solved Examples

Question 1: A person is sitting on a building of height 20m. The mass of the person is 55kg, calculate the mechanical energy?

Solution:
 
Given parameters are,
m = 55kg and h = 20m
Since the person is not moving, K. E = 0
Mechanical energy formula is,
M. E = $\frac{1}{2}$m$v^{2}$ + mgh
Since K.E is zero, the equation becomes,
M.E = mgh
M.E = 55$\times$9.81$\times$20 = 10791 J

 

Question 2: Calculate the mechanical energy of a 10kg object moving with a speed of 15m/s?

Solution:
 
Given parameters are,
m = 10kg and v = 15m/s
Since the person is moving, P. E = 0
Mechanical energy formula is,

M. E = $\frac{1}{2}$m$v^{2}$ + mgh

Since P.E is zero, the equation becomes,

M.E = $\frac{1}{2}$m$v^{2}$

M.E = $\frac{1}{2}$$\times$10$\times15^{2}$ = 1125 J

 

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