Derivation Of Formulas For Energy

I had a tough time deriving formulas for mechanical energy when given in school as assignment or as a question in exams. I don’t want any of you reading this to experience the same feeling. So, I would like to show you how we derive the conventional formulas for potential and kinetic energies to be later used in problems.

Potential Energy

We know that Work is equal to the product of the Force applied and the Distance travelled. So,

W = F x s

Also, Force is equal to the product of Mass of the body and the Acceleration. So,

W = ( m x a ) x s

Now, as the energy is being calculated on Earth, we have to substitute Acceleration with g ( acceleration due to gravity ) and the Distance with h ( height ). So,

W = ( m x g  ) x h

Therefore, we have derived our formula i.e.

W = m g h or EK = m g h


Kinetic Energy

We know that Work is equal to the product of the Force applied and the Distance travelled. So,

W = F x s

Also, Force is equal to the product of Mass of the body and the Acceleration. So,

W = ( m x a ) x s

Now, the Distance can be substituted with ( v2 – u2 / 2 a ) from the third equation of motion ( v2 – u2 = 2 a s )

W = ( m x a ) ( v2 – u2 / 2 a )

W =  m ( v2 – u2 / 2 )

W = ½ m ( v2 – u2 )

Usually, the bodies start from rest i.e. u = 0. So,

W = ½ m v2

Therefore, we have derived our formula i.e.

W = ½ m v2 or EP = ½ m v2

I hope that I have been able to explain the steps to be followed while deriving the equations. 🙂

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