Work Energy Theorem for Constant and Variable Force

The Post will give you knowledge about all the concepts of the Work-Energy theorem. Welcome to TheCScience, in this article you will learn about the Work-Energy Theorem and its Derivation. The Post gives you information in brief so you can easily revise for your examination.

First, we will talk about what is a work-energy theorem. Then we will derive the formula for constant and variable force. So let’s talk about what work-energy theory is.

Work Energy Theorem

According to this theorem, Work done is equal to a change in Kinetic energy.
W = Kf – Ki
Now, we have to prove this theorem by derivation so firstly we will solve it for constant force and then solve it for variable force.
Note:- Variable Force is Important from an examination point of view. We have to solve the variable force by integration method. So practice the derivations.

Work Energy Theorem for Constant Force

Work = Force x Displacement
W = FxS / F = ma
W = mas
From 3rd equation of motion
V² = U² + 2as
2as = V² – U²
as = V² – U²/2
as = V²/2 – U²/2
But as the value in W = mas
W = m(V²/2 – U²/2)
Multiply m in bracket
W = mV²/2 – mU²/2
Arrange the half in first
W = 1/2mV² – 1/2mU²
Kinetic energy Formula = 1/2mV²
so W = Kf – Ki
Hence, Proved

Work Energy Theorem for Variable Force

W = mas
Both Side Integration
∫dw = ∫mads \ a = dv/dt
w = mdv/dt.ds
Replace s with v
w = mds/dt.dv \ ds/dt = v
w = ∫vdv
w = m [v²/2] Integral v and u
w = m [ v²/2 – u²/2]
w = 1/2mv² – 1/2mu²
w = Kf – Ki
Hence, Proved

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