Work Energy Theorem for Constant and Variable Force

Yashwant Parihar,

The Post will give you knowledge about all the concepts of the Work-Energy Theorem for Constant and Variable Force Class 11th. 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. In the examination, the question will be asked in this form: “State and prove the work energy theorem for a variable force”

First, we will talk about the 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

Work Energy Theorem

According to this theorem, Work done equals 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 using the integration method. So practice the derivations.

Derive Work Energy Theorem for Constant Force

Work = Force x Displacement
W = FxS / F = ma
W = mas
From the 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 the 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-constant-force

Derive 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

Work-energy-theorem-for-variable-force

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