Question

state and derive an experssion of work energy theorem

Answer 1

From Newton’s Second Law of motion, we know that F = ma, and because of the definition of acceleration we can say that



If we multiply both sides by the same thing, we haven’t changed anything, so we multiply by v:



But remember that v = dx/dt:



We rearrange and integrate:

F dx = mv dv



Fx = m(½v2) = ½mv2 = Ek

But Fx = Work; therefore Work = ΔEk.



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Answer 2

Heya user ,
Here is your answer !!

According to the work energy theorem the work done by a force on a moving body is equal to the increase in its kinetic energy .

Derivation :

Let a body of mass M moving with an initial velocity 'u' . When a constant force F is applied on the body along its direction of motion , it produces an acceleration 'a' and the velocity of the body changes from 'u' to 'v' in moving a distance S .

Then ,

Force F = m . a ...... ( i )
Work done by the force = force × displacement
or , W = F × S ...... ( ii )
From relation , v^2 = u^2 + 2as .
Displacement S = ( v^2 - u^2 ) / 2a

substituting the values of 'a' and S from equations ( i ) and ( iii ) in eq. ( ii) , we get

W
= m . a . ( v^2 - u^2 ) / 2a
= 1/2 m ( v^2 - u^2 )
= 1/2mv^2 - 1/2mu^2 .


Hope it helps you !!