Question

Hey !!!

Explain about work energy theorm .


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Answer 1

WORK - ENERGY THEOREM :
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It states that the work done by the net force acting on a body is equal to the change produced in the kinetic energy of the body .

PROOF OF W - E THEOREM FOR A CONSTANT FORCE :
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Suppose a constant force F acting on a body of omass m produces acceleration a in it . After covering distance s , suppose the velocity of the body changes from u to v .

Now , using 3rd equation of motion ,

v² - u² = 2 as

Multiplying both sides by ½ m ,

½ mv² - ½ mu² = mas

By Newton's 2nd Law , F = ma .

Therefore,

½ mv² - ½ mu² = Fs = Work done ( W )

K ( f ) - K ( i ) = W

Change in K.E. of the body = Work done on the body by the net force.

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Answer 2

$\textbf{\large{Answer -}}$

Work Energy Theorem :

The work done by the net force (whether it is conservative or non conservative) or net work done by all forces is equal to change in kinetic energy. This is known as work energy theorem.

Proof :

Let a body of mass $m$ move under a net force $F$ by which it's velocity changes from $u$ to $v$

Let at any instant the displacement of body is $ds$ then at that instant,

$dw \: = F.ds$

$dw = m \frac{dv}{dt} ds$

$dw = mvdv$

Therefore, the total workdone by net force,

By integrating mvdv we get,

$w=m{[\frac{{v}^{2}}{2}]}^{v}_{u}$

$w=m[\frac{{v}^{2}}{2}-\frac{{u}^{2}}{2}]$

$w=\frac{1}{2}{mv}^{2}-\frac{1}{2}{mu}^{2}$

$w=K.E_{f}-K.E_{i}$

$w =\delta \: K.E$

$\textbf{\underline{Proved}}$