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state the work-energy theorem

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VIRΑTKΣHLIGO

Work Energy Theorem :-

  • It states that net work done on any body is equal to the change in its kinetic energy .

We could derive this , as ;

  • Consider a body of mass m being pushed by a force F acting along the horizontal , due to which it is displaced s m away .
  • Since the angle between the force and the displacement is 0° , work done will be ,

[tex]\sf \longrightarrow Work = F s cos\theta \\ [/tex]

[tex]\sf \longrightarrow Work = (ma)(s)(cos0^o)\\[/tex]

[tex]\sf \longrightarrow\pink{ Work = m \ a \ s } \dots (i)[/tex]

  • Now let's use the third equation of motion namely,

[tex]\sf \longrightarrow 2as = v^2 -u^2[/tex]

where the symbols have their usual meaning.

[tex]\sf \longrightarrow as =\dfrac{1}{2}(v - u)^2\\ [/tex]

Multiplying both sides by m,

[tex]\sf \longrightarrow mas = \dfrac{m}{2}(v-u)^2 [/tex]

Now from equation (i),

[tex]\sf \longrightarrow Work = \underbrace{\dfrac{1}{2}mv^2-\dfrac{1}{2}mu^2} [/tex]

Above term on RHS is change in the Kinetic energy , therefore ,

[tex]\sf \longrightarrow \underline{\boxed{\bf Work = \Delta Energy_{(Kinetic)} }}[/tex]

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