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]
