Question

state the work-energy theorem

Answer 1

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 ,

$\sf \longrightarrow Work = F s cos\theta$

$\sf \longrightarrow Work = (ma)(s)(cos0^o)$

$\sf \longrightarrow\pink{ Work = m \ a \ s } \dots (i)$

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

$\sf \longrightarrow 2as = v^2 -u^2$

where the symbols have their usual meaning.

$\sf \longrightarrow as =\dfrac{1}{2}(v - u)^2$

Multiplying both sides by m,

$\sf \longrightarrow mas = \dfrac{m}{2}(v-u)^2$

Now from equation (i),

$\sf \longrightarrow Work = \underbrace{\dfrac{1}{2}mv^2-\dfrac{1}{2}mu^2}$

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

$\sf \longrightarrow \underline{\boxed{\bf Work = \Delta Energy_{(Kinetic)} }}$