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 =(1)/(2)(v - u)^2\\`

Multiplying both sides by m,

`\sf \longrightarrow mas = (m)/(2)(v-u)^2`

Now from equation (i),

`\sf \longrightarrow Work = \underbrace{(1)/(2)mv^2-(1)/(2)mu^2}`

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

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