state work energy theorem for CONSTANT FORCE

Work-Energy principle for a body, under the action of an unbalanced force, can be stated as follows:

Constant Force

It states that, “The net work done (Wnet) by the forces acting on a body is equal to the change in the kinetic energy of the body”.

So, Wnet = ½ mv2 – ½ mu2

                 = Kf – Ki

If work is done on the body, its K.E increases and if work is done by the body, its K.E. decreases.

Consider a force F acting on a moving body. As a result of this, the body moves from A to B and gets its velocity increased from u to v as shown in the below figure.

If dW is the work done in moving through a small distance ‘ds’,

dW = \vec{F}.\vec{s}

So, dW = F ds cos 0º

            = F ds

            = ma ds

Here ‘a’ is the acceleration of the body.

Since, a = m(dv/dt)

So, dW = [m(dv/dt)].ds

            = m dv (ds/dt)

dW = mv dv

Integrating both sides,

\int_{0}^{W} dW =\int_{u}^{v}mv dv, \left [ W ight ]_{0}^{W} = \int_{u}^{v}dv

[W-0] = m[v2/2]

or, W = m[v2/2 – u2/2]

or, W = ½ mv2 – ½ mu2 = Final K.E – Initial K.E

Thus, Work done = Change in kinetic energy

Therefore, the change in kinetic energy of a body equals the total work done by all the forces (conservative and non-conservative).

This is in accordance with the law of conservation of energy.