Work Energy Theorem

According to this principle, work done by a force in displacing a body, gives the measure of the change in kinetic energy of the body.

When a force does some work on a body, the kinetic energy of the body increases by the same amount. Conversely, when an opposing force is applied on a body, its kinetic energy decreases. The decrease in its kinetic energy is equal to the work done by the body against the retarding force. Thus, work and kinetic energy are equivalent quantities.

Suppose, m= mass of a body

u = initial velocity of the body

dw = F ds

= (ma)ds (since F = ma)

Total work done by the force in increasing the velocity of the body from u to v is

\ W= change in the kinetic energy of the body

Sub Topics

Potential energy

Potential energy

Let us study another type of energy, called the potential energy. Potential energy is the energy that can be associated with the configuration (or arrangement) of a system of objects that exert forces on one another. If the configuration of the system changes, then the potential energy of the system can also change.

One type of potential energy is the gravitational potential energy that is associated with the state of separation between objects, which attract one another via the gravitational force. For example, when Andrey Chemerkin lifted the record breaking weights above his head in the 1996 Olympics, he increased the distance between the weights and earth. The work he did, changed the gravitational potential energy of the weights and earth system because it changed the configuration of the system.

Another type of potential energy is elastic potential energy, which is associated with the state of compression or expansion of an elastic object, say a spring. If we compress or extend a spring, we do work to change the relative locations of the coils within the spring. The result of the work done by our force, is an increase in the elastic potential energy of the spring.Consider the example of two charged particles, A and B. A is positive and B is negative and because of mutual attraction, the particles are accelerated towards each other and the kinetic energy of the system increases. Although, no external force is applied on the system, the kinetic energy changes. The particle B exerts a forceon A. As A moves towards B, this force does work. The work done by this force is equal to the increase in the kinetic energy force does work on B. Similarly, A exerts a force F_B_A on B. This force does work on B and this work is equal to the kinetic energy of B.

The work byand the work byare equal to the increase in total kinetic energy of the two particles.