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### Modes of Mechanical Energy

#### Energy:-

Energy can be in several forms like mechanical energy, electrical energy, heat, sound, pressure. The present context is of mechanical energy possessed by a body due to its position or motion. Hence, mechanical energy can be of two types :

1. Potential  Energy and
2. Kinetic Energy.

#### 1) Potential energy:-

The energy which a body possess by virtue of its position or configuration is called potential energy. Few examples to clarity the concept of potential energy are following:

(a) If a body of mass m is raised through a height h above of datum level, then the work done on it by the gravitational force is written as

This energy is stored in the body as potential energy. In coming down to the original position, the body is capable of doing work equal to mgh.

(b) If a spring is twisted through an angle ϴ by application of a torque varying from zero in the beginning to T in the end, the work done by the average torque T2 is written as

This is the potential energy of the spring due to its configuration.

(c) If a spring of stiffness k is stretched, the force F acting on it does not remain constant, but increases with displacement x undergoes by the spring. At any time,

Therefore, average force acting on the spring is

Hence, the work done by the average force F for displacement x of the spring is written as

This is the potential energy of the spring due to its configuration.
Gravity force, elastic spring, and torsional spring are examples of conservative forces. Thus, potential energy is the measure of the amount of work done by a conservative force in moving a body from one position to another .

#### 2) Kinetic Energy:-

The energy which a body possess by virtue of its motion is called kinetic energy. It is measured by the amount of work required to bring the body to rest.

Let a body of mass m moving with velocity v be brought to rets by the application of a constant force F which causes a retardation – a. if s is the distance through which the body moves in this period, the kinetic energy is given by the work done by the force F on the body. Using third equation of linear motion,

Therefore, kinetic energy is determine as

A system of particles or body can have both forms of mechanical energy. During motion or change in the amount or direction forces, one form of energy gets converted into another form.