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Work, energy and power

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Work

It is said to be done whenever a force acts on a body and the body moves through some distance in the direction of the force.

Conditions

- A force acts on the body.
- The point of application of the force moves in the direction of the force.

 Work done = Force × distance moved in the direction of forces.


Nature of work done

Although work done is a scalar quantity yet it's value may be positive, negative or zero.

Positive work

If a force acting on a body has a component in the direction of displacement , then the work done by the force is positive.

Negative work

If a force acting on the body has a component in the opposite direction of displacement, the work is be negative.

Zero work

Work done by force is zero if the body gets displayed along a direction perpendicular to the direction of the applied force. 

For a varying force the work done is equal to the definite integral of the force o we the given displacement.


Energy

Energy of a body is , as it's capacity or ability to do work. 
The energy of a body is measured by the amount of work the body can perform, like work, energy is a scalar quantity.

Kinetic energy

The energy possessed by a body by virtue of it's motion.
A moving object can do work. The amount of work that a moving object can do before coming to rest is equal to its kinetic energy.

- The kinetic energy of a body is equal to one half the product of the mass of the body and the square of it's velocity.

Work energy theorem

Work energy theorem  states that the work done by the net force acting on a body is equal to the change produced in the kinetic energy of the body.

- The work energy theorem is not independent of Newton's second law. 
- It holds in all inertial frames.

Potential energy

It is the energy stored in a body or a system by virtue of it's position in a field of force or by it's configuration, is known as potential energy.

- It is also called mutual energy or energy of configuration.

Gravitational Potential energy

It is the potential energy associated with the state of separation of two bodies, which attract one another through the gravitational force.

Elastic Potential energy

It is associated with the state of compression or extension of an elastic object.

Electrostatic Potential energy

The energy due to the interaction between two electric charges is electrostatic Potential energy.

Conservative Force

A force is conservative if the work done by the force in moving a particle any closed path is zero.

Non - Conservative Force

If the amount of work done in moving an object against a force from one point to another depends on the path along which the body moves, then such a force is non conservative.
- The work done in moving an object against a non - conservative Force along a closed path is not zero.

Principle of conservation of mechanical energy

This principle states that if only the conservative forces are doing work on a body, then it's total mechanical ( k.E. and P.E ) remains constant.

Einstein's Mass energy equivalence

In 1905, Albert Einstein discovered that mass can be converted into energy and vice versa. 
He showed that mass and energy are equivalent and related by, 
        
         E= mc^2

c is speed of light 
m is mass 
E is energy

- Energy generation in the sun and stars be the energy generated in the sun and stars due to the conversion of mass into energy.

Principle of conservation of energy 

- Energy can neither be created, nor be destroyed.
- The total energy of an isolated system remains constant.
- As the entire universe may be regarded as an isolated system, the total energy of the universe is constant. 
- If one part of the universe loses energy, another part must gain an equal amount of energy.

- In this, we include mass into total energy because mass can be converted into energy.


Power 

It is defined as the ratio of two scalar quantity work and time .
Work per unit time.

It's SI unit is watt.

Instantaneous power

The power of an agent may not be constant during a time interval.
The instantaneous power is defined as the limiting value of the average power as the time interval approaches zero.

1 kilowatt= 1000 watt
1 horsepower = 746 watt
1  kWh = 3.6× 10^6

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