Introduction: Work and energy

Work

Work is defined as the product of the force applied on an object and displacement caused due to the applied force in the direction of the force. Work is a scalar quantity. It has no direction of its own but a magnitude.

Example of work done are:

• Moving a chair from one location to another
• Lifting a book from the shelf and placing it on a table
• Pushing a pebble lying on the ground.

In all these situations we are applying a force on an object which is then changing the state of rest or motion of the object. So, we can conclude that work is done if and only if:

• A force is applied to an object.
• If the object is displaced from one point to another point.

Energy

• Energy is defined as the ability to do work. Its unit is the same as that of work.SI unit of energy or work = Joule (Nm)

Energy has different forms: Light, heat, chemical, electrical or mechanical.
Mechanical energy is the sum of:
(i) Kinetic energy (K.E)
(ii) Potential energy (P.E) 

Kinetic Energy

Objects in motion possess energy and can do work. This energy is called Kinetic Energy.
Kinetic Energy = K.E= 1/2 mv² (taking initial velocity u=0)
When two identical bodies are in motion, the body with a higher velocity has more K.E.

Work-energy theorem

The work-energy theorem states that the net work done by a moving body can be calculated by finding the change in KE. 

W _net = KE _final − KE _initial

Factors affecting kinetic energy-

1. Mass
2. Velocity
3. Momentum

Potential Energy

Energy can get stored in an object when work is done on it. For example, stretching a rubber string. The energy that is possessed by a body by virtue of its configuration or change in position is known as Potential Energy.

The potential energy of an object at a height. When an object is raised to a certain height, work is done against gravity to change its position. This energy is stored as Potential Energy.

               W = F.s
F = ma
 In the case of increasing the height, F = mg
Therefore , W (P.E) = mgh   ⇒ ΔPE=mg(h _final−h _initial)

Law of conservation of energy states that energy can neither be created nor destroyed, but can be transferred from one form to another.

The total energy before and after the transformation remains constant. For example: consider a ball falling freely from a height.

At height h, it has only PE = mgh.By the time it is about to hit the ground, it has a velocity and therefore has K.E = ½ mv² Therefore, energy gets transferred from PE to KE, while the total energy remains the same.

Total energy = KE + PE

Power

The rate of doing work or the rate of transfer of energy is called power. It is denoted by P

P = W/T
SI unit is Watt (Js⁻¹).
Average power =  Total energy consumed/Total time taken
The commercial unit of power is kWh i.e. energy used in 1 hour at 1000 Joules/second.
1kWh=3.6×10⁶J.