Power, Energy and Efficiency

I've simplified a few concepts here, hope it helps

POWER

1. The power,P, is the rate at which work is done or the rate of change of energy.
 
  Power, P = Work done ,W / Time taken , T

  Or
 
  Power, P = Change of energy /  Time taken , T

2. The SI unit of power is watt (w).
3. 1 watt is defined as the power required to perform 1 joule of work in 1 second.
4. Power depends on the time taken and the work done  as an analogy, people or engine with high power rating can get the work done in short time.
6. For a force F which produces a constant velocity, V,or a stationary object , the power generated is:
  P = Fv
  Proof:
 
  Power =  Work /  Time
  = (Force x Displacement) /  Time

  =Force x ( Displacement/  Time)
  = Force x velocity
 P = Fv

POTENTIAL ENERGY
1. Potential energy is the energy possessed by an object due to its position or state.
2. Potential energy can be classified into gravitational potential energy and elastic potential energy.


GRAVITATIONAL POTENTIAL ENERGY 
The gravitational potential energy of an object depends on:
a) its mass
b) its height
c) the gravitational field


RELATIONSHIP BETWEEN WORK AND GRAVITATIONAL POTENTIAL ENERGY


The work done against the force of gravity is known as the gravitational potential energy

Gravitational potential energy= mgh
Where,
  m= mass
  g= Acceleration due to gravity
  h= Change in the height of the object

ELASTIC POTENTIAL ENERGY 
1.Energy is needed to compress and extend an elastic material such as a spring and rubber.
2.The spring obtains its energy when work is done on it by compressing or stretching it.
3. The energy which an object possesses when it is compressed or stretched is known as the elastic potential energy .

RELATIONSHIP BETWEEN WORK AND ELASTIC POTENTIAL ENERGY 

Work done = mean force x displacement
  W= 1/2 fx
 
• The extension of spring will increase if the force applied increases.
• Therefore, the elastic potential energy stored in the spring.
=Work done
= 1 / 2 Fx

KINETIC ENERGY

1. Kinetic energy is the energy acquired by an object due to its motion.
2. The kinetic energy of a moving object depends on its mass and speed.
Kinetic Energy= 1/2 mv^2   = (one over two multiply mass multiply velocity squared)

Where m is the mass of an object, v is speed of the object.


RELATIONSHIP BETWEEN WORK AND KINETIC ENERGY

1. Newton’s first Law of motion states that an object that moves with constant velocity will continue to move at this velocity if no external force acts on the object.
2. That mean an object which moves with constant velocity will conserve its kinetic energy.
3. Work is done when the kinetic energy increases or decreases. The change in kinetic energy of an object is equal to the work done on that object.
4. W= change in kinetic energy
  = 1/2 (mv^2- mu^2)

 PRINCIPLE OF CONSERVATION OF ENERGY

 The principle of conservation of energy states that energy can neither be destroyed nor created but it can change from one form to another.
 The changes of kinetic energy to gravitational potential energy also proves the equation of kinetic energy, v = u -2gh


EFFICIENCY 

The efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy.
 
Efficiency = ( Useful energy output / energy input) x 100 %


 EFFICIENCY OF MACHINES

1.Machines are devices that make our work easier.
2.Machines require energy to work. This energy is called the input.
3.Machines transforms this input into other forms of energy to perform useful works.
4.However, the useful work obtained is not equal to the input as there is energy “loss” In this process. This loss is mainly due to work done against frictional forces and takes the forms of heat.
5.So, a machines is not perfect because the work done by the effort or input energy is not entirely used to overcome the load.