# Work, Energy and Power

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Syllabus for Competitive and Government Exams

## Work

Work is said to be done when a body or object moves with the application of external force.

Two conditions need to be satisfied for work to be done:

1. A force should act on an object

2. The object must be displaced.

Work is the scalar product of force and displacement along the direction of the force.

Work done (W) Force (F) ⨯ distance moved along the direction of force (S)

W = fs cosθ

### Unit of Work

SI unit of work – Joule or Newton-meter

CGS unit of work – Erg or Dyne-cm

• 1 Joule = 10Erg
• 1 Erg = 10-7 Joule

### Type of Work

1. Positive work done
2. Negative work done
3. Zero work done

### Positive work done

The work done on an object is said to be positive when force and displacement are in the same direction.

When 0 ≺θ≺π/2

cosθ = +ve

Example: When a force is applied to a body and the body moves in the same direction as the force, positive work is done.

### Negative work done

The work done is said to be negative when the force and displacement are in opposite directions.

W = FS cosθ

= FS C0S180⁰ [ θ =180⁰ ]

= -FS

Example: A body is being pulled vertically upwards. The work done by the gravitational force is negative.

### Zero work done

The work done is said to be zero when the force and displacement are in a perpendicular direction.

W = FS cosθ

= FS cos90⁰ = 0

Example: When a man holding a box and moving forward then the work done by the gravitational force on the box is zero because gravitational force acts the displacement of the box is in a perpendicular direction.

• When the displacement of a moving object is zero, the work done will be zero.

## Energy

The capacity of doing work by a body is called its energy.

(i) Energy is a Scalar Quantity like work.

(ii) SI unit of energy is Joule (J) and the CGS unit is erg.

(iii) Dimensional formula of energy is [ML2T-2] same as that of work.

(iv) Energy is developed in a body due to work done on it is mechanical energy.

(v) Mechanical energy is two types:

1. Potential energy
2. Kinetic energy

### Potential energy

The capacity of doing work developed in a body due to its position or configuration is called its Potential energy.

Example: 1. energy of stretched or compressed spring 2. energy of water collected at a height 3. energy of spring in a watch 4. stretched bow

PE of a body in the gravitational field of the earth is mgh.

where m = mass, g = acceleration due to gravity, and h = height of the body from surface to earth.

### Kinetic energy

The energy possessed by a body due to its motion is called kinetic energy of the body.

If a body of mass is m is moving with speed v, then the kinetic energy of the body is ½ mv2

Example: 1. All moving vehicles possess kinetic energy 2. Flowing water also possesses kinetic energy as it is used to run water mills.

### Principle of Conservation of Energy

Energy can neither be created nor destroyed. Only energy can be transformed from one form to another form. The sum total of energy, in this universe, remains constant.

• When a ball is thrown vertically upward its potential energy increase, kinetic energy decreases but the total energy remains constant.

Forms of energy: Energy is of several forms. Mechanical energy, heat energy, sound energy, light energy, electrical energy, nuclear energy, atomic energy, chemical energy, magnetic energy etc.

### Some Equipment used to transform Energy

 Equipment Energy Transformed 1. Dynamo Mechanical energy into electrical energy 2. Candle Chemical energy into light and heat energy 3. Microphone Sound energy into electrical energy 4. Loud Speaker Electrical energy into sound energy 5. Solar Cell Solar energy into electrical energy 6. Tube light Electrical energy into light energy 7. Electric Bulb Electrical energy into light and heat energy 8. Battery Chemical energy into electrical energy 9. Electric motor Electrical energy into mechanical energy 10. Sitar Mechanical energy into sound energy 11. Photocell Light energy into electrical energy

## Power

The rate of doing work is called power.

• Power = Work / Time
• Power is a scalar quantity.

### Unit of Power

• CGS unit of power is erg/sec.
• SI unit of power is watt named as respect to the scientist James Watt.
• Watt = Joule/sec.
• The bigger unit of power is kilowatt(kW) and mega watt (MW)
• 1 kW = 103 watt, 1MW = 106 watt
• Horsepower is a practical unit of power.
• 1 H.P. = 746 watt
• 1 watt second = 1 watt ⨯1 second = 1 joule.
• 1 watt hour(Wh) = 3600 joule
• 1 kilo watt hour(kWh) = 3.6 ⨯106 joule.