WORK AND ENERGY THEOREM PROOF

INTRODUCTION: In day-to-day life, we consider any useful physical or mental labour as work. Activities like  cooking food, watering plant, playing violin, watching TV,  can not be considered as work. According to physics  Work is an act where movement of object in direction of force is involvd.  There are two conditions for work :

  • On object force should be acted.
  • The object must get displaced.

If any of the above two conditions is not met, then scientifically we say that no work has been done. Work is defined as the product of force and the distance moved by a body under this force. Mathematically: W= F X S

Work is a SCALAR quantity. It has only magnitude.

 

                                                        TYPES OF WORK

Work is of three types  depending on the angle between the force and the displacement.

  • Positive work
  • Negative work
  • Zero work.

 

                                 POSITIVE WORK

When displacement of body is done in the direction of force then the work is positive.

 

EXAMPLES

  • Work done by gravity if a body falls towards the earth.
  • Work done by a horse pulling a cart.
  • Work done by the stretching force acting on a spring.

                                                               NEGATIVE WORK

When displacement of the body is in the opposite direction of the force then the work is negative.

EXAMPLES

  • Work done by the braking force when brakes are applied to a vehicle.
  • Work done by the friction.
  • Work done by the force of gravity when a body is projected away from the surface of the earth.

 

                                                  ZERO WORK

Work done is said to be zero if the applied force is zero or displacement is zero or the angle between displacement and force is 90°.

EXAMPLES

  • The pendulum string movement which moves into extreme point to starting point .
  • Work done by centripetal force.
  • When a porter carrys load and walks in a straight line path.

 

                                            UNITS OF WORK

In cgs system, the absolute unit of work is erg : 1 erg= 1 dyne  X 1 cm

If a force of one dyne displaces a body through a distance of one centimeter in its own direction then work done is said to be one erg.

In SI  system, the absolute unit of work is joule(J). Mathematically, we have

1 joule = 1 N X 1 m = 105 dyne X 102 cm = 107erg

If a force of one newton displaces a body through a distance of one metre in it’s own distance then work done is said to be one joule.

 

ENERGY : It is the capacity for doing work. We must have energy to accomplish work. With the help of energy work can be performed.  To do 100 joule of work, we must expend 100 joule  of energy. WORK  and ENERGY are related by the following relation : work = change in energy.

 

UNITS OF ENERGY : Energy is measured in different units; joule (J)  and calorie (cal). Relation between joule (J) and calorie (cal)

                         1 cal  =  4.2 J (approx)

Sometimes a larger unit of energy is called kilojoule (KJ) and megajoule (MJ) .

                          1 KJ = 103 J

                          1 MJ = 106J.

 

                        DIFFERENT FORMS OF ENERGY

FORMS OF ENERGY DESCRIPTION EXAMPLE
Mechanical energy ·         It is moving energy

·         All moving objects produce mechanical energy

·         The movement within machines is mechanical energy

 

Rolling of bicycle;

  Running cars;

Moving of gear.

Sound energy ·         It is produced when an object is made to vibrate

·         This energy travels out as waves in all directions

·         Sound needs a medium to travel through like air, water, wood and metal.

Voices;

Whistle;

Horns;

Musical instrument.

 

Chemical energy (another type of Potential energy) ·         It is the energy stored in food, gasoline or chemical combination. Striking a match;

Combining vinegar and baking soda to form CO2

Electro-magnetic energy ·         It is a combination of heat and light energy.

·         Light energy travels out in all directions in waves.

 

A light bulb;

The glowing coil on a toaster;

The sun and headlights on car;

 

Electrical energy ·         Energy produced by electrons moving through a substance is known electrical energy.

·         It lights our homes, runs motors and makes our TVs and radios work.

 

CD players;

TV;

Video games

 

Nuclear energy ·         It is produced when atom is splitted.

·         A tremendous amount of energy is released when this happen.

Atomic bomb;

Nuclear power plant;

Nuclear submarine;

The Sun.

 

Solar energy It is the energy radiated by the Sun.  

Solar cooker;

Solar cell.

 

TYPE OF MECHANICAL ENERGY:

Kinetic energy  and Potential  or Mutual energy

KINETIC ENERGY: When a body is in a motion it possesses energy called kinetic energy.  It is measured as the amount of work, that a body can perform before coming to the rest.

EXAMPLES  

  • A bullet fired from a gun penetrates a target due to the kinetic energy it possesses.
  • Energy possessed by a moving hammer as it drives a nail into a piece of wood.
  • The kinetic energy of flowing water .
  • A falling coconut from tree.

 

EXPRESSION FOR KINETIC ENERGY: A body of mass m initially lying at rest i.e. u=0  on a perfectly frictionless surface. Let the body possess a velocity v after sometime, then the kinetic energy of the body is

k = 1/2 mv2

Kinetic energy  is equal to half of the product of mass and square of it’s velocity.

 

POTENTIAL OR MUTUTAL ENERGY:  The energy possessed by a body by virtue of its positive or centrifugation is called potential energy or mutual energy  or energy of centrifugation.

TYPES OF POTENTIAL ENERGY

It is of the following three types:

  • Gravitational potential energy
  • Elastic potential energy
  • Electrostatic potential energy

EXAMPLES

  • Water stored in a dam.
  • Potential energy of a stretched bow.
  • Potential energy of a compressed gas.
  • Potential energy of a system of charges.

EXPRESSION FOR GRAVITATIONSAL POTENTIAL ENERGY: We define this energy of an object at a point above the ground as the work done in raising it from the ground to that point against gravity. This can be expressed as:

W = F X S

In another way, W = mgh (here h is the height teavelled by the object)

This expression is obtained if gravitational potential energy is taken as zero  on the surface of the earth. Therefore, u = mgh

This work is stored in the body as it’s gravitational potential energy.

So, the gravitational potential energy for the earth body system is given by u = mgh.

                                           ENERGY TRANSFORMATION

According to the law of conservation of energy , The energy  can not be created or destroyed; it can be transformed from one type to another.

 

   

ORIGINAL FORM OF ENERGY TRANSFORMATION FORM OF ENERGY EXAMPLES
Mechanical energy Electrical energy In the reservoir of adam ,water has potential energy. When water falls, it loses its potential energy and gains kinetic energy.
Electrical energy Mechanical energy An electric motor is an arrangement in which electrical energy changes into the mechanical energy.
Electrical energy Heat energy Electric heater, oven, geyser convert electrical energy into heat energy when in use.
Electrical energy Sound energy A loudspeaker when in use, converts electrical energy into the sound energy.
Electrical energy Light energy When an electric bulb glows possessing electric current through it emitting heat and light.
Light energy Electrical energy In a  solar cell or photoelectric cell  electrical energy is produced by light energy.
Heat energy Mechanical energy  A steam engine moves by burning of coal where burning produces heat energy which makes the engine move.
Chemical energy Electrical energy This conversion takes place in a chemical cell, the chemical energy of the cell is converted into electrical energy.
Chemical energy Heat energy When fossil fuels such as wood, coal, gas are burnt chemical energy of these fuels changes into the heat energy.
Chemical energy Mechanical energy In automobiles, the chemical energy of petrol and diesel change into the mechanical energy.
Sound energy Electrical energy A microphone converts sound energy into the electrical energy.
Electrical energy Chemical energy The inverters which we use in our homes first convert electrical energy into chemical energy and later chemical energy back into electrical energy.

 

 

 

 

 

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