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law of conservation of energy:Definition,formula and examples

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According to the law of conservation of mechanical energy:”Energy can neither be created nor is it destroyed.It can only be transformed from one form to another.A loss in one form of energy is accompanied by an equal increase in the other forms of energy.The total energy remains constant.”

Explanation

The kinetic and potential energies are both different forms of the same basic quantity, mechanical energy.The total mechanical energy of a body is the sum of the kinetic energy and potential energy.In our previous discussion of a falling body, potential energy may change into kinetic energy and potential energy change into kinetic energy,but the total energy remains constant.Mathematically it is expressed as:

Total Energy = P.E + K.E = Constant

It is one of the fundamental law of physics. We daily observe many energy transformations from one form to another. Some forms, such as electrical and chemical energy, are more easily transferred than others, such as heat. Ultimately all energy transfers result in the heating of the environment and energy is wasted. For example, the P.E of the falling object changes to K.E, but on striking the ground, the K.E changes into the heat and sound. If it seems in an energy transfer that some has disappeared, the lost energy is often converted into heat. This appears to be the fate of all available energies and is one reason why new sources of useful energy have to be developed.

According to Einstein’s mass-energy relation:

E=mc² ,energy can be converted into mass and mass can be converted to energy.Pair production is the example of conversion of energy into mass.

On the other hand nuclear fission and nuclear fusion are examples of conversion of mass into energy.

 Conservation of Energy formula

Total energy = kinetic energy +  potential energy

 conservation of energy equation

law of conservation of energy

Consider a body of mass “m” placed at a point “p” which is at a height “h” from the ground.

P.E of the body at A =mgh

K.E of the body at point A =0

Total energy of the body at point P=K.E +P.E =0 + mgh

Total energy at P=mgh …………(1)

If the body is allowed to fall freely under the action of gravity then its potential energy will go on decreasing while its kinetic energy will go on increasing.

Just before hitting the ground the potential  energy of the body will be minimum or zero while the K.E of the body will be maximum.If “v” be the velocity of the body just before hitting the ground then K.E of the body=½mv².

law of conservation of energy equation formula and derivation

law of conservation of energy equation formula and derivation

Total energy at Q =K.E + P.E

=mgx + mgh – mgx

Total energy at Q = mgh  ————(3)

 

From equations (1),(2) and (3) it can be seen that the total energy of the body remains constant everywhere provided there is no force of friction involved during the motion of the body.

If there is some force of friction acting on the body then a friction of P.E is lost in doing work against the force of friction.Thus:

Total energy =K.E + P.E + Loss of energy or work done against force of friction.

 conservation of energy examples

  • When we switch on an electric bulb, we supply electrical energy to it which is converted into heat and light energies.i.e.

Electrical energy = Heat energy + Light energy

  • Fossil fuels e.g coal and petrol is stores of chemical energy.When they burn, chemical energy is converted into heat energy i.e .

Chemical energy = Heat energy + losses

  •  The heat energy present in the steam boiler can be used to derive a steam engine.Here heat energy is converted into kinetic (mechanical energy) ,i.e .

Heat energy =Mechanical energy + Losses

  • In rubbing our hands we do mechanical work which produces heat,i.e

Mechanical energy = Heat energy + losses

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