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What is the law of conservation of enegy

What does law of conservation of energy mean?

According to law of conservation of 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.”

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.

Energy conservation 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.

The velocity of the body can be found by formula:

\2gh={ V }_{ f }^{ 2 }-{ V }i^{ 2 }\\ Where\quad \quad { V }_{ i }=Initial\quad velocity\quad at\quad 'A'=0\\ { V }_{ f }=final\quad velocity\quad at\quad O=v\\ 2gh={ v }^{ 2 }-{ 0 }^{ 2 }\\ { V }^{ 2 }=2gh\\ K.E\quad at\quad O=\frac { 1 }{ 2 } m\times 2gh=mgh\\ P.E\quad at\quad O\quad (near\quad ground)=0\\ Total\quad energy\quad of\quad the\quad body\quad at\quad 'O'=K.E\quad +\quad P.E\\ =mgh\quad +0\\ =mgh\quad ................(2)\\ Let\quad at\quad any\quad instant\quad the\quad point\quad B\quad which\quad is\quad at\quad a\quad distance\quad "x"\quad from\quad B.\\ If\quad V\quad be\quad the\quad velocity\quad of\quad the\quad body\quad at\quad point\quad B\quad then:\\ K.E\quad at\quad B=\frac { 1 }{ 2 } m{ v }^{ 2 }\\ P.E\quad at\quad B\quad =mg(h-x)=mgh\quad -mgx\\ V\quad can\quad be\quad found\quad by\quad formula:\\ 2gh\quad ={ V }_{ f }^{ 2 }-{ V }i^{ 2 }\\ Where\quad { V }_{ i }=0\quad \quad \quad \quad { V }_{ f }=\acute { V } \quad \quad and\quad h=x\\ 2gx={ (\acute { V } ) }^{ 2 }-{ (0) }^{ 2 }\\ ={ (\acute { V } ) }^{ 2 }=2gx\\ \therefore \quad K.E\quad at\quad B=\frac { 1 }{ 2 } m\times 2gx=mgx\\ Total\quad energy\quad at\quad B=K.E\quad +\quad P.E\\ =mgx\quad +mgh\quad -mgx\\ Total\quad energy\quad at\quad B=mgh\quad \quad .............(3)\\

From equations (1),(2) and (3) it can be seen that the total energy of the body remains constant every where 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.

Examples of law of conservation of energy:

  1. 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

2: 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

3: 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

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

Mechanical energy = Heat energy + losses

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