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Law of Conservation of Energy – Equation

December 17, 2012

Conservation of Energy is an important concept in Physics. We can define the Law ofConservation of Energy as “Energy can neither be created nor be destroyed but can be

transformed from one form to another”. For example, chemical energy can become kinetic
energy; heat energy can become light energy; but the energy remains within the system only.
From this, we can understand that energy is not lost but only transformed and is available in
another form within the system. The sum of all the energies within the system, together form a
constant. So, the Law of Conservation of Energy states that energy that is totally present in an
isolated system can be seen to remain same i.e. constant over time. In other words the Law of
Conservation of Energy states that the total energy of an isolated system is said to be conserved
over time as only the form of energy changes but the quantity does not change.

Equation of Law of Conservation of Energy
The Law of Conservation of Energy Equation is given by,
Energy spent in one activity/form = Energy gained in the related activity/form.

If some thing placed on a table falls down, then the potential energy of the thing is transformed
into the kinetic energy. Here, the Law of Conservation of Energy Formula is given by:
mgh = ½ mv^2

Here,

“Potential Energy = mass x acceleration due to gravity x height”
“Kinetic Energy = ½ * mass * square of velocity”

By applying values in the above equation, we get:
P.E. = – K.E, that can be rewritten as P.E. + K.E = 0

The sum of the potential energy and the kinetic energy gives the total mechanical energy. Thus,
the conservation of enrgy is given by “E = T + V”, in mechanics. Here, “T” and “V” refer to kinetic
energy and potential energy respectively. The prerequisites for applying this formula are that
both T and V should not be the explicit functions of time. With regard to velocities, the kinetic
energy is a quadratic form but on the contrary, the potential energy does not depend on the
velocities. The value of E i.e. the total energy is directly proportional to the frame of reference’s
motion.

Example of Law of Conservation of Energy
One of the best examples of law of conservation of enrgy is pendulum.

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