# Conservation of Energy.

The principle of conservation of energy:
It states that ‘energy is neither created nor destroyed’ but can be changed from one form to another.

In any system, the total original energy is equal to the total final energy. For example, electrical energy is changed to light energy in the bulb. However, the bulb also feels hot because some of the energy is changed to heat.
Therefore, light energy plus the heat energy is equal to the electrical energy supplied.

Thus from this principle, we conclude that;
No new energy is created
Total existing energy is not destroyed
Energy is only changed from one form to another.

As energy is changed from one form or state to another, an energy converter (Device) is required to ease the conversion. Examples of such devices are shown in the table below.

A body of mass m at a height h above the ground, has a potential energy, P.E = mgh. At this point, the velocity of the body is 0ms-1 hence it has no kinetic energy. (K.E. = 0J).
When the body is released, it begins to fall with an acceleration g. The velocity of the body thus increases as the height, h decreases. The body therefore gains kinetic energy at the expense of potential energy.
When the body is just reaching the ground, the height, h is zero (h = 0m) while its velocity is given by;

The above illustration shows that energy is conserved. Mechanical energy is continually transformed between kinetic and potential energy.

A swinging pendulum.
The transformation of energy between kinetic and potential energy can also be seen in a swinging pendulum.

At the end (extremes) of the swing, the energy of the pendulum bob is only potential.
As it passes the central position, it has only kinetic energy.

In other positions between the extreme ends and the central position, it has both potential and kinetic energies.

As the bob falls from the left towards the central position, it gains K.E at the expense of P.E.
As it rises from the central position towards the left end, it gains P.E at the expense of K.E.

Example:
A ball of mass 200g falls freely from a height of 20m above the ground and hits a concrete floor and rebounds to a height of 5m. Given that g = 10ms-1, find the;
i) P.E of the ball before it fell.
ii) Its K.E. as it hits the concrete.
iii) Velocity with which it hits the concrete.
iv) K.E as it rebounds.
v) Velocity with which it rebounds.
vi) Velocity when it has fallen through a height of 15m.

Solution:
(i) P.E=mgh (h=height from which the ball is dropped)

P.E=0.2×10×20

P.E=40J

(ii)
As it hits the concrete, Total P.E is converted to K.E

K.E=0.2×10×20

K.E=40J

(iii)
As it hits the concrete, Total P.E is converted to K.E

(iv)
As the bounces from the concrete, the K.E used to move the it from the bottom to the height h1 is converted to P.E at h1and it is momentarily at rest.

(v)
As the bounces from the concrete, the K.E used to move it from the bottom to the height h1 is converted to P.E at h1and it is momentarily at rest.

Example 2:
A 5Kg mass falls from a height of 20m. calculate the potential energy lost.

Example 3:
A 200g ball falls from a height of 0.5m. Calculate its kinetic energy just before hiting the ground.

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