Law of Conservation of Energy

According to this law,
energy can only be converted from one form to another; it can neither be created or destroyed. The total energy before and after the transformation remains the same.”

The law of conservation of energy is valid in all situations and for all kinds of transformations.

Consider a simple example. Let an object of mass, m be made to fall freely from a height, h.

At the start, the potential energy is mgh and kinetic energy is zero. It is zero because its velocity is zero. The total energy of the object is thus mgh.
As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, the kinetic energy would be ½mv2.
As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h = 0 and v will be the highest. Therefore, the kinetic energy would be the largest and potential energy the least.

However, the sum of the potential energy and kinetic energy of the object would be the same at all points.

That is,
potential energy + kinetic energy = constant

T E = mgh + 1/2 mv2 = Constant
The sum of kinetic energy and potential energy of an object is its total mechanical energy.
We find that during the free fall of the object, the decrease in potential energy, at any point in its path, appears as an equal amount of increase in kinetic energy. (Here the effect of air resistance on the motion of the object has been ignored.) There is thus a continual transformation of gravitational potential energy into kinetic energy.

Law of Conservation of Energy Derivation

Considering the potential energy at the surface of the earth to be zero. Let us see an example of a object falling from height .

Consider a point A, which is at height ‘h’ from the ground on the tree, the velocity of the fruit is zero hence potential energy is maximum there.

E = mgh———- (1)

When the fruit is falling, its potential energy is decreasing and kinetic energy is increasing.

At point B, which is near the bottom , the fruit is falling freely under gravity and is at a height X from the ground, and it has speed as it reaches point B. So, at this point, it will have both kinetic and potential energy.

Examples of the law of conservation of energy
The majority of scientific discoveries are based on the idea that energy is conserved when it is changed from one form to another. Numerous mechanical and electrical devices only rely on the law of energy conservation to function. Here, we’ll talk about a few instances.

The chemical energy of the batteries in a torch is transformed into electrical energy in a torch, which is then transformed into light and heat energy.
Water falls that fall from a great height onto the turbines in hydroelectric power plants. In turn, this causes the turbines to turn and produces electricity. Thus, the kinetic energy of the turbine is created from the potential energy of the water, which is then transformed into electrical energy.

Electrical energy is transformed into sound in a loudspeaker.

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