# Law of Conservation of Energy Derivation, Law of Conservation of Energy (For CBSE, ICSE, IAS, NET, NRA 2022)

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# Law of Conservation of Energy Derivation

• Consider the potential energy at the surface of the earth to be zero. Take an example of a fruit falling from a tree.
• Consider a point A, which is at some height ‘H’ from the ground on the tree, the velocity of the fruit is zero hence potential energy is maximum there.

• When the falling of fruit, its potential energy is decreasing and kinetic energy is increasing.
• At point B, which is near the bottom of the tree, 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.
• Thus, at this point, it will have both kinetic and potential energy.

According to third equation of motion,

Using (1) , (2) and (3)

• Similarly, if we see the energy at point C which is at the bottom of the tree, it will come out to be mgH.
• We know that at that point,

is the new energy

Where

is the new height.

As the body is at height X from the ground,

Using (4) and (5) we get,

is referred to the new height

## Examples of Law of Conservation of Energy

• In a generator, mechanical energy is converted into electrical energy.
• Water can produce electricity. Water falls from the sky, converting potential energy to kinetic energy. This energy is then used to rotate the turbine of a generator to produce electricity. In this process, the potential energy of water in a dam can be turned into kinetic energy which can then become electric energy.
• In hydroelectric power plants, waterfalls on the turbines from a height. This, in turn, rotates the turbines and generates electricity. Hence, the potential energy of water is converted into the kinetic energy of the turbine, which is further converted into electrical energy.
• When playing pool, the cue ball is shot at a stationary 8 ball. The cue ball has energy. When the cue ball hits the 8 ball, the energy transfers from the cue ball to the 8 ball, sending the 8 ball into motion. The cue ball loses energy because the energy it had has been transferred to the 8 ball, so the cue ball slows down.
• In a torch, the chemical energy of the batteries is converted into electrical energy, which is converted into light and heat energy.
• In a microphone, sound energy is converted into electrical energy.
• You ran across the room and bumped into her brother, pushing him to the floor. The kinetic energy you possessed because of your movement was transferred to her brother, causing him to move.
• When a moving car hits a parked car and causes the parked car to move, energy is transferred from the moving car to the parked car.
• When playing the lawn game bocce ball, a small ball is thrown with the intention of hitting larger balls and causing them to move. When a larger ball moves because it was hit by the small ball, energy is transferred from the small ball to the larger one.
• In a loudspeaker, electrical energy is converted into sound energy.
• When you push a book across the table, the energy from your moving arm is transferred from your body to the book, causing the book to move.
• When fuels are burnt, chemical energy is converted into heat and light energy.
• A cat sitting on the highest branch of a tree has what is known as potential energy. If he falls off the branch and falls to the ground, his potential energy is now being converted into kinetic energy.
• Chemical energy from food is converted to thermal energy when it is broken down in the body and is used to keep it warm.
• When kicking a football that is sitting on the ground, energy is transferred from the kicker՚s body to the ball, setting it in motion.

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