Question

State the principle of conservation of energy.

Answer 1

Hint: In this question we have been asked to state the principle of conservation of energy. Therefore, to answer this question we shall discuss the principle of conservation of energy. We shall discuss the mathematical formula and its derivation. We know that the principle of conservation of energy states that energy can neither be created nor it can be destroyed.

Complete solution:
In physics, according to the principle of conservation energy, the energy between interacting bodies in a system always remains constant. The energy can neither be created nor can it be destroyed. However, the energy can be transformed from one form to another. As an object is moving through time, the kinetic, potential, gravitational energy of a closed system is always conserved. Therefore, the total energy remains the same. It is necessary that the system be an isolated system.
Let us take an example of a pendulum. When the pendulum is resting at equilibrium position, there is no energy in the system. However, when we pull the pendulum at an angle, it gets displaced vertically. Therefore, potential energy is now stored in the pendulum by conversion from kinetic energy produced due to pulling. As soon as the pendulum is released the potential energy is converted into kinetic energy and the pendulum starts to swing. Therefore, everytime a pendulum reaches its maximum amplitude on either side the kinetic energy is converted to potential.
The total energy of a system is given by the sum of potential and kinetic energy.

Therefore, by principle of conservation of energy we can say that,
\[K{{E}_{initial}}+P{{E}_{initial}}=K{{E}_{final}}+P{{E}_{final}}\]

Note:
One of the consequences of the principle of conservation of momentum is that the perpetual motion machine does not exist. The perpetual motion machine is a hypothetical machine that is supposed to use all the energy provided as input and provide 100 % output. There is always some amount of energy that will be leaked to the surrounding or will be used by other unnecessary parts of the system.