Answer:
The law of conservation of energy states that for an isolated system (net external forces = 0), the total energy of the system remained conserved: in other words, energy cannot be created or destroyed, but only converted from one form to another.
We can use the following two examples to show this law:
1) A ball dropped from a cliff and in free fall (no air resistance).
In this situation, the ball when it is stationary on the cliff has gravitational potential energy:
U = mgh
where m is its mass, g the gravitational acceleration, h the heigth of the cliff. As the ball falls down, h decreases, so its potential energy decreases; however, the ball gains speed, so its kinetic energy increases, according to:
where v is the speed of the ball: so, in this case, gravitational potential energy is converted into kinetic energy.
2) A bow throwing a dart
When the bow is stretched, there is elastic potential energy stored in the bow, due to the fact that the cord of the bow is stretched. As the bow is released, its position return to normal, so the elastic potential energy decreases , and it is converted into kinetic energy of the dart, since the dart gains speed.