the law of conversation of energy and describe the energy transformations that occur as you coast down a long hill on a bicycle and then apply the brakes to make the bike stop at the bottom.

Potential energy is transformed into kinetic energy

friction work decreases kinetic energy

Explanation:

The law of conservation of the mechanical energy is the sum of kinetic energy plus the different forms of potential energy, this energy is constant throughout the trajectory if the dissipative force (friction) is zero.

Let us apply this to our case, in the upper part of the trajectory almost all the mechanical energy is potential, and a very small part is kinetic, the bicycle goes very slowly, as it descends without pedaling the speed increases so that the kinetic energy it increases and the height decreases therefore the potential energy decreases, but the sum of the two energies remains constant.

Potential energy is transformed into kinetic energy

When the brakes are applied, a dissipative force enters the system that causes part of the energy to be transformed into heat and part into work of this dissipative force against the wheel, two resulting in a net decrease in mechanical energy and therefore a decrease in the speed of the bicycle, the value of this decrease is given by

W = DK