The energy in a bicycle is 6000 J at the top of a hill. The brakes are applied and its potential energy at the bottom of the hill is 2000 J. How much thermal energy was produced?
The total energy of the bicycle at the top of the hill is 6000 J. As it comes lower and the height decreases, potential energy is transformed into kinetic energy and the bicycle's velocity should increase. This is prevented here by the application of the brakes that brings the bicycle to a halt at the bottom of the hill.
The potential energy of the bicycle is 6000 J at the top of the hill and at the bottom of the hill the potential energy is 2000 J. The difference between the two is 6000 - 2000 = 4000 J. This should have been the kinetic energy of the bicycle but it is converted to heat due to the application of the brakes.
The heat produced due to the application of the brakes is 4000 J.