A bicyclist first goes up and then down a hill with constant speed. He ends up at the same height as at the start? I dont understand why to explain the law of conservation of energy my book has stated that all of the cyclists chemical energy eventually ends up as thermal energy? Please explain.
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$\begingroup$ The chemical energy has to go somewhere if energy is conserved. From the problem, there is no net change in KE or PE. So they say the chemical energy went into thermal energy via body heat $\endgroup$– ZacharyCCommented Mar 2, 2020 at 20:57
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When the bicyclist goes up the hill at constant speed, there is no change in kinetic energy of the bicyclist. Therefore, at the top of the hill part of chemical potential energy of the bodies muscles has done work that is stored as gravitational potential energy, part has been dissipated as heat internal to the body since the body is not 100 percent efficient in converting chemical potential energy into external work, and some is dissipated in other sources of friction (air resistance, friction in bicycle moving parts, etc.).
When the bicyclist goes down the hill at constant speed, none of the gravitational potential energy at the top of the hill is converted into an increase in kinetic energy, as in the case of a freely falling object. That means the energy the bicyclist used to give it gravitational potential energy had to go somewhere, and that would again be in the form of heat, primarily heat in the brakes of the bike, heat dissipated in the bicyclist's muscles when they apply force to the brakes, and other sources of friction (air, moving parts, etc.).
Bottom line: Since there is no overall change in kinetic or gravitational potential energy going up and down the hill, in one way or another all of the chemical potential energy used by the bicyclist winds up as heat, either internal to the body, or as external friction heating.
Hope this helps.
