Energy When Friction Is in the System

A roller coaster losing height on each hill isn't losing energy, it's losing usable mechanical energy to friction and air resistance. Every bit of kinetic or potential energy that seems to vanish has actually gone into jostling atoms in the wheels, the track, and the air, which shows up as a rise in temperature. That's thermal energy, and once you count it, the total energy of the coaster plus track plus air is exactly the same as it started.

This is why bar charts need a thermal energy bar whenever friction is present. Before friction acts, energy might be all kinetic or split between kinetic and potential. As the object slides or rolls against a rough surface, bars for kinetic and potential energy shrink and a thermal bar grows to match, so the total bar height never changes. The rule behind this is the work-energy relationship: the work done by friction, equal to the friction force times the distance traveled, equals the energy transferred into that thermal bar.

This connects directly to the work done by non-conservative forces in the broader energy equation: initial mechanical energy plus work done on the system equals final mechanical energy plus energy lost to friction. Where earlier topics in this unit let you assume mechanical energy stays constant, friction is the signal that you need the fuller accounting, treating thermal energy as just another entry in the ledger rather than a loss.