# Does the work done by friction include the energy lost as heat in a system?

1. Nov 13, 2014

### Hereformore

So friction as a nonconservative force, is path dependent when it comes to how much work is lost from a system right?

What confuses me however is understanding what that means, in terms of energy. So the work done by friction includes the energy that was neeeded to stop an obect (like a braking car) PLUS the heat released during the transition right?

Its weird because it means we assume that the friction force times the distance takes into account heat as well. I thought heat didnt count.

2. Nov 13, 2014

### A.T.

When you stop an object, energy is released, not needed. The work done by friction on this object is negative, in the frame where it stops.

Why plus? released heat energy = negative work done = reduction of kinetic energy

3. Nov 13, 2014

### Staff: Mentor

The work done by friction equals both the energy lost by the car and the "heat" released.

Think of work as a transfer of energy between two objects. If you stop the car by running it head-on into a spring, the car loses kinetic energy and the spring gains an equal amount of elastic potential energy. The work done by the spring is the means by which the energy is transferred. If you stop the car by jamming on the brakes, the car loses kinetic energy and the tires and road gain an equal amount of thermal energy (they become warmer). The work done by the friction is again the means by which the energy is transferred.

In everyday language we call the energy gain of the road and tires "heat", but when you study thermodynamics you'll find that physicists don't call this "heat." To us, "heat" is energy transfer that is caused solely by a temperature difference between two objects (e.g. when you put a hot object into cold water). All other energy transfers are "work" of some kind. This is encoded in the First Law of Thermodynamics: ΔU = Q + W (the change in a system's internal energy equals heat plus work).