Interactions that depend only on position can have a potential energy.

These are called conservative forces (保守力)

Final Initial

For conservative forces, the change in energy does not depend on the path taken. Final Initial

For conservative forces, moving in a loop (闭合路径) causes no change in energy. Final Initial

All fundamental forces are conservative.

A conservative force is the negative gradient of its potential energy Example:

What about friction?

The interaction does not depend on position; it depends on the direction of the velocity. Therefore, it is not a conservative force. So there is no potential energy associated with friction.

Block and table both heat up. Δx Block and table both heat up. Kinetic energy is converted to thermal energy (热能).

The total change in energy over the return trip is not zero. Δx The total change in energy over the return trip is not zero. Kinetic energy was lost to heat both times.

We cannot calculate the work done by the table on the block We cannot calculate the work done by the table on the block. Friction is too complicated! All we know is the change in thermal energy ΔEthermal of the (block + table) system.

The energy principle for systems with internal friction where Important: This is not the work of one object on the other. It is the change in thermal energy of the whole system.

Air drag and fluid drag are also non-conservative forces. Object falling through fluid:

Air drag and fluid drag are also non-conservative forces. Object falling through air: In both cases,

Example: Skiing, with friction System: Skier + hill + Earth Surroundings: none Example: Skiing, with friction Initial state: Skier on top of hill, at rest μk = 0.090 θ Final state: Skier moving at base of hill; skis and hill a bit hotter L h θ

Example: Skiing, with friction Energy principle: No work done on system, so

Example: Skiing, with friction Energy principle: No work done on system, so

Example: Skiing, with friction Energy principle: No work done on system, so