Conservative and Nonconservative forces

Let us list the key elements of the two situations we just discussed:

1. The system consists of two or more objects.

2. A force acts between a particle-like object (tomato or block) in the system and the rest of the system.

3. When the system configuration changes, the force does work (call it ) on the particle-like object, transferring energy between the kinetic energy of the object and some other form of energy of the system.

4. When the configuration change is reversed, the force reverses the energy transfer, doing work in the process.

In a situation in which is always true, the other form of energy is a potential energy, and the force is said to be a conservative force.As you might suspect, the gravitational force and the spring force are both conservative (since otherwise we could not have spoken of gravitational potential energy and elastic potential energy, as we did previously).

A force that is not conservative is called a nonconservative force.The kinetic frictional force and drag force are nonconservative. For an example, let us send a block sliding across a floor that is not frictionless. During the sliding, a kinetic frictional force from the floor does negative work on the block, slowing the block by transferring energy from its kinetic energy to a form of energy called thermal energy (which has to do with the random motions of atoms and molecules). We know from experiment that this energy transfer cannot be reversed (thermal energy cannot be transferred back to kinetic energy of the block by the kinetic frictional force). Thus, although we have a system (made up of the block and the floor), a force that acts between parts of the system, and a transfer of energy by the force, the force is not conservative. Therefore, thermal energy is not a potential energy.

When only conservative forces act on a particle-like object, we can greatly simplify otherwise difficult problems involving motion of the object. The next section, in which we develop a test for identifying conservative forces, provides one means for simplifying such problems.