7.5 Nonconservative forces

Learning objectives

By the end of this section, you will be able to:

• Define nonconservative forces and explain how they affect mechanical energy.
• Show how the principle of conservation of energy can be applied by treating the conservative forces in terms of their potential energies and any nonconservative forces in terms of the work they do.

The information presented in this section supports the following AP® learning objectives and science practices:

• 4.C.1.2 The student is able to predict changes in the total energy of a system due to changes in position and speed of objects or frictional interactions within the system. (S.P. 6.4)
• 4.C.2.1 The student is able to make predictions about the changes in the mechanical energy of a system when a component of an external force acts parallel or antiparallel to the direction of the displacement of the center of mass. (S.P. 6.4)

Nonconservative forces and friction

Forces are either conservative or nonconservative. Conservative forces were discussed in Conservative Forces and Potential Energy . A nonconservative force    is one for which work depends on the path taken. Friction is a good example of a nonconservative force. As illustrated in [link] , work done against friction depends on the length of the path between the starting and ending points. Because of this dependence on path, there is no potential energy associated with nonconservative forces. An important characteristic is that the work done by a nonconservative force adds or removes mechanical energy from a system . Friction , for example, creates thermal energy that dissipates, removing energy from the system. Furthermore, even if the thermal energy is retained or captured, it cannot be fully converted back to work, so it is lost or not recoverable in that sense as well.

How nonconservative forces affect mechanical energy

Mechanical energy may not be conserved when nonconservative forces act. For example, when a car is brought to a stop by friction on level ground, it loses kinetic energy, which is dissipated as thermal energy, reducing its mechanical energy. [link] compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in [link] (a) first before studying more complicated systems as in [link] (b).