What is nonconservative force

Forces are either conservative or nonconservative. Conservative forces were discussed in Chapter 7. 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 Figure 1 , 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.

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.

Figure 2 compares the effects of conservative and nonconservative forces. We often choose to understand simpler systems such as that described in Figure 2 a first before studying more complicated systems as in Figure 2 b. Now let us consider what form the work-energy theorem takes when both conservative and nonconservative forces act.

We will see that the work done by nonconservative forces equals the change in the mechanical energy of a system. As noted in Chapter 7. That is,. Consider Figure 3 , in which a person pushes a crate up a ramp and is opposed by friction. In Figure 3 , this is the work done by the person minus the work done by friction. So even if energy is not conserved for the system of interest such as the crate , we know that an equal amount of work was done to cause the change in total mechanical energy.

This means that the amount of work done by nonconservative forces adds to the mechanical energy of a system. For example, when you push a lawn mower at constant speed on level ground, your work done is removed by the work of friction, and the mower has a constant energy. Consider the situation shown in Figure 4 , where a baseball player slides to a stop on level ground. Fossil Fuels. Nuclear Fuels. Acid Rain. Climate Change. Climate Feedback. Ocean Acidification.

Non-conservative forces are dissipative forces such as friction or air resistance. These forces are path dependent; therefore it matters where the object starts and stops. The work done by a conservative force is independent of the path; in other words, the work done by a conservative force is the same for any path connecting two points:.

The work done by a non-conservative force depends on the path taken. Equivalently, a force is conservative if the work it does around any closed path is zero:.

The work done going along a path from B to A is the negative of the work done going along the same path from A to B, where A and B are any two points on the closed path:.

You might ask how we go about proving whether or not a force is conservative, since the definitions involve any and all paths from A to B, or any and all closed paths, but to do the integral for the work, you have to choose a particular path. There are mathematical conditions that you can use to test whether the infinitesimal work done by a force is an exact differential, and the force is conservative.

These conditions only involve differentiation and are thus relatively easy to apply. You may recall that the work done by the force in Example 7. For that force,. Can you see what you could change to make it a conservative force? Which of the following two-dimensional forces are conservative and which are not?