velocity vs. time | acceleration vs. time | |F| cos(theta) vs.position

Please wait for the animation to completely load.

When we talk about energy we tend to focus on the change in kinetic energy and change in potential energy, where the change in potential energy is the negative of the work done by conservative forces. But what happens with nonconservative and external forces? (Note that some books lump external forces with nonconservative forces.) Well, these are the forces that cause the total energy of the system to change. In other words, without a nonconservative force or an external force, the total energy would never change. This is what we mean by the statement of energy conservation, ΔKE + ΔPE = 0.

If there are nonconservative or external forces, the total energy will change. When we say nonconservative forces we usually are thinking about kinetic friction. Kinetic friction is a special force that always decreases the total energy of the system (the amount of work that it does on an object is always negative). If friction exists in a system, and you wait long enough, all of the energy will dissipate. What about external forces? Do they add or take energy from the system? Well, it depends.

Consider the cart in the animation. The cart interacts with the two-handed image if the image is near the left-hand or right-hand end of the cart (position is given in meters and time is given in seconds). The arrow below the cart shows the direction and strength of the external force applied. Reset the animation if the cart goes off the end of the track. Restart.

Move the cart around and look at each of the graphs. Now focus on the |F| cos(theta) vs.position graph, which tells you about the work done by the external force (the hand). Is it always positive or is it always negative? It can be positive or negative depending on the circumstances. If the work done by the force is positive, the energy of the system (the cart and Earth) increases. Since the potential energy of the cart remains fixed (since it does not change height), all of this energy is seen as kinetic energy. If the work done by the force is negative, the energy of the system decreases. Again, the change in energy is seen as kinetic energy.