Now let's use this. Suppose I have a very low-friction cart with a constant-strength force pushing on it (in this case, it has a fan mounted on top). Since there is a force, the cart will speed up. Here's what that looks like.

We can now use the momentum principle to find the change in speed over some time interval. Here are some mostly real values for the cart above (I made some slight modifications due to measurement errors).

• Cart mass = 0.85 kg
• Fan force = 0.15 newtons
• Time interval = 3.0 seconds

With the force and the time interval, I get a change in momentum (F × Δt) of 0.45 kgm/s. Dividing this change in momentum by the mass, I get a final speed (assuming it starts from rest) of 0.53 m/s. Yay.

OK, let's do it again. This time with TWO fans. Here is a cart with two equal forces pushing in opposite directions. After turning on the two fans, I give the cart a push so that it moves to the right.

In this case, the net force on the cart is zero newtons since the force pushing to the right has the same magnitude as the force pushing to the left. With zero net force, there is zero change in momentum and the cart moves along at a constant speed.

One more case. Suppose I take a box with some masses and pull it along the table at a constant speed. In this case, there is a force pulling to the right (the string) and a frictional force pulling to the left.

Again, since the net force is zero, there is no change in momentum. Everything is fine.

Work-Energy Principle

This isn't completely new. In fact, you can derive this idea from the momentum principle. The work-energy principle says that the work (W) done on a point mass is equal to its change in kinetic energy. Work is done by a force moving a certain distance. Actually, it's only the force in the direction of motion that matters. As an equation, it looks like this.