Impulse

times acceleration. It can apply, too, to things where the mass is changing, as in a rocket that loses mass as it expends fuel.

IMPULSE

The actual effect of a specific force on an object depends on how long the force is acting on the object as well as the magnitude of the force. Small forces would have to act over a long period of time to cause the same change in momentum as a large force. The concept of this from a physics perspective is the change in momentum. This is the force multiplied by the change in time. This change in momentum is referred to as “impulse”. It is the average net force multiplied by the time the force acts.

While you may not have heard of impulse, you intuitively understand how it works. Things like dashboard padding in a car and airbags allow the net force to act over a much larger square area and over a longer period of time when the vehicle has a sudden stop. The force to bring the occupant to a stop will be less if it acts over a larger period of time. Longer collision times will equal decreased force applied. This is why racing cars are made to collapse versus being rigid; the impulse to the drive is less when the automobile crashes.

So far, you have determined that force, acceleration, and momentum are vectors. Because of this, impulse is also a vector. If something strikes a wall with a certain velocity directly versus at an angle to the wall, there will be a difference in the impulse because the force on the wall will be different. This will lead to a difference in the impulse on the wall.

One issue that comes to mind is that forces are not usually constant. Forces can vary over time so that you need to get some type of average effective force that produces as close to the same result as a time-varying force as possible. Figure 38 shows the force varying over time for a ball that bounces off the floor.

Figure 38.

The area under the curve is the momentum and, the impulse is the change in momentum between two periods of time. Of course, there can be more complex mathematical calculations that determine force over time that are beyond the scope of this course. This is why the effective force is used.

The important thing to remember about momentum is that it must be conserved. It does not seem to be conserved within a small system; however, it will be conserved if the system is sufficiently large enough. An example of this might be a football player that bounces with momentum against a goalpost. The player will have a force applied that will bounce the player backward. There will also be a minor momentum and force applied to the ground that holds the goalpost and to the earth itself, which are so minor that they are not usually put into play in equations regarding this situation.

What would happen in a system where there are two bodies of roughly the same mass that collide with one another. Say, for example, that two cars of equal mass are going in the same direction but the car in the back is faster and hits the car in the front. If friction is negligible, the car behind will slow its momentum and car in front gains momentum. The total momentum of the 2-car system will remain constant. Figure 39 shows this conservation of momentum: