Everybody knows that a heavy truck is harder to stop than a small car moving at the same speed. We state this fact by saying that the truck has more momentum than the car. Specifically, momentum is defined as the product of the mass of an object and the objects velocity, or P=mv. (We use "P" to indicate momentum.) From this definition, we can see that a moving object can have a large momentum if either it's mass or its velocity is large. The truck has more momentum than the car because it has a greater mass. If the truck were at rest, it would have no momentum at all.

Changes in momentum occur when there is either a change in mass or in velocity. Since mass usually remains constant, a change in momentum is almost always a change in velocity. When momentum changes, acceleration occurs. Thus, from Newton's first law, we know that a force must act on the object. So a force causes a change in momentum. However, there is something else that is important in the changing of momentum-time. Apply a force for a brief amount of time, and a small change in momentum occurs. Apply the same force for a longer amount of time, and a larger change of momentum occurs. We name the product of force and the time interval (the change of momentum) impulse. Impulse is force times time, or P=ft. (the symbol means "change in".) By putting in the formula for momentum, we get this new formula: P=ft=mv. With this formula, you can calculate the change of momentum if you are given force & time or mass & velocity.

If you with to increase the momentum of something as much as possible, you must not only apply the greatest possible amount of force, but also apply it over the largest amount of time. Long-range cannons have long barrels. The longer the barrel, the larger the velocity of the cannonball when it emerges from the barrel. This is because the force of the gunpowder acts on the cannonball for a greater time when the barrel is longer than when it is shorter.

If you are in a car that is out of control and going to crash, would you rather crash into a brick wall or a haystack? The haystack, of course. You don't need physics to know this, but physics will help you understand why a haystack will not hurt your car as much as a brick wall. In both cases, your momentum will be changed by the same amount. Your car will go from some momentum to no momentum. So the impulse required to stop your car will be the same when crashing into a brick wall or a haystack. Remember, impulse is force multiplied by time. If we want to decrease the force of impact, we must lengthen the time. This is what the haystack does for you. The hay moves and rebounds, extending the time of the impact. Therefore, the force of the impact will decrease. The wall will not move at all. The change of momentum will occur during a very short time interval, so the force will be large.

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When you are hit in the head with a basketball, obviously it hurts. But it will hurt even more if the basketball bounces off your head! This is because the impulse needed to stop the basketball, and then, in effect, throw it back up again is more than is needed to just stop the basketball. To produce that greater impulse, the force must be larger. Ouch!

Remember from lesson 3 that Newton's second law says that to accelerate something we must apply an outside force to it. We say the same thing in this chapter when we say that for an object to change it's momentum it must be acted on by an impulse. In both cases, the force (or impulse) must be external. An internal force or impulse can not change the acceleration or momentum of an object. (we talked about this at the end of lesson 3.) Consider a gun. When the gun fires the bullet, all forces are internal. Therefore, the total momentum can not change. We also see that by Newton's laws of action and reaction that the force on exerted on the bullet is also exerted on the gun, so the gun recoils. Looking closer, we see that the momentum of the recoiling gun is exactly the same as the momentum of the fired bullet. Since the momenta are in opposite directions, they cancel out and the total momentum remains the same.

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The important idea to be gained here is that momentum is conserved. The momentum before and after firing is the same. No momentum was gained, no momentum was lost. Momentum is always conserved in collisions. The total momentum before the collision and the total momentum after the collision is always the same whether the objects involved bounce off each other, stick together, or fly off in strange directions.

It is important to note that momentum vectors can be added by vector addition. If two objects collide at an angle, the sum of their momentum before the collision will equal the sum of their momentum vectors added together.

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