Momentum

Momentum can be defined as inertia in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. A moving train has a whole lot of momentum. A moving ping pong ball does not. You can easily stop a ping pong ball, even at high speeds. It is difficult, however, to stop a train even at low speeds.

Mathematically, momentum is mass times velocity, or p = mv.

Momentum is a vector quantity, because it’s based on velocity, so you’ll expect to have a number and a direction in your answer for momentum questions. The heavier something is and/or the faster it’s moving the more momentum it has. The more momentum something has, the more force it takes to get it to change velocity and the more force it can apply if it hits something.

Think about baseball. When you hit a baseball, do you just smack it with the bat or do you follow through with the swing? You follow through right? Do you see how impulse relates to your baseball swing? If you follow through with your swing, the bat stays in contact with the ball for a longer period of time. This causes the ball to go farther. Follow through is important in golf, bowling, tennis and many sports for the same reason. The longer the force is imparted, the farther and faster your ball will go.

Ok, let’s add impulse and momentum together and see what we get. Impulse changes momentum. If an object puts an impulse on another object, the momentum of both objects will change. If you continue to push on your stalled car, you will change the momentum of the car right? If you are riding your bike while not paying any attention and crash into the back of a parked car, you will put an impulse on the car and you and the car’s momentum will change. (As a kid, I did this pretty often. That’s what you get when you ride and wonder at the same time. Believe me when I tell you that my momentum changed a lot more than the car’s did!!)

In fact, there is a mathematical formula about this impulse and momentum thing. Impulse = change in momentum or Ft = change in mv. Force x time = mass x velocity. Does that sound familiar to anyone? It’s awfully similar to Newton’s second law (F=ma) isn’t it? In fact it’s the same thing: F t = m v

Now if we divide both sides by “t” we get F = mv / t.

Another way to say v is d/t (distance over time). So now we have F = m (d/t) / t. Those two “t’s” together are the same as t² and d/t² is “a” (acceleration). So what we have now is F = ma!

Here is a quick experiment… first, find a wall. Then hit it with your bare fist. (Take it easy, just hit it with enough force that you feel the impact.) Now put a pillow in front of the wall and hit it with about the same force as you hit it before. With the pillow in front of the wall, you can hit it a little harder if you like but again, don’t go nuts!

What did the pillow do? It slowed the time of impact. Remember our formula Ft = mv. When the momentum of your moving fist struck the wall directly, the momentum was cut to zero instantly and so you felt enough force to hurt a bit. When the pillow was in the way it took longer for your momentum to come to zero. So you could hit the pillow fairly hard without feeling much force. Basically a bike helmet is like a pillow for you head. It slows the time of impact, so when you fall off your bike, there is much less force on your head. Just be glad your mom doesn’t make you wear a pillow on your head!

So let’s go back to momentum for a minute. Momentum is inertia in motion. It is how much force it takes to get something to slow down or change direction. One more concept I’d like to give you this month, is conservation of momentum. This is basically momentum equals momentum or mathematically mv = mv. (Momentum is mass times velocity.) When objects collide, the momentum that both objects have after the collision, is equal to the amount of momentum the objects had before the collision. Let’s take a look at this with this experiment.

Second Law of Motion: Momentum is conserved. Momentum can be defined as mass in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. A moving train has a whole lot of momentum. A moving ping pong ball does not. You can easily stop a ping pong ball, even at high speeds. It is difficult, however, to stop a train even at low speeds.

Materials: garden hose connected to a water faucet

A rebound is a special kind of collision where objects bounce off each other instead of sticking to each other. There’s a change in the direction and a speed change.

Imagine a tennis ball striking a brick wall. The ball initially has a sped of 10 m/s, and after it hits the wall, it bounces back in the opposite direction at half the speed. What is the velocity change? It’s 10+5 m.s or 15 m/s.

Would the acceleration be greater or less than a ball that rebounds with a speed of 8 m/s? (Greater, since acceleration depends on velocity change, and the change in velocity for the second throw is 12 m.s). Which has the greatest momentum change? (The first case, since momentum change depends on velocity change.)

Sometimes an object will have the same (or nearly the same) speed as it had before impact, and these are called elastic collisions. These kinds of collisions also have the same kinetic energy and same momentum before and after the collision.

The Third Law of Motion shows up in collisions between objects. When two objects hit each other, they experience forces of the same magnitude but in opposite directions at impact. Those forces cause one object to speed up and the other to slow down. Even though the forces between the two objects are equal in magnitude, their accelerations are not.

Newton’s Second Law of Motion states that acceleration depends on force and mass, which means if you smack a ping pong ball with a bowling ball, one is going to have a higher acceleration than the other after the collision.

Golfers and baseball players use this principle to drive the ball far from their collision point by swinging the club or bat at high speeds, and even though the ball and bat experience the same force (in magnitude) at impact, the acceleration of the ball is much higher than the bat because the ball has a much lower mass. If you’re playing pool, then you can expect the billiard balls to experience the same accelerations after impact since the balls are all the same mass.

The Conservation of Momentum tells us that the total momentum of a system (a set of objects) is a constant value that doesn’t change. The total momentum of two objects before the collision is equal to the total mo momentum of the two after the collision. The momentum lost by one object is gained by the other. You can think about momentum as money being exchanged between two people. If each person has $20, and one person gives the other $5, the money transfers from one person to the other. The money lost by the first person is gained by the other, but the total amount of money is the same before and after the transaction ($40).

Physics isn’t all about equations, though. Here’s a real experiment you can do with a couple of steel ball bearings, a strong magnet, and a toilet paper tube:

Sometimes it’s easiest to solve the problem by shrinking all the objects down to tiny particles. But in order to do that, you have to account for how lumpy and heavy (or light) your object. A baseball bat doesn’t balance in the exact middle of the bat. You have to account for the fact that the grip is skinnier than the end you hit with. But how would you figure that out? Here’s how…