Conservation of Momentum

What is conservation of momentum?
- Sadd (age 13)

Sadd -

The word momentum basically means how much something is moving, and which way. In math terms (sorry!), you can figure out something's momentum by taking its velocity (like its speed, only also saying what direction) and multiplying it by its mass (like its weight). For example, let's say you have a ball with a mass of 2 kg, and it's moving east with the velocity of 3 m/s. Then it's momentum is (2 kg)(3 m/s) = 6 kg*m/s in the east direction. So the more something weighs or the faster it's going, the more momentum it has.

"Conservation of Momentum" is a rule that says the total momentum of a system won't change unless an external force acts on it, even if the parts of the system bump into each other or explode or whatever..

Let's say we're looking at two cars. One car with the mass of 300 kg is sitting still. Another car with the same mass is driving at 40 mph east and hits the first car. If the first car doesn't have its brakes on, this will probably mean that both cars will be moving after they hit. So the momentum at the beginning is 0 for the first car (since its velocity is zero) and (300 kg)(40 mph) = 12,000 kg*mph for the second car.

This will still be the total momentum after they hit, too. So if we know that one car was moving at 30 mph afterwards, we can figure out how fast the other car would end up going. The momentum of the 30 mph car afterwards would be (300 kg)(30 mph) = 9000 kg*mph. Since the momentum started off at 12,000 kg*mph, and one car got 9000 kg*mph of it, there's 3000 kg*mph left for the other car's momentum. Divide this by the car's mass (300 kg), and you get its speed, 10 mph. So even though the speed of each car changed, the total momentum didn't.

Another situation where conservation of momentum matters is if you have something that's moving, and its mass changes. If its mass gets bigger, then it will have to slow down. And if its mass gets smaller, then it will speed up. This is because its momentum (mass*velocity) will stay the same. For example, let's take a cart that weighs 20 kg moving at 3 m/s west. If we drop a 10 kg weight on it while it's moving, then its total mass will change. So we started off with the momentum of (20 kg)(3 m/s) = 60 kg*m/s. This momentum won't change after the weight is added. Afterwards the total weight is 30 kg, so its velocity has to be 2 m/s west (because (30 kg)(2 m/s) = 60 kg*m/s). So adding the weight changes how fast it's going, but its momentum doesn't change at all!

One more example... (last one, I promise!). Say we've got a bomb that's about to explode. (Let's say it's a really wimpy bomb.) It weighs 3 kg and is sitting still. When it explodes, it breaks into two pieces of 2 kg and 1 kg each. Each piece moves in opposite directions...let's say that the 2 kg piece moves the the north and the 1 kg piece moves south. So know you're probably wondering how this can happen if it started off not moving. Well, the reason is that they're moving in /opposite directions/. When you talk about velocity, you have to pay attention to direction.

So let's say that the 2 kg piece flies off going at 10 m/s to the north. It's velocity would be -10 m/s, if we call north negative and the opposite way, south, positive. So its momentum is (2 kg)(-10 m/s) = -20 kg*m/s. Since the whole thing started off with momentum of 0 (not moving), this means that the other piece has to have the momentum of +20 kg*m/s, so that the total momentum won't change. Since that piece weighs 1 kg, it has to end up going at 20 m/s. So the bigger piece moves slower in one direction, and the smaller piece moves faster in the other... and the total momentum doesn't change. Momentum is conserved!

Hope this helps!

-Tamara

(published on 10/22/2007)