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page 2 a... a basketball? a pumpkin? a big wad of cookie dough? *blink*blink* after a while, he throws the object to the left, and he rolls off to the right. 
and there are these big purple words that show up: that's nice. what's momentum? momentum is the one thing we really have to worry about when we're talking about rockets. there are two things you need to know about it: 1) momentum is mass times velocity. so, if something has a lot of mass, like a dump truck, it will still have sizeable momentum even if it is moving slowly. ever try to stop a dump truck that's had the emergency brake taken off? i don't recommend it. another way something can have a lot of momentum is if it is moving very fast. even though a bullet is not massive, it still has a lot of momentum when it comes out of a gun. this is how bullets do so much damage. so, mass (not weight) times velocity gives an object's momentum. 2) momentum depends upon the direction of motion. this is important when you are trying to figure out the total momentum of a group of objects. if one object is moving to the left with the same momentum as an object moving to the right, they have equal but opposite momenta. if you add their momenta, they cancel each other out. why? just because they are moving in opposite directions. so let's get back to our blue dude on skates. at first, he's not moving, so his velocity is zero. momentum is mass times velocity, so his momentum is also zero. the total momentum of the system (blue dude plus ball) is zero. got it? okay, then he throws the "ball", and i still have purple letters there claiming the total momentum of the system (ball and blue guy) is zero. how do i know this? there is a "law" in physics called the law of conservation of momentum. (i hate calling these things laws because it makes it sound like some physics cop will arrest you for breaking it. it's not like that. you can't break it. it's built into the universe and we're stuck with it.) what the law of conservation of momentum states is, roughly, that unless an outside force acts on a system, the total momentum in that system can not change. Note, that when the guy throws the ball, there is no outside force acting on the system. the blue dude's arms act on the ball -- everything involved is still part of the system of the dude and the ball. what was the momentum of the system before he threw the ball? okay, good... it was ZERO. no outside force acted on the system. what must the total momentum be after he throws the ball? it still has to be ZERO, right? go ahead and re-read this a few times if it's escaping you, but this is how i know the total momentum of the dude plus the ball is zero after the ball has been thrown. "hey, duckmonger," you're thinking. "this is all nice, but what happened to the rocket?" take the picture of the person with the ball. instead of the person, put a rocket there. instead of the ball, put some hot exhaust gas. the same principle is what accelerates a rocket and what continues to give it its "push" even in space. it's all conservation of momentum. now, i know we still haven't gotten to how fast a rocket can go. that'll be on our last page on this subject. i do want to let you know first that we'll hit a little heavy on the math on the next page. if you just want the answer, review what logarithms are and scroll to the bottom of the next page. the full deal is adapted from section 4.5 of Symon, Mechanics, 3rd Edition, Addison-Wesley Publishing, except i'm going to see if i can do it without mentioning forces. are you ready? |