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[QUOTE]Originally posted by Guardian 2000: [QB] [QUOTE]Originally posted by Identity Crisis: [qb] "You wouldn't let it lie..."[/qb][/QUOTE]� That is correct. � [QUOTE]Momentum is a vector quantity not a scalar one. You have to add it according to vector rules.[/QUOTE]� Yes, yes, a magnitude and a direction. That's all well and good, but it won't allow for a doubling of the momentum . . . how you add it up is irrelevant compared to that. � [QUOTE]But even according to your simplistic system of scalar addition the momentum is conserved. 2[mv] goes into the system (mv for the ship and -mv for the ship, both in the x-axis) and 2[mv] comes out of the system (-mv for the ship and mv for the particle, but now both in the y-axis).[/QUOTE]� That's zero for the ship resulting in 2mv! What are you even talking about? � Look, just forget the tube for a moment. I think the axes are confusing you. If you put a plate at the back of the ship and have it attached to the ship, then when the ejected cannonball hits it the cannonball and the ship will stop relative to one another. In effect, it cancels the momentum of each individual participant, and overall momentum is conserved. � The principle with the tube is the same. The y-axis components of the hits (one "down", one "up") cancel one another out, leaving us with no y-ward momentum. We're left with the two x-axis hits. � In your example, each one of these produces mv on the ship on the x-axis . . . one stops the ship, the other sends it flying backward. If two 90 degree-trajectory-change collisions can produce this effect, why not a single 180 degree collision, as with the plate? � The answer is, they can't. Otherwise, four 45 degree-trajectory-change collisions would propel the ship backwards at 4 times the rate . . . but that doesn't happen. � The first collision (your step #3) should not have caused 1mv(-x) and 1mv(-y). The collision should've caused 1/2mv(-y) and 1/2mv(-x). (In other words, the force on the ship would've driven her both backward and downward simultaneously.) Why? See below: [IMG]http://www.st-v-sw.net/momentum2.gif[/IMG] Your version of events is colored red and purple. My version is in blue and green. I'll try to use the proper lingo in explaining the image. The ball, when it strikes the angled wall (or another ball), transfers force along the line connecting their centers (the diagonal blue line). We can take the original momentum of the ball (which is 1mv(-x)) and render it as two vectors . . . the one along that center-line, and a perpendicular one (the green one going up and to the left which, since this is to be a friction-free event, won't experience any change in magnitude). Meanwhile, like the swinging ball desktop toy, momentum will be transferred to the ball as well, along that centerline. From the wall, that's the green line going up and to the right. The result is the same for the ball . . . it will head upward along the green line with 1mv(y). For the ship, however, the result is quite different. Isolating the two wall-hits for the moment, we find that they both result in .7071mv to the ship in their respective diagonal directions, or 1mv(-x) along the x axis. The other 1mv of the occasion was along the y axis, but it effectively cancels itself out during the process of changing the cannonball's course (remember, there's no such thing as negative momentum). Since the ship had a momentum of 1mv(x) from ejecting the ball in the first place, the 1mv(-x) results in a final velocity change of zero. That means that if the ship were moving with any velocity beforehand, it is now going to continue moving with that same velocity. If it were stationary, it will remain so. Now, I'll grant that there may be an error on my part somewhere. Despite the fact that I have an intuitive grasp of (and ability to visualize) some of the more exotic physics issues even beyond my mathematical understanding, it remains a curious irony that certain issues of mechanics just give me a headache. (On the other hand, I kick ass at pool, so go figure.) But, if I have made an error, I can't see (or visualize) it. [/QB][/QUOTE]
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