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When objects fall
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<blockquote data-quote="arscott" data-source="post: 1977985" data-attributes="member: 17969"><p>Momentum is vastly important in collisions. But it's usefullness is in determining movement after collision. for instance, say we have two spheres, moving towards eachother at 10 m/s, one with mass 20 and the other with mass 10. momentum equals mass times velocity, so</p><p>the momentum of the first sphere is 200 mkg/s and the momentum of the second sphere is -100 mkg/s (it's negative because it's moving in the opposite direction of the first sphere. This will become important pretty quickly)</p><p></p><p>In any collision, momentum is always conserved. So if these two spheres collide, the total momentum of the result would be 100 mkg/s. But that momentum could be expressed in different ways. It might mean that the spheres remain in contact and travel at 33 m/s in the direction that the heavy ball was traveling. It might mean that the heavy ball stops but the light sphere bounces and goes 100m/s in the opposite direction. It might mean that both spheres bounce, the heavy one moving away at 50 m/s and the light one at 200 m/s. whatever happens, momentum is contained.</p><p></p><p>But momentum doesn't really matter much with our specific example. The reason? it's a gravity problem. Gravity is an attractive force exerted by each object in the universe on every other object in the universe. So that means as the earth pulls us towards it, we pull it towards us too. Fortunately, the earth is so much bigger than us that it's safe to ignore that fact in basic falling problems (like the one in my previous post). But it also means that when you gain momentum by falling towards the earth, the earth gains that same momentum by falling towards you. And when you hit, those momentums cancel out.</p><p></p><p>This assumes no bounce (as did my previous post), but if you've hit the ground hard enough to bounce significantly, then it's probably a moot point.</p><p></p><p>but the damage dealt isn't determined by momentum. It's deformation.</p><p>When you hit the ground, your directional kinetic energy is tranformed into different types of energy. Some is transformed into heat. Some is transformed into sound. But the greatest part of it is removed by the work applied by the stopping force over the deformation distance (or in game terms, 1d6 per 10 feet fallen).</p></blockquote><p></p>
[QUOTE="arscott, post: 1977985, member: 17969"] Momentum is vastly important in collisions. But it's usefullness is in determining movement after collision. for instance, say we have two spheres, moving towards eachother at 10 m/s, one with mass 20 and the other with mass 10. momentum equals mass times velocity, so the momentum of the first sphere is 200 mkg/s and the momentum of the second sphere is -100 mkg/s (it's negative because it's moving in the opposite direction of the first sphere. This will become important pretty quickly) In any collision, momentum is always conserved. So if these two spheres collide, the total momentum of the result would be 100 mkg/s. But that momentum could be expressed in different ways. It might mean that the spheres remain in contact and travel at 33 m/s in the direction that the heavy ball was traveling. It might mean that the heavy ball stops but the light sphere bounces and goes 100m/s in the opposite direction. It might mean that both spheres bounce, the heavy one moving away at 50 m/s and the light one at 200 m/s. whatever happens, momentum is contained. But momentum doesn't really matter much with our specific example. The reason? it's a gravity problem. Gravity is an attractive force exerted by each object in the universe on every other object in the universe. So that means as the earth pulls us towards it, we pull it towards us too. Fortunately, the earth is so much bigger than us that it's safe to ignore that fact in basic falling problems (like the one in my previous post). But it also means that when you gain momentum by falling towards the earth, the earth gains that same momentum by falling towards you. And when you hit, those momentums cancel out. This assumes no bounce (as did my previous post), but if you've hit the ground hard enough to bounce significantly, then it's probably a moot point. but the damage dealt isn't determined by momentum. It's deformation. When you hit the ground, your directional kinetic energy is tranformed into different types of energy. Some is transformed into heat. Some is transformed into sound. But the greatest part of it is removed by the work applied by the stopping force over the deformation distance (or in game terms, 1d6 per 10 feet fallen). [/QUOTE]
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