Commons

a / How can we prove that this collisionis impossible?We can show it’s impossible by looking at it in a different frameof reference, b. This camera follows the light ball on its way in, soin this frame the incoming light ball appears motionless. (If youever get hauled into court on an assault charge for hitting someone,try this defense: “Your honor, in my fist’s frame of reference, itwas his face that assaulted my knuckles!”) After the collision, welet the camera keep moving in the same direction, because if wedidn’t, it wouldn’t be showing us an inertial frame of reference.To help convince yourself that figures a and b represent the samemotion seen in two different frames, note that both films agree onthe distances between the balls at each instant. After the collision,frame b shows the light ball moving twice as fast as the dark ball;an observer who prefers frame a explains this by saying that thecamera that produced film b was moving one way, while the ballwas moving the opposite way.b / The collision of figure a isviewed in a different frame of reference.Figures a and b record the same events, so if one is impossible,the other is too. But figure b is definitely impossible, because itviolates conservation of energy. Before the collision, the only kineticenergy is the dark ball’s. After the collision, light ball suddenly hassome energy, but where did that energy come from? It can onlyhave come from the dark ball. The dark ball should then have lostsome energy, which it hasn’t, since it’s moving at the same speed asbefore.Figure c shows what really does happen. This kind of behavioris familiar to anyone who plays pool. In a head-on collision, theSection 2.3 Momentum 43