Relativity Lite

Mixmaster Universe | 25 Figure 2. Catherine Wong playing rugby (used by permission). These are each different experiences of our three-dimensional world of momentum that have in common the pain characteristic of the deposition of energy into your body, the final entry in this gang of four, { energy/c , northward momentum , westward momentum , upward momentum }. Just as we usually write the spacetime four-dimensional vector as abbreviated symbols { c t , x , y , z }, so too the energy-momentum four-dimensional vector is written in abbreviated symbols { E/c , p x , p y , p z }. Why the momentum is p x , and not m x , is historical and avoids confusion with the symbol m used for mass. I do not knowCatherine’s weight, so let us just pin it at a nice round number like 100 pounds. Suppose instead of her, a 200-pound player going at the same speed runs into you. How will the pain compare? (It will be worse.) As you might expect, smaller people can often get going much faster than larger people, so imagine now that Catherine is running twice as fast as the 200-pound player. Who is going to hurt you more? That is right, she will. Even if she is only going 50% faster, she will wham you worse and cause more pain. This is a life lesson in respect that is important to learn. It turns out that a player who runs into you at twice the speed of a second one will hurt you four times as much, but an equal-speed player who is twice as heavy as the first one will hurt you only twice as much. That can be quantified by the relation KE mv = 1 2 2 . * * You can verify that a ball falling 5 meters in 1 second will have a velocity of 10 m/s. Its kinetic energy is equal to the grav- itational potential energy it had before falling, KE m m mgh = ( ) = ( )( ) = 1 2 10 10 5 2 m/s m/s/s m , where g is the acceleration of gravity (10 m/s/s) and h is 5 m.