Last week, we investigated the principle of conservation of angular momentum on a spinning carousel. In this episode we illustrate the linear version of the same principle — conservation of linear momentum — as illustrated by the physics-based computer game Red. The goal of the game is to avoid being crushed by a relentless barrage of incoming meteorites, by deflecting them with cannon balls. Understanding a little bit about conservation of momentum is a consolation in the face of the reality that sooner or later you are going to get flattened.
Linear momentum (
p) is defined as the product of the mass and velocity of an object. (Mathematically speaking,
p = mv). According to the principle of conservation of momentum, if there is a collision between two objects, although the momentum of an individual object can change, the total momentum of the two objects added together remains constant.
All of the collisions in Red elegantly adhere to the principle of conservation of momentum. It’s important to realize that momentum is a vector which means it has a direction associated with it. Since the collisions in the game are two-dimensional we can analyze them more easily by looking at the horizontal components of the momentum separately from the vertical.
Notice how, in order to keep the meteorites from hitting you, you have to create a lot of “glancing” or off-center collisions between your ammo and the falling rocks. During these, you impart a horizontal momentum to an incoming meteorite, which knocks it safely to the side. This is compensated for by the horizontal momentum acquired by your cannon ball in the opposite direction. Your system didn’t gain any horizontal momentum — you just redistributed it. For example, if your system started with zero horizontal momentum, after the collision you still have zero: however much momentum the meteorite gains to the left is exactly equal to the oppositely directed momentum of your cannon ball to the right. It cancels out.
Although the game moves too fast to make any accurate measurements, if we could get some speeds and directions on these things we’d also be able to estimate the mass of those pesky meteorites (relative to the cannon balls). You can bet that those relative masses are coded in the game software along with the conservation-of-momentum equations.
Finally, all of the collisions in the game appear to be perfectly elastic. This means that not only is momentum conserved in the collisions, but kinetic energy is as well. A perfectly elastic collision is a “bouncy” collision — the objects rebound off each other like bouncy balls, whereas in a perfectly inelastic collision the objects stick together like globs of clay. Although kinetic energy is not conserved in inelastic collisions, momentum still is. It would be an interesting addition to the game if some of the meteorites were sticky, thus resulting in some inelastic collisions — but you can’t have everything, and it would make surviving more difficult than it already is.
If you want to contemplate a little bit of physics while trying to keep yourself from getting obliterated by a meteorite, Red is the game for you.
Adam Weiner is the author of Don’t Try This at Home! The Physics of Hollywood Movies.