Elastic, Inelastic and Two-Dimensional Collisions for AP Physics B & C

Practice problems for these concepts can be found at: Momentum Practice Problems for AP Physics B & C

Elastic and Inelastic Collisions

This brings us to a couple of definitions.

If you're unfamiliar with the concept of kinetic energy (KE), take a few minutes to skim Chapter 14 right now.

When the satellite and the UFO bounced off each other, they experienced a perfectly elastic collision. If kinetic energy is lost to heat or anything else during the collision, it is called an inelastic collision.

The extreme case of an inelastic collision is called a perfectly inelastic collision.

The second collision between the satellite and the UFO was a perfectly inelastic collision. BUT, MOMENTUM IS STILL CONSERVED, EVEN IN A PERFECTLY INELASTIC COLLISION!

Two-Dimensional Collisions

The key to solving a two-dimensional collision problem is to remember that momentum is a vector, and as a vector it can be broken into x and y components. Momentum in the x-direction is always conserved, and momentum in the y-direction is always conserved.

We want to analyze the x-component of momentum and the y-component of momentum separately. Let's begin by defining "right" and "up" to be the positive directions. Now we can look at the x-component.

We can't do much more with the x-component of momentum, so now let's look at the y-component.

(Note the negative sign on Maggie's y-velocity!)

Okay. Now we have two equations and two unknowns. It'll take some algebra to solve this one, but none of it is too hard. We will assume that you can do the math on your own, but we will gladly provide you with the answer:

The algebra is not particularly important here. Get the conceptual physics down—in a two-dimensional collision, you must treat each direction separately. If you do so, you will receive virtually full credit on an AP problem. If you combine vertical and horizontal momentum into a single conservation equation, you will probably not receive any credit at all.

Practice problems for these concepts can be found at: Momentum Practice Problems for AP Physics