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## Pixar in a Box

### Course: Pixar in a Box>Unit 7

Lesson 2: The physics of particle systems

# Particle collisions

What happens when particles hit each other or a surface? When particles collide, their velocity changes depending on the angle they hit and the elasticity of the collision. Elasticity is a number between 0 and 1 that measures how bouncy a collision is in order to determine how much energy is lost during the collision.

## Want to join the conversation?

• I don't think I really got the idea between and
• E is a percentage. If E is 0.9 that means we only keep 90% of our energy after the collision, so we multiply Vperp by 0.9 so we don't bounce as high next time.
• My seventh grade brain trying to understand high school physics when all I wanted to do was mess with a ball simulator be like...
• Don't both the ball and the surface have elasticity? How do we use both?
• Even though I am in high school, I still don't get vectors.
• I know.

Vectors were in Algebra I, but you may have missed it because it was briefly discussed.

Vectors are simply the speed of an object, but it also includes the direction of the object. The "speed" of the object is replaced by "magnitude."

Hope that helps!
• where do I make my movie
• yeah, I've been asking that for the past few videos..
(1 vote)
• This is getting confusing as I get into more, and more videos. Can someone help me understand the equations.
• what is 9 and the sum of ten
• Theoretically, what would happen if the elasticity was less than zero or more than one? Would the particle gain energy from the bounce?
(1 vote)
• Hypothetically, if the elasticity was more than one, then the particle would gain energy from the bounce (like you said).
An elasticity of zero would mean that the particle would lose all energy (and stop moving) on the collision. I guess that an elasticity less than zero would indicate the particle is moving through the surface/particle it collides with.
(1 vote)
• At , how do we calculate the parallel and perpendicular vectors?
(1 vote)
• We use trigonometry. For example, to find Vperp, we would use sin(θ)V.
(1 vote)
• why would we need this in life??
(1 vote)
• Say you wanted to work at Pixar.
These skills would be the skills you need to do so!
Hope this helps!
(1 vote)

## Video transcript

(metal clanging) - We finished going over the first of three things you need to create a particle simulator. We have formulas that describe how particles will move based on the laws of physics. In this video, we'll develop formulas that describe how particles will behave during collisions. If velocity is perpendicular to the floor at the moment of collision, and the collision is perfect, then the velocity reverses. In the real world, its direction reverses, and the magnitude is slightly reduced due to friction. As we introduced in lesson one, we can model the frictional losses by multiplying by a factor that measures the elasticity of the collision. So if V is the downward velocity before the collision with the floor, then the velocity, called V prime, after the collision is given by V prime is equal to negative E times V. Here E is the elasticity, a number between zero and one, and the minus sign indicates the direction reverses after the collision. If E equals one, the collision is perfect, and no energy is lost. If E is less than one, then some energy will be lost, but what if the velocity makes an angle with the floor. Let's observe what happens on video. Notice that the ball bounces just like a light ray reflects off a mirror. That is, if the incoming velocity V makes an angle Theta with the floor, then the outgoing velocity called V prime makes the same angle. To compute V prime from V, let's write V as the sum of two vectors, a velocity parallel to the floor, V parallel, and the velocity perpendicular to the floor, V perpendicular. The only force during the collision is perpendicular to the floor because the floor pushes up on the ball. So the parallel component won't change, and the perpendicular component, as before, will be reversed, meaning that V prime is equal V parallel minus V perpendicular. Adding elasticity into the mix, we get this equation. Cool, we can use the idea of writing the velocity as the sum of parallel and perpendicular components to study the case when two particles I and J of the same mass collide. Let's draw a picture to make this clear. The line I, J from the center of particle I to the center of particle J plays the role of the perpendicular to the floor. (bell dinging) So we write V, I as a sum of two vectors, as shown here. We can do the same for V, J. The only force acting on the particles during the collision is along the line I, J. As before, since no force is acting in the parallel direction, the velocities in the parallel directions won't change. To figure out exactly what happens in the perpendicular direction requires using more advanced topics, namely, conservation of energy and momentum. (chiming) If we apply those concepts and assume that the particles have the same mass, we find that particle I gets J's perpendicular velocity, and vice versa. That is, they swap perpendicular velocities. (bell chiming) That means after the collision, the velocities V prime I and V prime J are given by these equations. That's it for particle collisions. In the next exercise, you'll have a chance to review these equations, which describe collisions. (cheerful music)