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## The physics of particle systems

Current time:0:00Total duration:3:25

# Particle collisions

## 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)