# 2D elastic collisions with equal masses

1. Jul 25, 2007

Hi everyone, i was just wondering, when two objects of the same mass collide (in an elastic collision) the angles that they bounce off from should combine to 90 degrees. right? so i'm trying to prove this, but i'm a little stuck. i used vector component equations, but i arrived at a little problem. i was just wondering if anyone knew that if the velocities of two objects after the collision multiplied to equal zero...what does that mean?

2. Jul 25, 2007

### Manchot

I don't think that's true. In the limiting case of two balls just barely glancing off each other, the angle they bounce off at will approach 0.

3. Jul 25, 2007

but the real question i was asking was what does it mean when two final velocities multiply to equal zero in a 2D collision that's elastic and the masses are equal...my teacher offered this as extra credit and said that the two objects bounce off each other at should add up to be 90 degrees

4. Jul 25, 2007

### olgranpappy

no, that is wrong. the angle is not zero. it is 90 degrees--or rather the limit is 90 degrees. In an exactly head on *elastic* collision the initially moving ball will be at rest with a velocity zero which is normal to any other velocity vector.

Start by considering collisions which are very far from head-on. The balls will indeed move apart at 90 degrees. As the collision becomes closer and closer to head-on the magnitude of the velocity of the initially moving ball will shrink and shrink but it will always remain at 90 degrees from that of the other ball.

for some reason, people always find this counter-intuitive... that is because real billiard balls will be spinning and so for a head on collision the final velocity of the initiall moving ball will be determined entirely by the spin, etc...

5. Jul 25, 2007

### olgranpappy

this fact is very tedious to derive because of all the algebra, but the derivation can be found in any text on classical mechanics. For example, Fetter and Walecka "Theorectical Mechanics of Particles and Continua."

6. Jul 25, 2007