# Coefficient of restitution definition

1. Jan 24, 2008

### ehrenfest

[SOLVED] coefficient of restitution

1. The problem statement, all variables and given/known data
My book defines the coefficient of restitution as

$$\epsilon = \frac{|v_2-v_1|}{|u_2-u_1|}$$

but does not really explain what u_1, u_2, v_1, and v_2 mean. Those terms are all scalars since the coefficient of restitution only "works" in one direction. But do they mean the difference between the magnitudes of the initial and final velocities? I am asking whether those terms can be negative depending on the direction the particles are moving after the collisions.

2. Relevant equations

3. The attempt at a solution

2. Jan 25, 2008

### Shooting Star

Just one dimensional scalars. u1 means velo of object 1 before impact etc. The velocities used are the components pointing along the direction of impact. If u1 and u2 point in opp dircn, they have to be added.

So, e = magnitude of relative velo after impact/mag of rel velo before impact.

Last edited: Jan 25, 2008
3. Jan 25, 2008

### ehrenfest

I'm not really sure that you answered my question. Here is an example.

Suppose particle a and particle b live on a line.

Suppose b is initially at rest. Suppose a is travelling at 5 m/s from the left towards b. After the collision, a travels at 2 m/s to the left and b travels at 4 m/s to the right. What are u1,u2,v1,v2?

4. Jan 25, 2008

### Shooting Star

(Pl read the my edited 1st post.)

u1=5, u2=0, v1=-2, v2=4.

mod(u2-u1)=5,
mod(v2-v1)=mod[4-(-2)]=6.

(Here, e>1 !)