Coefficient of restitution definition

[ehrenfest]

[SOLVED] coefficient of restitution

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[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.

 

[ehrenfest]

Just magnitudes and scalars.

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 traveling 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?

 

[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 !)