Elastic Collisions in Two Dimensions

[Ben Taylor]

Elastic Collisions in Two Dimensions deals with the results of particles colliding.
The standard ball to wall collision involves 5 variables:
u = the initial velocity of the particle.
α = the angle between the wall and the initial direction of the particle.
v = the final velocity of the particle.
β = the angle between the wall and the final direction of the particle.
e = the Coefficient of Restitution (separation ÷ approach )

What I wanted to know is is it possible to find the final velocity (v) and the final angle (β), given just the initial velocity (u) and initial angle (β)?

I am interested because I am working on a billiards project, and wanted to know if it was possible to predict the outcome of a collision between a pool/snooker ball and the wall (cushion), given the initial information.
The difficulty is the coefficient of restitution that is calculated using information before and after.

If it is not possible to work out e, is there a constant value for e that works consistently for pool and snooker?

 

[yoscar04]

What have you tried so far?

 

[Paul Belino]

This would be a pretty boring and predicable model. You have no spin on the balls, the most important skill in a player.

 

[Deleted member 4993]

Elastic Collisions in Two Dimensions deals with the results of particles colliding.
The standard ball to wall collision involves 5 variables:
u = the initial velocity of the particle.
α = the angle between the wall and the initial direction of the particle.
v = the final velocity of the particle.
β = the angle between the wall and the final direction of the particle.
e = the Coefficient of Restitution (separation ÷ approach )

What I wanted to know is is it possible to find the final velocity (v) and the final angle (β), given just the initial velocity (u) and initial angle (β)?

I am interested because I am working on a billiards project, and wanted to know if it was possible to predict the outcome of a collision between a pool/snooker ball and the wall (cushion), given the initial information.
The difficulty is the coefficient of restitution that is calculated using information before and after.

If it is not possible to work out e, is there a constant value for e that works consistently for pool and snooker?

I think you want:

find the final velocity (v) and the final angle (β), given just the initial velocity (u) and initial angle (α)?​

The coefficient of restitution cannot be calculated without knowing all other variables. Of course you can make assumptions like perfectly elastic or perfectly plastic collision.

Do a google search and tell us what you found.

 

[DebbieHaag]

Elastic Collisions in Two Dimensions deals with the results of particles colliding.
The standard ball to wall collision involves 5 variables:
u = the initial velocity of the particle.
α = the angle between the wall and the initial direction of the particle.
v = the final velocity of the particle.
β = the angle between the wall and the final direction of the particle.
e = the Coefficient of Restitution (separation ÷ approach )

What I wanted to know is is it possible to find the final velocity (v) and the final angle (β), given just the initial velocity (u) and initial angle (β)?

I am interested because I am working on a billiards project, and wanted to know if it was possible to predict the outcome of a collision between a pool/snooker ball and the wall (cushion), given the initial information.
The difficulty is the coefficient of restitution that is calculated using information before and after.

If it is not possible to work out e, is there a constant value for e that works consistently for pool and snooker?

You will find many videos for this on youtube:

I think this will be good for you..

 

[HallsofIvy]

You talk about "elastic collisions" but then add the "coefficient of restitution". Do you mean "inelastic collisions"? In an elastic collision the "coefficient of restitution" is, by definition, 1.