Physics EE (Extended Essay) Advice: Conservation of momentum

[CrzCz]

I am not sure if I am at the right place and I hope that I am...

For my EE I want to do an investigation on something related to pool table and games so it will definitely be related to momentum. And one of the common techniques in pool games is that the player aims the ball on the rail of the pool table and so reflecting to ball to hit another ball at an angle. This should be also be counted as linear momentum (?). And I just have a question in mind, that whether the density of the rail will affect the momentum that is conversed after the collision. Not sure if this will be a good enough EE question. I have been exploring a lot of different types of momentum experiments (Rails, heights, 2 balls collision etc. ) but I want to stick with an investigation that is more related to real life.

 

[Nidum]

Search on 'Elastic and inelastic collisions' + 'Coefficient of restitution'

 

[CrzCz]

Search on 'Elastic and inelastic collisions' + 'Coefficient of restitution'

So basically the coefficient can also be understood as the coefficient of how much energy the object that the ball collides on conserves?

 

[CrysPhys]

What does "EE" stand for in this context?

 

[CrzCz]

What does "EE" stand for in this context?

Ohh sorry, extended essay.

 

[berkeman]

I am not sure if I am at the right place and I hope that I am...

For my EE I want to do an investigation on something related to pool table and games so it will definitely be related to momentum. And one of the common techniques in pool games is that the player aims the ball on the rail of the pool table and so reflecting to ball to hit another ball at an angle. This should be also be counted as linear momentum (?). And I just have a question in mind, that whether the density of the rail will affect the momentum that is conversed after the collision. Not sure if this will be a good enough EE question. I have been exploring a lot of different types of momentum experiments (Rails, heights, 2 balls collision etc. ) but I want to stick with an investigation that is more related to real life.

The physics of the game of pool is fairly complicated. You will need to include more things in your analysis if you want to get a moderately accurate model, IMO.

If you take the much simpler game of "Carom" shown below, can you see how it is simplified compared to pool/billiards? Since the reflections off the walls are mostly elastic, and there is no rolling of balls involved, the analysis is much simplified. What do you need to add into your pool analysis beyond the things you've already mentioned?

https://images.hayneedle.com/mgen/master:CM059.jpg?is=300,300,0xblack&cvt=jpg

 

[CrzCz]

The physics of the game of pool is fairly complicated. You will need to include more things in your analysis if you want to get a moderately accurate model, IMO.

If you take the much simpler game of "Carom" shown below, can you see how it is simplified compared to pool/billiards? Since the reflections off the walls are mostly elastic, and there is no rolling of balls involved, the analysis is much simplified. What do you need to add into your pool analysis beyond the things you've already mentioned?

https://images.hayneedle.com/mgen/master:CM059.jpg?is=300,300,0xblack&cvt=jpg
View attachment 209095

Thanks Berkeman.

Before I have thought about whether the density of the wall/rail/object will affect the momentum conserved after collision, I have also though of whether the amount of force applied to a ball will affect the type of collision that will occur when the ball hits another ball. I just thought that the force can be controlled with a spring.

Also, it seems like I can work with Carom too :D

 

[berkeman]

Before I have thought about whether the density of the wall/rail/object will affect the momentum conserved after collision, I have also though of whether the amount of force applied to a ball will affect the type of collision that will occur when the ball hits another ball. I just thought that the force can be controlled with a spring.

In pool, the frictional forces on the spinning/rolling balls from the tabletop and the bumpers has a big effect. The energy in the rotation of the balls is also important, and changes by varying amounts with each collision. The spinning of the ball affects how it bounces off of the bumpers, for example, and some spin can be exchanged between two balls at their collision.

Have a look at this old (long) PF thread about "English" and pool balls... https://www.physicsforums.com/threa...s-with-english-goes-straight-at-first.897911/



EDIT / ADD -- @jambaugh may be able to add his thoughts about the physics of pool...

 

[CrzCz]

In pool, the frictional forces on the spinning/rolling balls from the tabletop and the bumpers has a big effect. The energy in the rotation of the balls is also important, and changes by varying amounts with each collision. The spinning of the ball affects how it bounces off of the bumpers, for example, and some spin can be exchanged between two balls at their collision.

Have a look at this old (long) PF thread about "English" and pool balls... https://www.physicsforums.com/threa...s-with-english-goes-straight-at-first.897911/

Ooo thanks berkeman for the link to this post... So I now get that there are a lot more of factors that are needed to be recorded and analyzed

So, so far I have made notes that the factors below contributes to the results of the change in coefficient of restitution or direction of the ball:
1. Contact time
2. Surface area of collision
3. Friction between 2 objects
4. Density (affects contact time) / Stiffness of cue-tip (?)
The largest and most significant factors are probably the surface area of collision and the friction between the 2 objects.

So if a more elastic collision means a more predictive shot/game, does inelastic collisions mean a less predictive game which is generally not wanted?

But now that I know all these, I think that it is almost impossible to collect data for my experiment It will be a pretty hard experiment to keep track of

 

[CrzCz]

So if I will the surface area between the cue and the ball during collision play a significant role to how elastic the collision is? Or whether the ball slides forward or starts spinning.

 

[jambaugh]

As an avid pool player, I'll share my understanding of the behavior of pool balls bouncing off rails.
In the ideal case, say with very hard elastic balls and very hard elastic rails with low friction then you'd have conservation of momentum parallel to the rail and ball would reflect perfectly at the angle of incidence. The two major factors affecting this are friction and the softness of the rail.

When the ball bounces into the rail which is felt over a rubber bumper, the ball sinks into the rail and the rail conforms around the ball which will tend to impart some lateral force as well as force normal to the rail. It is small but I have observed that when hitting the ball harder into the rail, that it loses more lateral momentum coming off the rail at a bit more perpendicular angle. But it is hard to be sure of this since ball spin has a more significant effect.

When shooting the cue ball off the rail the standard technique is to put enough lateral spin (English) on the ball so that it rolls along the rail as it touches it and this prevents loss of momentum parallel to the rail as the ball bounces. To a finer degree you can control angle off the rail this way and also must account for spin picked up off one rail when predicting secondary behavior. Since this is a matter of practice and pragmatic adjustment I cannot say to what extent one is also adjusting for the previously mentioned effect.

This is also why it is critical in getting good at pool to practice practice practice making consistent shots with controlled side "english". My preferred warm up drill is to simply roll the cue ball straight down the center table as if to break (but with no balls racked) and try to consistently get the cue to roll straight back to my cue tip. (This also helps me follow through and stop standing up as I stroke). It is quite difficult to do consistently and it shows you how easily one introduces inadvertent side spin and how much it affects the carom of the ball. (And then for fun I'll see how far I can get the ball to "throw" left and right by using spin).

A final point. I was curious about the physics of the Masse shot (where you make the cue ball roll along a curved path) and was able to show that the final angle at which the cue ball rolls given the angle of the cue and where the cue ball gets struck is independent of the coefficient of friction of the table surface. The friction determines how soon all the axial spin gets converted to rolling motion but it has no effect on the final direction.

 

[ellan106]

Found cool article on this topic. Maybe it could help http://www.real-world-physics-problems.com/physics-of-billiards.html
But it's more about the basics)