Investigating Mechanics in Snooker Shots

[bijou]

Hi Guys,

Ok, I am taking on a mechanics investigation based around a snooker/pool/billiards style shot. I plan to model the ideal shot to get out of a snooker and pot a ball. In order to do this I plan to find the coefficient of friction between the table and the ball and the coefficient of restitution between the ball and the cushion then work out the angle and minimum initial velocity required. Something like this.

I plan to conduct experiments with a ball on an inclined glass plane. I will assume that the ball slips down the plane (no friction or rotation) and will work out the velocity as it leaves the plane. I will also measure the distance it travels from the point it leaves the plane (B) to the point is stops (C). Using these I hope to calculate the resistive force acting on the ball in order to stop it. I then hope to calculate the coefficient of friction.

If I work out the initial velocity of the ball as it leaves the plane (using PE = KE), is it acceptable to use v^2=u^2 + 2as to work out the deceleration of the ball? Then use F=ma to work out the retardant force on the ball?

Do I need to worry about angular momentum as at this point that the ball meets the table it will start rolling? If so, is there any loss of energy due to angular momentum or is it all due to friction?

As you can probably tell, I've gotten myself a bit tangled up here. If you can give any advice at all it would be greatly appreciated.

 

[LowlyPion]

Welcome to PF.

First of all you may want to consider angular momentum. Though what it takes away initially, it also gives back in coming to rest.

I would be suspicious that a snooker ball could travel down a glass slide to begin with by totally slipping. But regardless some energy would necessarily go into angular energy at some point as it rolls, but as it slows it would be eaten up again by the work of friction.

You may be better off having it roll down a felt slide to insure that there is no slippage to begin with.

 

[bijou]

Welcome to PF.

First of all you may want to consider angular momentum. Though what it takes away initially, it also gives back in coming to rest.

I would be suspicious that a snooker ball could travel down a glass slide to begin with by totally slipping. But regardless some energy would necessarily go into angular energy at some point as it rolls, but as it slows it would be eaten up again by the work of friction.

You may be better off having it roll down a felt slide to insure that there is no slippage to begin with.

Thanks for this, sorry I never replied sooner. I ended up assuming that the ball wasn't rolling at all, just sliding on the table. This was on the advice of the tutor, I guess as bringing angular momentum and rolling friction into things would have gotten very complicated.

The reason I used a glass plane was so that I could get a figure for the velocity of the ball at the bottom of the plane. I know that technically some energy will be lost to friction on the plane but glass was the lowest friction surface I could think of. I was pretty confident that the owners of the snooker hall wouldn't be keen on me bringing a sheet of ice into do experiments!

Now my major problems are with the coefficient of restitution between the balls. I made a thread here if you have any ideas, https://www.physicsforums.com/showthread.php?t=321296

If not, thank you anyway :)