Physics help?

mikepage

AzB Silver Member
Silver Member
You are ignoring the energy absorption of the tip and incorrectly applying momentum laws.

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Yes, my response assumes an elastic collision.

But what do you mean by incorrectly applying momentum laws?
 

logical

Loose Rack
Silver Member
Yes, my response assumes an elastic collision.



But what do you mean by incorrectly applying momentum laws?
It's really not that important since this whole discussion is what it is, but because a force (your arm) is applied during collision it is no longer an isolated system where momentum is the same before and after the collision. Unless you let go of the cue just before impact, it is not an isolated system that the law can be applied to.

I think leaving out the behavior of the tip is pretty significant. Two billiard balls colliding would approximate an elastic collision. Wrap one of them in thick leather and it will be a very different collision.


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mikepage

AzB Silver Member
Silver Member
It's really not that important since this whole discussion is what it is, but because a force (your arm) is applied during collision it is no longer an isolated system where momentum is the same before and after the collision. Unless you let go of the cue just before impact, it is not an isolated system that the law can be applied to.
[....]

From the impulse (change in momentum) and the knowledge the contact takes about a millisecond, you can estimate the tip-ball force during the collision. It is very high compared to anything you can apply with your arm and fleshy hand.
 

Cron

AzB Silver Member
Silver Member
It's really not that important since this whole discussion is what it is, but because a force (your arm) is applied during collision it is no longer an isolated system where momentum is the same before and after the collision. Unless you let go of the cue just before impact, it is not an isolated system that the law can be applied to.

I think leaving out the behavior of the tip is pretty significant. Two billiard balls colliding would approximate an elastic collision. Wrap one of them in thick leather and it will be a very different collision.


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Of course you can apply the math, add the arm to m_cue and tip change to u_cue (or cr). It's naive to think this simple formula can't be reworked, you're just arguing to argue.

Anyways thanks for this. I'm going to go and add in the Earths rotation and my altitude to factor out that +/- .0000000001 error ratio :p.
 

logical

Loose Rack
Silver Member
Hit it harder and the ball will go really fast. Hit it softer and it will go slower. Don't hit it at all on most bar tables and it will eventually move.

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Bob Jewett

AZB Osmium Member
Staff member
Gold Member
Silver Member
From the impulse (change in momentum) and the knowledge the contact takes about a millisecond, you can estimate the tip-ball force during the collision. It is very high compared to anything you can apply with your arm and fleshy hand.
And it's not just a theoretical estimate. It was measured as part of the Jacksonville Experiment in 1998. It turns out that the stick does almost instantly go down to 50% of its initial speed and then over a period of about 20 milliseconds go back up to about 80% of its initial speed as the hand and wrist finally get more force into the stick after contact.

The spring constant of the tip-ball collision is quite high which is why contact takes only 1-2 milliseconds.

The spring constant of the grip-hand is much lower and cannot apply much force until it is wound up a little, which takes time and cue travel.

We just had this conversation a little while ago, I believe, and before:
https://forums.azbilliards.com/showthread.php?t=494978
https://forums.azbilliards.com/showthread.php?p=4631030

As for whether any of this is useful, probably not. If the fact that your hand pressure is irrelevant at contact allows some players to give up their death grip on break shots, then maybe it is useful.

Let the cue do the work.
 

logical

Loose Rack
Silver Member
And it's not just a theoretical estimate. It was measured as part of the Jacksonville Experiment in 1998. It turns out that the stick does almost instantly go down to 50% of its initial speed and then over a period of about 20 milliseconds go back up to about 80% of its initial speed as the hand and wrist finally get more force into the stick after contact.

The spring constant of the tip-ball collision is quite high which is why contact takes only 1-2 milliseconds.

The spring constant of the grip-hand is much lower and cannot apply much force until it is wound up a little, which takes time and cue travel.

We just had this conversation a little while ago, I believe, and before:
https://forums.azbilliards.com/showthread.php?t=494978
https://forums.azbilliards.com/showthread.php?p=4631030

As for whether any of this is useful, probably not. If the fact that your hand pressure is irrelevant at contact allows some players to give up their death grip on break shots, then maybe it is useful.

Let the cue do the work.

Watch any pro who really breaks hard and you'll notice how they power through the point of contact to minimize the deceleration at impact. Most of us hit "at" the ball and allow that significant deceleration of cue speed that only picks back up after the cue is gone.
 

dr_dave

Instructional Author
Gold Member
Silver Member
Hey PJ

What is the correct formula to use to calculate:

energy transfer from cue tip to cue ball? In other words, how fast is the cue ball traveling at the time of impact?

I have been lead to understand that with a dead center hit, the cue ball leaves with about an additional 10% of speed.
Randy,

Here's a complete analysis:

TP A.30 – The effects of cue tip offset, cue weight, and cue speed on cue ball speed and spin

I know you and others are probably not interested in all of the detailed math and physics, but Equation 8 is fairly simple and pertinent to your question.

Regards,
Dave
 

Chopdoc

AzB Silver Member
Silver Member
Welllllll, at the time of impact the cueball is moving, as Earth does rotate. You can take this to insane depths, but a general base is all that is needed here.

Indeed.

And the "general base", meaning to answer the question correctly as posed is to say that the ball is not moving at the time of contact.

Simple really. :smile:
 

vinay

Registered
And it's not just a theoretical estimate. It was measured as part of the Jacksonville Experiment in 1998. It turns out that the stick does almost instantly go down to 50% of its initial speed and then over a period of about 20 milliseconds go back up to about 80% of its initial speed as the hand and wrist finally get more force into the stick after contact.

Do you know if they published a high-speed video of the hand holding the cue at the moment of impact? I suspect one would see a lot more movement than one would expect, even with a death grip. I'm thinking of those slow motion videos of people's faces jiggling like jello after getting hit with something.
 

Bob Jewett

AZB Osmium Member
Staff member
Gold Member
Silver Member
Do you know if they published a high-speed video of the hand holding the cue at the moment of impact? I suspect one would see a lot more movement than one would expect, even with a death grip. I'm thinking of those slow motion videos of people's faces jiggling like jello after getting hit with something.
The Jacksonville Experiment video did show the grip hand at impact for some shots. Quite remarkable were the ripples in the skin of the hand, IIRC. The video was distributed starting in 1999 or so and for a while the whole thing was on AZB.
 

vinay

Registered
If people want to see this in action, see:

HSV B.40 – Stroke speed and acceleration analysis, with Bob Jewett

Enjoy,
Dave

The fact that cue speed drops by about 40% actually is a very good indication that the weight of the arm doesn't contribute meaningfully to the impact. Given a cue that's 3x as heavy as the ball and a coefficient of restitution of 0.75, you'd expect the cue to retain 56% of its speed after impact. If the arm doubled the effective mass of the cue, you'd expect it to retain 75% of its speed.
 

logical

Loose Rack
Silver Member
The fact that cue speed drops by about 40% actually is a very good indication that the weight of the arm doesn't contribute meaningfully to the impact. Given a cue that's 3x as heavy as the ball and a coefficient of restitution of 0.75, you'd expect the cue to retain 56% of its speed after impact. If the arm doubled the effective mass of the cue, you'd expect it to retain 75% of its speed.
Except this assumes an isolated system where the cue (or the cue and your arm) are detached and hurtling toward the cue ball. The fact that you are continuing to apply force through impact is why the cue doesn't slow to that lower predicted speed that ignores the external force. The less your strength allows the cue to slow at impact the more momentum is transferred to the ball. A power hitter in baseball has to be fast and strong.

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vinay

Registered
Except this assumes an isolated system where the cue (or the cue and your arm) are detached and hurtling toward the cue ball. The fact that you are continuing to apply force through impact is why the cue doesn't slow to that lower predicted speed that ignores the external force. The less your strength allows the cue to slow at impact the more momentum is transferred to the ball. A power hitter in baseball has to be fast and strong.

You want to actually read my post and try again?
 

Patrick Johnson

Fish of the Day
Silver Member
... this assumes an isolated system where the cue (or the cue and your arm) are detached and hurtling toward the cue ball.
The fact that you are continuing to apply force through impact is why the cue doesn't slow to that lower predicted speed that ignores the external force. The less your strength allows the cue to slow at impact the more momentum is transferred to the ball.
I think Bob and Dave and Mike are saying the soft skin of the hand effectively isolates the cue from your hand/arm during the millisecond of contact.

pj
chgo
 
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