Sort of a physics question

C

Clusterbuster

AzB Silver Member
Silver Member
I was laying awake the other night pondering many things: Barbecue, the zombie apocalypse, Kentucky basketball, etc. and about 2:00 a.m. I started thinking about the physics of stop shots, so this maybe ought to be addressed to Dr. Dave or someone of his ilk. Here is my question:

Obviously, when a sliding cue ball hits an object ball of equal weight straight on, the cue ball comes to a dead stop and the object moves forward. A classic stop shot. It's maybe the most fundamental shot in pool and there is no question about what happens. My question is why does that happen? With two balls of equal mass, all of the energy is transferred from the moving ball to the stationary ball but why do (if you can put it this way) the laws of physics mandate that with both balls being of equal mass, it is the stationary ball that moves and the cue ball which comes to a halt. It seems that it would be just as reasonable (not that nature ever asked me) for the object ball to remain stationary and the cue ball to bounce straight backwards or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed. These sorts of issues keep a guy awake at 2:00 a.m.

There's got to be an answer that a very mathematically challenged English major could understand.

Any help?
 
Clusterbuster said:
I was laying awake the other night pondering many things: Barbecue, the zombie apocalypse, Kentucky basketball, etc. and about 2:00 a.m. I started thinking about the physics of stop shots, so this maybe ought to be addressed to Dr. Dave or someone of his ilk. Here is my question:

Obviously, when a sliding cue ball hits an object ball of equal weight straight on, the cue ball comes to a dead stop and the object moves forward. A classic stop shot. It's maybe the most fundamental shot in pool and there is no question about what happens. My question is why does that happen? With two balls of equal mass, all of the energy is transferred from the moving ball to the stationary ball but why do (if you can put it this way) the laws of physics mandate that with both balls being of equal mass, it is the stationary ball that moves and the cue ball which comes to a halt. It seems that it would be just as reasonable (not that nature ever asked me) for the object ball to remain stationary and the cue ball to bounce straight backwards or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed. These sorts of issues keep a guy awake at 2:00 a.m.

There's got to be an answer that a very mathematically challenged English major could understand.

Any help?
Click to expand...
The collision velocity study is at its simplest, the Conservation of Momentum, if we ignore all the forms of energy and where they dissipate.

Don't you need more than that?
 
Clusterbuster said:
I was laying awake the other night pondering many things: Barbecue, the zombie apocalypse, Kentucky basketball, etc. and about 2:00 a.m. I started thinking about the physics of stop shots, so this maybe ought to be addressed to Dr. Dave or someone of his ilk. Here is my question:

Obviously, when a sliding cue ball hits an object ball of equal weight straight on, the cue ball comes to a dead stop and the object moves forward. A classic stop shot. It's maybe the most fundamental shot in pool and there is no question about what happens. My question is why does that happen? With two balls of equal mass, all of the energy is transferred from the moving ball to the stationary ball but why do (if you can put it this way) the laws of physics mandate that with both balls being of equal mass, it is the stationary ball that moves and the cue ball which comes to a halt. It seems that it would be just as reasonable (not that nature ever asked me) for the object ball to remain stationary and the cue ball to bounce straight backwards or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed. These sorts of issues keep a guy awake at 2:00 a.m.

There's got to be an answer that a very mathematically challenged English major could understand.

Any help?
Click to expand...
The particular laws of physics that dominate (but do not totally control) this situation are the conservation of energy and the conservation of momentum. The unusual solutions you suggest do not conserve momentum and the second one does not conserve energy either.

It is hard to know how far down to go to further explain the answer since it's really hard to do if I have to assume no math and no physics, but let's go a little ways.

In the first case above, where the cue ball bounces back and the object ball doesn't move, the cue ball must have pushed on the object ball in order to reverse direction. But if it was pushed, the object ball has to move away. The standard chant is, "For every action there is an equal and opposite reaction," which really means that if one thing pushes on another (which is to say, causes a force between them) both sides feel the force (or push), and that force is in opposite directions. The Earth pulls on me with 160 pounds of force and I pull on the Earth with the same force, which the Earth probably does not much notice, since it is paying a lot more attention to the Moon and Sun.

For the second case, it's not clear what you mean. If the object ball goes to 50% of the cue ball's speed and the cue ball loses half its speed, they would be going the same speed and in the same direction. If instead you mean (for example) that the cue ball is originally moving right at 100% and after the collision the object ball moves right at 50% and the cue ball to the left at 50%, the momentum has a problem because the total momentum in the result is 0 (momentum includes direction so the equal left and right cancel). Also, the energy has a problem because energy is proportional to the square of how fast the ball is moving and the two energies afterwards total to only half of the original energy since the square of a half is a quarter.
 
If you freeze five balls to a rail and slide one ball at the combo...you make one ball.
...if you slide two balls, you make two balls.
...if you slide three balls, you make three balls.
This picture in your mind will do you more good than a bunch of complex equations...
....academics don't fare too well in action....unless they clear their mind.

Jonni Fulcher, who is well known in the world of physics, has had victories at pool and
snooker....he can run 100 at snooker and straight pool...and has won Euro 9-ball tourneys
and snooker tourneys.....I recall from an interview him saying that INSTINCT is your
most important asset.

Here's a pic of Albert after losing to an APA two....

IMG_3929.JPG
 
Clusterbuster said:
...or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed.
Click to expand...
Now here's a physics quiz question.

Let's say after collision both balls are traveling in the same direction at half the CB's original speed. Conservation of momentum is satisfied...mv = m*(0.5v) + m*(0.5v). However, conversation of energy seemingly is not...mv^2 != m*(0.5v)^2 + m*(0.5v)^2. After collision half of the energy appears to half disappeared.

So, what's going on here?
 
jsp said:
Now here's a physics quiz question.

Let's say after collision both balls are traveling in the same direction at half the CB's original speed. Conservation of momentum is satisfied...mv = m*(0.5v) + m*(0.5v). However, conversation of energy seemingly is not...mv^2 != m*(0.5v)^2 + m*(0.5v)^2. After collision half of the energy appears to half disappeared.

So, what's going on here?
Click to expand...

If you're playing pool, you're down here on earth, where there are other factors.
...the heavier the cloth, the more resistant the object ball is to impact.

I was raised on 26 oz snooker cloth....what would be a pocket-weight half-ball cut on the
black-ball only made it about half way to the pocket on 40 oz cloth in a British club.
 
jsp said:
Now here's a physics quiz question.

Let's say after collision both balls are traveling in the same direction at half the CB's original speed. Conservation of momentum is satisfied...mv = m*(0.5v) + m*(0.5v). However, conversation of energy seemingly is not...mv^2 != m*(0.5v)^2 + m*(0.5v)^2. After collision half of the energy appears to half disappeared.

So, what's going on here?
Click to expand...

A physical impossibility is what is going on there...hence why it doesn't fulfill both equations.

The thing about the balls hitting each other, is that it is very close to a perfectly elastic collision which means the kinetic energy is conserved. Your equations don't allow for that in the slightest when you use the conservation of momentum equation alone and 'assume' that the velocities of the two balls are going to be the same. You need to use both equations to solve for the two variables (a very basic math altruism--if you have multiple unknowns, you need the same number of equations to solve for those unknowns).
 
jsp said:
Now here's a physics quiz question.

Let's say after collision both balls are traveling in the same direction at half the CB's original speed. Conservation of momentum is satisfied...mv = m*(0.5v) + m*(0.5v). However, conversation of energy seemingly is not...mv^2 != m*(0.5v)^2 + m*(0.5v)^2. After collision half of the energy appears to half disappeared.

So, what's going on here?
Click to expand...

The elephant had mud on him.
 
Bob Jewett said:
The particular laws of physics that dominate (but do not totally control) this situation are the conservation of energy and the conservation of momentum. The unusual solutions you suggest do not conserve momentum and the second one does not conserve energy either.

It is hard to know how far down to go to further explain the answer since it's really hard to do if I have to assume no math and no physics, but let's go a little ways.

In the first case above, where the cue ball bounces back and the object ball doesn't move, the cue ball must have pushed on the object ball in order to reverse direction. But if it was pushed, the object ball has to move away. The standard chant is, "For every action there is an equal and opposite reaction," which really means that if one thing pushes on another (which is to say, causes a force between them) both sides feel the force (or push), and that force is in opposite directions. The Earth pulls on me with 160 pounds of force and I pull on the Earth with the same force, which the Earth probably does not much notice, since it is paying a lot more attention to the Moon and Sun.

For the second case, it's not clear what you mean. If the object ball goes to 50% of the cue ball's speed and the cue ball loses half its speed, they would be going the same speed and in the same direction. If instead you mean (for example) that the cue ball is originally moving right at 100% and after the collision the object ball moves right at 50% and the cue ball to the left at 50%, the momentum has a problem because the total momentum in the result is 0 (momentum includes direction so the equal left and right cancel). Also, the energy has a problem because energy is proportional to the square of how fast the ball is moving and the two energies afterwards total to only half of the original energy since the square of a half is a quarter.
Click to expand...

I just hit the cue ball a little below center.
Thats easier then the above. :shrug:
 
Bob Jewett said:
The particular laws of physics that dominate (but do not totally control) this situation are the conservation of energy and the conservation of momentum. The unusual solutions you suggest do not conserve momentum and the second one does not conserve energy either.

It is hard to know how far down to go to further explain the answer since it's really hard to do if I have to assume no math and no physics, but let's go a little ways.

In the first case above, where the cue ball bounces back and the object ball doesn't move, the cue ball must have pushed on the object ball in order to reverse direction. But if it was pushed, the object ball has to move away. The standard chant is, "For every action there is an equal and opposite reaction," which really means that if one thing pushes on another (which is to say, causes a force between them) both sides feel the force (or push), and that force is in opposite directions. The Earth pulls on me with 160 pounds of force and I pull on the Earth with the same force, which the Earth probably does not much notice, since it is paying a lot more attention to the Moon and Sun.

For the second case, it's not clear what you mean. If the object ball goes to 50% of the cue ball's speed and the cue ball loses half its speed, they would be going the same speed and in the same direction. If instead you mean (for example) that the cue ball is originally moving right at 100% and after the collision the object ball moves right at 50% and the cue ball to the left at 50%, the momentum has a problem because the total momentum in the result is 0 (momentum includes direction so the equal left and right cancel). Also, the energy has a problem because energy is proportional to the square of how fast the ball is moving and the two energies afterwards total to only half of the original energy since the square of a half is a quarter.
Click to expand...

This! The physics of the OP's question is pretty straightforward.
Basically the energy is being mostly transferred to the static object, because they are of equal mass.
 
Those desk knocker toy things are the epitome of a perfect stop shot!
 
As others have pointed out, the Laws of Physics require that both energy and momentum be conserved during a collision. The physics and math details for a more general case (at any cut angle, including 0) is here:

TP 3.1 - 90° rule

For a straight shot (with no cut angle), the only way both energy and momentum conservation equations can be satisfied is if the CB stops and the OB moves away with the original CB speed (neglecting energy loss). It may seem hard to believe that the world needs to obey equations, but a better way to think about it is the equations just happen to described what actually happens in the real world.

Regards,
Dave


Clusterbuster said:
I was laying awake the other night pondering many things: Barbecue, the zombie apocalypse, Kentucky basketball, etc. and about 2:00 a.m. I started thinking about the physics of stop shots, so this maybe ought to be addressed to Dr. Dave or someone of his ilk. Here is my question:

Obviously, when a sliding cue ball hits an object ball of equal weight straight on, the cue ball comes to a dead stop and the object moves forward. A classic stop shot. It's maybe the most fundamental shot in pool and there is no question about what happens. My question is why does that happen? With two balls of equal mass, all of the energy is transferred from the moving ball to the stationary ball but why do (if you can put it this way) the laws of physics mandate that with both balls being of equal mass, it is the stationary ball that moves and the cue ball which comes to a halt. It seems that it would be just as reasonable (not that nature ever asked me) for the object ball to remain stationary and the cue ball to bounce straight backwards or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed. These sorts of issues keep a guy awake at 2:00 a.m.

There's got to be an answer that a very mathematically challenged English major could understand.

Any help?
Click to expand...
 
When a sliding CB impacts a stationary OB,

The CB ends up with SIN(a) of the velocity.
The OB ends up with COS(a) of the velocity.

A dead straight shot
leave the CB with SIN(0)*Voriginal
and leaves OB with COS(0)*Voriginal.

SIN(0) = 0, COS(0) = 1.

Now, this is completely ignoring the energy loss due to the inelasticity of the collision (93%-97% of the velocity is transferred)

Notice, also; that a cut of 45 degrees leaves CB with 71% of its original velocity and delivers 71% of the CB's original velocity into OB. SIN(45) = COS(45) = 0.71.....

An 89 degree contact, leaves the CB will essentially all of its original velocity, and imparts a tiny fraction into OB. This is why one ha to hit thin cuts so hard.

Now, you may want to reconsider not taking physics in HS.
 
Clusterbuster said:
I was laying awake the other night pondering many things: Barbecue, the zombie apocalypse, Kentucky basketball, etc. and about 2:00 a.m. I started thinking about the physics of stop shots, so this maybe ought to be addressed to Dr. Dave or someone of his ilk. Here is my question:

Obviously, when a sliding cue ball hits an object ball of equal weight straight on, the cue ball comes to a dead stop and the object moves forward. A classic stop shot. It's maybe the most fundamental shot in pool and there is no question about what happens. My question is why does that happen? With two balls of equal mass, all of the energy is transferred from the moving ball to the stationary ball but why do (if you can put it this way) the laws of physics mandate that with both balls being of equal mass, it is the stationary ball that moves and the cue ball which comes to a halt. It seems that it would be just as reasonable (not that nature ever asked me) for the object ball to remain stationary and the cue ball to bounce straight backwards or maybe for the object ball to pick up half the velocity and the cue ball to lose half so that both are now travelling directly away from each other at half the cue ball's original speed. These sorts of issues keep a guy awake at 2:00 a.m.

There's got to be an answer that a very mathematically challenged English major could understand.

Any help?
Click to expand...

You can answer this yourself. A sliding cue ball will stop and transfer all of its energy on to the OB if hit straight on because they are equal in mass. Hit the identical CB shot into the rack of balls and it will bounce back and stop. Why: the rack of ball is made up of greater mass. If you can find a pool ball the same size but lighter, the CB would not stop with the same shot. It would slide right through collision and then begin to roll forward.
 
Last edited:
We didn't cover this in consumer math or general science.

Anybody want to know how to write a check or dissect a frog?
 
denwhit said:
A sliding cue ball will stop and transfer all of its energy on to the OB if hit straight on because they are equal in mass. Hit the identical CB shot into the rack of balls and it will bounce back and stop. Why: the rack of ball is made up of greater mass. If you can find a pool ball the same size but lighter, the CB would not stop with the same shot. It would slide right through collision and then begin to roll forward.
Click to expand...
For those interested, the effects of CB/OB mass and size differences are demonstrated and described in detail here:

ball weight, size, and wear effects resource page

Enjoy,
Dave
 
pt109 said:
If you're playing pool, you're down here on earth, where there are other factors.
...the heavier the cloth, the more resistant the object ball is to impact.

I was raised on 26 oz snooker cloth....what would be a pocket-weight half-ball cut on the
black-ball only made it about half way to the pocket on 40 oz cloth in a British club.
Click to expand...

Leave me out of this.
 
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