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From what I remember of physics, and how I understand it in my own simple
Thinking. The OB is pushing back at the CB with it's mass, and the CB is
Pushing on the OB with it's mass. This stops the CB because the mass cancels
Each other out... all that is left is the force, which pushes the OB forward. Not sure
If that explains it any better, but that is how I see it in my mind.
TD
Thinking. The OB is pushing back at the CB with it's mass, and the CB is
Pushing on the OB with it's mass. This stops the CB because the mass cancels
Each other out... all that is left is the force, which pushes the OB forward. Not sure
If that explains it any better, but that is how I see it in my mind.
TD
Bob,
Maybe it might be easier to say (and conceive) it this way: when the cueball approaches the object ball, it has a force equal to its mass times acceleration (at contact). The object ball gets "hit" with that force. That force is equal to the amount needed to make an object of that mass move at that speed. The object ball thus moves at the exact same speed as the equal mass cue ball. However, the object ball *also* exerts an equal and opposite force on the cue ball. This is exactly the amount of force required to bring an object of that mass from that speed down to zero. Thus one force propels the object ball to the same speed as the cue ball, and the equal and opposite force slows the cue ball to zero.
Does that make sense?
KMRUNOUT
Sent from my iPhone using AzBilliards Forums
The OP said "NO MATH". Now see what you've gone and done.
Disclaimer #1: I'm only replying because you seem interested enough in this that you won't mind being corrected, so please don't take offense. Disclaimer #2: I'm talking classical mechanics here, so if you are hitting the ball near the speed of light, this becomes a whole different conversation.
The cue ball doesn't have a force; forces describe the interactions between objects, so prior to contact with the object ball, the only force in play is the friction between the cue ball and the cloth (not entirely true, but we'll assume that wind resistance is minimal and the table is perfectly level for our purposes). That force on the cue ball is in the opposite direction of its motion, so it's actually slowing the cue ball down (releasing heat in the process) and causing it to rotate forwards. That's why a stop shot actually has to begin its journey towards the object ball with some backspin: it has to counter the forward spin it will pick up on the way there.
What the cue ball does have while it's in motion are kinetic energy and momentum, both of which are determined by the mass of the cue ball and its velocity, but describe two different things. Kinetic energy describes the amount of work the cue ball can do, and momentum describes the impulse created when the cue ball strikes the object ball. Both are conserved in a perfectly elastic collision (meaning no energy is dissipated). Billiard ball collisions aren't perfectly elastic (some heat and noise is given off), but they are close because of the rigidity of the balls.
The only way to conserve both momentum and kinetic energy between two objects of the same mass in a head-on collision is for them to exchange velocities. We're avoiding math here, so you'll just have to believe that it works out that way.
Now...back to the forces involved in the collision. The object ball accelerates, so it must have experienced a force, which means that the cue ball experienced an equal, opposite force in order to obey Newton's 3rd law. Since the masses are equal, the acceleration of the cue ball is exactly opposite that of the object ball, bringing it to a complete stop.
Unfortunately, I think that the original poster in this thread will find a lot of this rather unsatisfying, because it sounds like they were looking for an answer to why things work the way they do, and we've instead given a description of the way things work based entirely on our observation. Sure, we could drop down a level to particle physics and discuss this in terms of quantum mechanics, but the question still remains: Why? The answer: Nobody really knows. :wink:
We do know that energy must be conserved because there is nothing adding or taking away energy from the balls (ignoring non-ideal collision losses). We also know that momentum must be conserved because they are no external forces acting on the system (i.e., there is only an "internal force" acting between the balls during the collision). The only way both energy and momentum can be conserved is if all of the energy and momentum transfers from the CB and OB. If only a fraction of the momentum were transferred (with the CB retaining the other fraction), there would be a loss of energy, which is not possible. Here is the simple math showing why this is true:
m: ball mass (same for CB and OB)
v: original CB speed
vc: CB speed after collision
vb: OB speed after collision
Conservation of momentum: m*v = m*vc + m*vb
Conservation of energy: 1/2*m*v^2 = 1/2*m*vc^2 + 1/2*m*vb^2
These equations can be simplified by cancelling the equal masses, canceling the 1/2's, writing the squares (v^2) as multiplication (v*v), and assuming the initial speed is 1 (100% or full speed):
1 = vc + vb
1 = vc*vc + vb*vb
vc and vb must be numbers between 0 (no speed) and 1 (full speed). With a stop shot, the CB delivers all speed to the OB, so vc=0 and vb=1, and both equations are satisfied:
1 = 0 + 1 = 1
1 = 0*0 + 1*1 = 0 + 1 = 1
If the CB transferred only half of its speed to the OB, momentum is conserved, but energy is not:
1 = 1/2 + 1/2 = 1
1 = 1/2*1/2 + 1/2*1/2 = 1/4 + 1/4 = 1/2 (half of the energy is missing)!
The energy equation would fail for any fractions you try to use for vc and vb because when you square fractions, you get smaller fractions, which can't add to 1.
Sorry for the math, but in this case, the math is fairly easy to follow and understand.
Regards,
Dave
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the simple answer?
The simple answer is that you have kinetic energy transfer. An object at rest tends to stay at rest unless acted upon by an outside force. An object in motion tends to stay in motion unless acted upon by an outside force.
When two balls of equal mass come together where one is in motion relative to a stationary one, the one in motion will act upon the one at rest, transferring the energy. There is an equal and opposite force exerted upon the ball in motion and since the balls have ~the same mass, it causes the ball in motion to stop and the ball at rest to travel at ~ the same velocity as the ball that was in motion.
I say ~ because there is some energy lost due to friction, gravity etc... There are other forces involved. In a total vacuum where no gravity or other forces were acting on the balls, the ball would travel at exactly the same velocity.
Jaden
The simple answer is that you have kinetic energy transfer. An object at rest tends to stay at rest unless acted upon by an outside force. An object in motion tends to stay in motion unless acted upon by an outside force.
When two balls of equal mass come together where one is in motion relative to a stationary one, the one in motion will act upon the one at rest, transferring the energy. There is an equal and opposite force exerted upon the ball in motion and since the balls have ~the same mass, it causes the ball in motion to stop and the ball at rest to travel at ~ the same velocity as the ball that was in motion.
I say ~ because there is some energy lost due to friction, gravity etc... There are other forces involved. In a total vacuum where no gravity or other forces were acting on the balls, the ball would travel at exactly the same velocity.
Jaden
Thank you all for an enlightening discussion. I hope my questions about the zombie apocalypse will generate as spirited an exchange but those are more appropriately directed to a different forum.
Physics professor here.
I see a few well-intentioned answers here but none that really hit the mark.
Seems like some are complicating the answer with unnecessary grandiloquence.
Let me break it down for you.
Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system.
It is embodied in Newton's first law (the law of inertia). ... The forces between them are equal and opposite.
This is all pretty common knowledge but don't let it distract you from the simple fact that if one or more of your family members suffers from mesothelioma you may be entitled to financial compensation.
I see a few well-intentioned answers here but none that really hit the mark.
Seems like some are complicating the answer with unnecessary grandiloquence.
Let me break it down for you.
Conservation of momentum is a fundamental law of physics which states that the momentum of a system is constant if there are no external forces acting on the system.
It is embodied in Newton's first law (the law of inertia). ... The forces between them are equal and opposite.
This is all pretty common knowledge but don't let it distract you from the simple fact that if one or more of your family members suffers from mesothelioma you may be entitled to financial compensation.
That's the easy part, Dr. :wink:
My joke was meant to question the origins of nature in a more philosophical sense.
P.S. Can't give you any more rep, but I'm glad you threw the equations out there.
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I think that oversimplifies it. As Dave and Bob both pointed out, it's the combination of conservation of momentum and conservation of KE that explain the behavior of the two balls.