Does the ball ever stop bouncing?

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HalfWit
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Re: Does the ball ever stop bouncing?

Post by HalfWit »

Philosophy Explorer wrote: I believe you're referring to post #6. Maybe it does bounce an infinite number of times, maybe it doesn't. Math says it can bounce an infinite number of times in a finite time interval. Also it would take an infinite amount of energy to keep that ball bouncing indefinitely. Therefore I'm saying the ball must come to a stop eventually, with or without an infinite number of bounces.
I believe that the idea that a physical ball can bounce infinitely many times is complete nonsense. So let's drill this down a little.

If each bounce reaches a smaller height than the bounce before, then one of two things must be the case:

a) The bounces get smaller and smaller but never get any smaller than the Planck length.

or

b) The bounces eventually get smaller than the Planck length.

If you believe a ball could bounce infinitely many times, which of the above do you think would be true?

I must confess honestly that I find the notion of infinitely many bounces so profoundly and obviously false that I cannot comprehend the mindset of someone who believes it's possible. But clearly you are one such. So I want to know more about how you think this could happen.

Here's my thought process. Each bounce causes the system to lose some energy, until eventually the ball doesn't have enough energy to get off the ground.

So at some point there is still some nonzero amount of energy in the system, but not enough to get the ball off the ground. In fact a ball sitting on the ground that appears to the eye to be stationary, may still actually be "bouncing," but without enough energy to leave the ground. It's just pulsing internally along the vertical axis ... in other words it's vibrating from the last collision.

For all we know the vibrations never stop ... after a finite number of bounces the ball can no longer leave the ground, but the shape of the ball is still rebounding from the last collision ... and the one before that ... all those waves superimposed to model the actual shape of the ball ...

And some of that compression/expansion energy is converted to heat. So if we carefully measures the air around the ball, we'd see that it's getting warmer as the ball -- still sitting there perfectly still to the naked eye -- is actually pulsating from the sum of all the collisions, giving off heat ... forever? Well actually I don't know.

Now I imagine that this effefct must dissipate at some point ... the rebounding shape must eventually stabilize and stop pulsing. That would also happen in a finite amount of time, but I don't know anything about the physics of compressed, air-filled rubber balls. For that I'd ask a pro basketball player, they know more about this than anyone :-)

Conclusion:

There are three phases:

1) The bounce phase. The ball has enough energy to "bounce," ie separate itself from the earth by an appreciable distance. We'd have to define it but say if there's a space visible to the naked eye, then it bounced. By that definition. there will be a finite number of bounces in this phase. Eventually there won't be enough energy to leave the earth.

2) The decompression phase. This is when the naked eye can no longer perceive the ball as moving. But there's still energy in the ball from all the bouncing, each bounce deforming the physical material a little. If it's "elastic" it bounces well ... elastic is actually a technical term in physics, but I'm really out of my depth on the physics. But in the decompression phase, it's pulsating and giving off heat.

3) The still or "deep" phase. We say the ball is still when it's not only not bouncing, but when it's stopped decompressing from all the bounces it's taken. The balls surface temperature and the local air temp are the same ... it's stopped giving off heat from the decompression.

BUT: But what about all the quarks and gluons and strings and stuff they have these days? Back in the day I kept up at the Scientific American level and knew a photon from a proton. These days they're into some crazy stuff. So who really can say WHEN a ball stops bouncing? Maybe at some deeper level all of the tiny microparticles in there have had their states altered by the bounce? Perhaps at some deeper level, the ball is still striving for equilbrium? And will be forever?

PE, I think I have talked myself into a point of view that sees some merit in what you said. Perhaps a ball does bounce forever ... at some deep level of existence, perhaps a ball that bounces once, never stops bouncing. It wouldn't be a completed process ... but it would be forever. So I think I can imagine a definition of "bounce" that allows the possibility that a ball bounces forever, at some level.

I may have rambled a bit. What do you think?
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Philosophy Explorer
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Re: Does the ball ever stop bouncing?

Post by Philosophy Explorer »

Halfwit,

As time moves forward, the time between bounces keeps shrinking. If the shrinking proceeds fast enough, as per math specification, then there can be an infinite number of bounces within a finite time interval.

For me infinity is no sweat to understand. Just a matter of thinking about it logically. Here's a quick scenario about infinity: along a (straight) finite line, you can always find a midpoint. And between the midpoint and an endpoint, you can find a second midpoint. You can continue this process indefinitely which indicates the finite line contains an infinite number of points.

I can continue discussing infinity, but it's been well covered before. For me the strangest part of infinity isn't that it exists, rather it exists on several different levels.

Edit: I'll offer two examples that explains the mathematics. If the ball bounces in this manner: 1/2, 1/3, 1/4, 1/5, 1/6..., then it will continue to bounce indefinitely based on this series. If, however, it bounces in this manner: 1, 1/2, 1/4, 1/8, 1/16..., then it will stop bouncing at some point in time. That's the mathematics of it.
Last edited by Philosophy Explorer on November 15th, 2013, 12:49 pm, edited 1 time in total.
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Geordie Ross
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Re: Does the ball ever stop bouncing?

Post by Geordie Ross »

But that wouldn't quite work in practice, as the length of the bounce would eventually be smaller than the proton of an atom. So it could equally be argued that the static book on the table is bouncing an infinite number of times. And it could be argued that the bounce never actually happens, as the atoms never actually touch due to electrostatic repulsion, its more of a hover, even when static. So it's more of a far reaching question than I first gave it credit for.

Also it seems to be an oxymoron that it bounces an infinite number of times 'before stopping' as it implies it never stops.
The good life is one inspired by love, and guided by knowledge. - Bertrand Russell
Keithprosser3
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Re: Does the ball ever stop bouncing?

Post by Keithprosser3 »

A mathematically idealised ball isn't made of atoms or even matter but of 'pure maths' so will bounce forever with smaller and smaller amplitude.

A real ball will convert some of the kinetic energy into heat on each bounce so eventually there will not be enough kinetic energy for the ball to really bounce - all the energy will be taken up by the warmed-up atoms in the ball (and the surface it strikes) 'jiggling more' while remaining essentially stationary around some mid-point. I suspect that will happen long before the 'theoretical' amplitude of the bounce would be on the atomic or planck scales. Eventually even the extra jiggling will cease as thermodynamic equilibrium is reached.

Or not.
Steve3007
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Re: Does the ball ever stop bouncing?

Post by Steve3007 »

Halfwit
Does anyone dispute that a ball bounces infinitely many times before stopping?

Yes, I dispute that. Good grief. Are you saying you believe it?
Of course nobody believes that physical balls bounce an infinite number of times. This, as I pointed out in post #3, and as others (like Keith, above) pointed out, is an example of mathematical idealization versus complex reality.
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Geordie Ross
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Re: Does the ball ever stop bouncing?

Post by Geordie Ross »

I suppose it's similar to gravity and it's infinite range, it never reaches zero, it's strength simply deminishes exponentially.
The good life is one inspired by love, and guided by knowledge. - Bertrand Russell
Steve3007
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Re: Does the ball ever stop bouncing?

Post by Steve3007 »

Yes exactly. I guess there's sometimes misunderstanding of the way that the concept of infinity is used in physics - as a "limit" (as in the "theory of limits"). So things "tend to infinity" if, for any arbitrarily large value for that thing, there's no physical reason not to imagine a larger one. As you say, the strength of gravity "tends to zero" as the distance "tends to infinity". It doesn't mean that anyone thinks it's possible to actually reach infinite distance.
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Teralek
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Re: Does the ball ever stop bouncing?

Post by Teralek »

In perfect elasticity and perfect vacuum the ball will not stop bouncing

http://wiki.answers.com/Q/If_a_ball_is_ ... est#slide5
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Geordie Ross
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Re: Does the ball ever stop bouncing?

Post by Geordie Ross »

Not sure what "perfect elasticity" means, but... Assuming the source of the gravity is large enough to sustain a repetitive bounce, inertia would come into play? The two surfaces colliding would still cause impacted friction?
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Teralek
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Re: Does the ball ever stop bouncing?

Post by Teralek »

Does not matter. For every action there is an opposite equal reaction. There is no such thing as perfect elasticity because some of the energy gets transferred away from the system as heat and the ball will eventually stop even in perfect vacuum. Force of gravity is irrelevant. Only if there was no transfer of energy the ball could go on forever
Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. ~Bertrand Russell
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Geordie Ross
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Re: Does the ball ever stop bouncing?

Post by Geordie Ross »

Well we are in the realm of hypothetical. Assuming perfect elasticity existed and both surfaces are "perfectly elastic", in a "perfect vacuum, inertia would play a big role, the resistance to move, and the moving balls resistance to stop? No?
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Teralek
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Re: Does the ball ever stop bouncing?

Post by Teralek »

I don't think so Geordie. Inertia only means that a body which is in movement will tend to remain in movement and if it's motionless will tend to remain motionless. The bouncing ball is a dynamic system like a pendulum.

Inertia is what makes the ball bounce in the first place. It's the source of kinetic energy

With no energy transfer (perfect elasticity) the ball will bounce indefinitely. Like a pendulum with zero friction will move forever. These things though remain in the field of fantasy. There will always be energy transfer and minimum friction.
Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. ~Bertrand Russell
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Geordie Ross
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Re: Does the ball ever stop bouncing?

Post by Geordie Ross »

Ah, I was going off the wikianswer links definition of "perfect elasticity" meaning no internal friction, not "no energy transfer". But hypothetically, what would happen to the inertia of the ball? It has to go somewhere?

Or would the balls inertia, and source of gravity be in 'perfect' equilibrium?
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Teralek
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Re: Does the ball ever stop bouncing?

Post by Teralek »

Inertia is a property of objects, it doesn't go anywhere. If Kinetic energy goes off the system by any means the ball will stop.

Yes, from what I read inertia (kinetic system energy) and gravity would be in a perfect equilibrium if such system could be assembled.
Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. ~Bertrand Russell
HalfWit
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Re: Does the ball ever stop bouncing?

Post by HalfWit »

Philosophy Explorer wrote:Halfwit,

As time moves forward, the time between bounces keeps shrinking. If the shrinking proceeds fast enough, as per math specification, then there can be an infinite number of bounces within a finite time interval.
Per the math, yes, if this is an idealized mathematical point that's bouncing. But don't you understand that in the physical universe, a physical ball loses energy with each bounce, and that after finitely many bounces it will no longer have enough energy to leave the ground?
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