Does the ball ever stop bouncing?

[Philosophy Explorer]

Here's an experiment you can try at home. Take a rubber ball and bounce it against the ground. You'll see it go up and down faster and faster until it seems to stop. The mathematics, with certain assumptions, will say that the ball does indeed stop bouncing and I agree with this. I'm wondering if someone disagrees and why? What say you to this?

[Geordie Ross]

Thermodynamics tells us the ball must stop bouncing, otherwise perpetual motion would be possible. Its energy is shifted into noise, friction heat and the kinetic energy is absorbed by the surface it hits, so you see a gradual decrease in the energy retained by the ball until it eventually stops.

Though this could be countered by some extravagant methods, maybe with some oscillating magnets?

A little fun fact, a metal ball bounces higher and for a longer period of time than a rubber ball. But I don't want to give kids steel balls to play with...

[Steve3007]

I think this is an interesting illustration of the fact that mathematical models of reality have the same characteristic that all models have - they are idealized versions of reality and therefore can never be an entirely accurate description of reality in every respect. If they were, they wouldn't be models. They'd be reality.

As Geordie says, the ball inevitably loses energy on each bounce. And since the amount of energy lost at each bounce is theoretically, a fixed proportion of the total amount of energy remaining, the equation which describes the loss of energy/height over time is an exponential decay. And an exponential decay never reaches zero. If, at every bounce, you can only ever lose a fraction of your total energy which is less than 1 and greater than 0, you can never lose all your energy.

In practice, inevitably, the system is more complex than that, and exponential decay is just an initial approximation. Once the bounce height gets lower than a certain level, all sorts of other factors will become more and more significant, until they become dominant. E.g. there'll always be a slight difference in electrostatic charge between the ball and the floor, creating an extra force.

Cue my favourite physicsy joke about the perils of using the highly idealized and reductionist techniques of physics to model complex physical systems (like living things):

A physicist is asked to predict the winner of a horse race. Some time later, he is heard muttering: "OK, assume it's a spherical horse in a vacuum..."

I'm going to keep telling that joke until somebody laughs.

[Geordie Ross]

Yea, it can't ever reach zero, only it's minimal total potential energy, and that will always remain above zero.

I like that joke. Everything in physics must be reduced with minimal possible variants and nearest approximations. Its not an exact science

[Steve3007]

Actually I think I was slightly wrong in my previous post! It's not exponential decay.

I guess this is an example of Zeno's paradox? An infinite series with a finite sum. So even the mathematical idealization of the bouncing ball will come to rest in finite time, although it will take an infinite number of bounces to do it?

[Philosophy Explorer]

Actually I think I was slightly wrong in my previous post! It's not exponential decay.

I guess this is an example of Zeno's paradox? An infinite series with a finite sum. So even the mathematical idealization of the bouncing ball will come to rest in finite time, although it will take an infinite number of bounces to do it?

Give the man a cigar. Does anyone dispute this?

[HalfWit]

(Nested quote removed.)


Give the man a cigar. Does anyone dispute this?

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

Yes, I dispute that. Good grief. Are you saying you believe it?

[Philosophy Explorer]

(Nested quote removed.)


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

Yes, I dispute that. Good grief. Are you saying you believe it?

Sure do. Why, do you believe the ball has infinite energy to keep bouncing forever?

[Geordie Ross]

It cannot bounce an infinite number of times. (depending on your definition of bounce) Each time the ball is met with resistance, it loses kinetic energy to them point at which it cannot overcome gravity. It retains potential energy but that doesn't effect its 'bounces', unless the surface its resting on shifts position.

In essence its paradoxically and axiomatically impossible for a ball to bounce and infinite number of times "before stopping". It would help if you simplified it to "it doesn't stop bouncing"

[Philosophy Explorer]

It cannot bounce an infinite number of times. (depending on your definition of bounce) Each time the ball is met with resistance, it loses kinetic energy to them point at which it cannot overcome gravity. It retains potential energy but that doesn't effect its 'bounces', unless the surface its resting on shifts position.

In essence its paradoxically and axiomatically impossible for a ball to bounce and infinite number of times "before stopping". It would help if you simplified it to "it doesn't stop bouncing"

To give a more complete picture, the kinetic energy converts into potential energy as the ball bounces up from the ground, but the potential energy becomes less and less because the kinetic energy gets diminished until eventually the ball comes to rest on the ground; at that point kinetic energy = potential energy = 0.

[Geordie Ross]

There's a fundamental flaw there, you forgot to factor in the resistance of the surface the ball contacts. The kinetic energy equals the resistance, not the potential. The potential energy is intrinsically linked to the distance from the centre of gravity in this scenario. (In a vacuum/ without wind resistance)

[Philosophy Explorer]

There's a fundamental flaw there, you forgot to factor in the resistance of the surface the ball contacts. The kinetic energy equals the resistance, not the potential. The potential energy is intrinsically linked to the distance from the centre of gravity in this scenario. (In a vacuum/ without wind resistance)

When the ball reaches its maximum height from a particular bounce, it's all potential energy. Also with or without wind resistance, it loses kinetic energy, in either case it will come to rest eventually.

[Geordie Ross]

Agreed, the only reason I mention wind/air resistance is because Steve mentioned that race joke. and terminal velocity.

[HalfWit]

When the ball reaches its maximum height from a particular bounce, it's all potential energy. Also with or without wind resistance, it loses kinetic energy, in either case it will come to rest eventually.

Do you believe it bounces infinitely many times? I'm very confused about your early statement that "nobody could dispute" that it does so.

[Philosophy Explorer]

(Nested quote removed.)


Do you believe it bounces infinitely many times? I'm very confused about your early statement that "nobody could dispute" that it does so.

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.