How does Zeno's paradox apply to a bouncing ball?

[AbstractPacif]

So i was thinking, if you drop a ball that has a bouncy property to it, it will travel half as high after the bounce, then in theory it will bounce half as high, and half, and half, and half but never reaches zero

this is not true in reality though, because there of a loss of energy due to air resistance and stuff.

just a fun idea :P

 

[Bob_for_short]

The time intervals for each bounce reduce so their sum is convergent and finite: 1 +1/2 + 1/4 + 1/8 + ... = 2 or so.

 

[DaveC426913]

If we didn't have to consider the ugly exigencies of reality, such as friction and inelastic deformation, the ball would not bounce half as high each time; it would bounce the same height each time, ad infinitum.

As soon as you allow for inelastic rebound, you are opening the door to friction and energy loss. So why stop there?

 

[AbstractPacif]

Another thing that is cool along the lines of what you had said, is an increased bounce every time :O

so let's say that a bounce of .5 means it is times .5 for every bounce but what about 1.5! it would become infinitely faster until it broke from the walls of its containment and flew into space! - it could be a new rocket!

sadly this is seamingly impossible

 

[DaveC426913]

Another thing that is cool along the lines of what you had said, is an increased bounce every time :O

so let's say that a bounce of .5 means it is times .5 for every bounce but what about 1.5! it would become infinitely faster until it broke from the walls of its containment and flew into space! - it could be a new rocket!

sadly this is seamingly impossible

Well, yes.

In order to bounce higher, it would have to have an energy source (either internal or external) and a mechanism for transferring that into propulsion. So far, our best bet is mixing LHy and LOx*.


*OK, make your bagels & cream cheese jokes now...

 

[GeorgeT]

Another thing that is cool along the lines of what you had said, is an increased bounce every time :O

so let's say that a bounce of .5 means it is times .5 for every bounce but what about 1.5! it would become infinitely faster until it broke from the walls of its containment and flew into space! - it could be a new rocket!

sadly this is seamingly impossible

What an odd place to start -- my first post in this forum...

Here's one possibility: http://www.gutenberg.org/etext/23153" (Gutenberg.org)

 

[DaveC426913]

What an odd place to start -- my first post in this forum...

Here's one possibility: http://www.gutenberg.org/etext/23153" (Gutenberg.org)

Flubber...


Interesting. The Absent-Minded Professor written by Samuel W. Taylor hit the theatres in March 1961. The Big Bounce written by Walter S. Tevis was published in Galaxy mag in Feb. 1958.

 

[A.T.]

So i was thinking, if you drop a ball that has a bouncy property to it, it will travel half as high after the bounce, then in theory it will bounce half as high, and half, and half, and half but never reaches zero

At some point this movement becomes smaller than the movement of the molecules due to thermal energy.

 

[Molydood]

So i was thinking, if you drop a ball that has a bouncy property to it, it will travel half as high after the bounce, then in theory it will bounce half as high, and half, and half, and half but never reaches zero

this is not true in reality though, because there of a loss of energy due to air resistance and stuff.

just a fun idea :P

You might want to look up Zeno's paradox, it deals with a similar problem of ever decreasing finite steps towards zero without ever actually getting there, With Zeno's it deals with 'time' as the quantity you are dividing up, so perhaps a better example of a paradox (well it is for me anyway because I imagine your ball example follows a non linear relationship due to real life losses, whereas with time it's not quite that simple to debunk)