1158: "Rubber Sheet"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

User avatar
Quicksilver
Posts: 437
Joined: Wed Apr 29, 2009 6:21 am UTC

1158: "Rubber Sheet"

Postby Quicksilver » Wed Jan 09, 2013 5:33 am UTC

Image
http://xkcd.com/1158/
Alt Text: "It IS about physics. It ALL is."
Looks kind of dangerous. Why a bowling ball?

SteevyT
Posts: 16
Joined: Wed Dec 15, 2010 8:41 pm UTC

Re: 1158: "Rubber Sheet"

Postby SteevyT » Wed Jan 09, 2013 5:34 am UTC

That is one monster bowling ball.

User avatar
rhomboidal
Posts: 801
Joined: Wed Jun 15, 2011 5:25 pm UTC
Contact:

Re: 1158: "Rubber Sheet"

Postby rhomboidal » Wed Jan 09, 2013 5:35 am UTC

Hehe, I have to see a competitive version of this at Rio in 2016. Or in my backyard as soon as doable.

gormster
Posts: 233
Joined: Mon Jul 23, 2007 6:43 am UTC
Location: Sydney

Re: 1158: "Rubber Sheet"

Postby gormster » Wed Jan 09, 2013 5:58 am UTC

Extra credit: If the bowling ball weighs 1000kg, and the sheet is an infinite plane of 10mm thick latex rubber, how high does the ball bounce?

Note: I'm not sure if surface tension is required here, but if it is, google it and make an assumption.

Ninja edit: I just realised - I don't think any of that matters. It bounces as high above the sheet as the rope pulled it down (ignoring the absorption of energy by the sheet itself).
Eddie Izzard wrote:And poetry! Poetry is a lot like music, only less notes and more words.

doinkisaac
Posts: 11
Joined: Thu Oct 14, 2010 12:17 am UTC

Re: 1158: "Rubber Sheet"

Postby doinkisaac » Wed Jan 09, 2013 6:21 am UTC

Quicksilver wrote:Looks kind of dangerous. Why a bowling ball?

Because that way you think it's going to be a physics joke. Joke probably wasn't the word I meant, but It's 1:20 in the morning, and I can't think of the actual word.

tblersch
Posts: 2
Joined: Fri Nov 30, 2012 4:14 pm UTC

Re: 1158: "Rubber Sheet"

Postby tblersch » Wed Jan 09, 2013 6:32 am UTC

Looks like a perfect explanation of dark energy to me. And you even use string theory to do it.

User avatar
creaothceann
Posts: 34
Joined: Fri Jan 26, 2007 9:44 am UTC
Location: Germany

Re: 1158: "Rubber Sheet"

Postby creaothceann » Wed Jan 09, 2013 7:23 am UTC

Randall wrote:It IS about physics. It ALL is.
Randall wrote:http://xkcd.com/435/

Mmmh...

User avatar
Red Hal
Magically Delicious
Posts: 1445
Joined: Wed Nov 28, 2007 2:42 pm UTC

Re: 1158: "Rubber Sheet"

Postby Red Hal » Wed Jan 09, 2013 7:28 am UTC

gormster wrote:Extra credit: If the bowling ball weighs 1000kg, and the sheet is an infinite plane of 10mm thick latex rubber, how high does the ball bounce?

Note: I'm not sure if surface tension is required here, but if it is, google it and make an assumption.

Ninja edit: I just realised - I don't think any of that matters. It bounces as high above the sheet as the rope pulled it down (ignoring the absorption of energy by the sheet itself).
Gotta disagree with you there. Try it with different types of rubber sheets at varying tensions to see why.
Lost Greatest Silent Baby X Y Z. "There is no one who loves pain itself, who seeks after it and wants to have it, simply because it is pain..."

User avatar
Dr What
Posts: 69
Joined: Wed Dec 26, 2012 6:43 am UTC

Re: 1158: "Rubber Sheet"

Postby Dr What » Wed Jan 09, 2013 7:51 am UTC

So... according to the 3rd and 4th pic, it must be about gravitational wave!

User avatar
J L
Posts: 242
Joined: Mon Jan 25, 2010 11:03 am UTC
Location: Germany
Contact:

Re: 1158: "Rubber Sheet"

Postby J L » Wed Jan 09, 2013 8:10 am UTC

He just invented anti-gravity, didn't he?

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1158: "Rubber Sheet"

Postby Kit. » Wed Jan 09, 2013 8:15 am UTC

If it's about physics, the landing WON'T be fun.

User avatar
alvinhochun
Posts: 54
Joined: Wed Nov 14, 2012 3:07 pm UTC

Re: 1158: "Rubber Sheet"

Postby alvinhochun » Wed Jan 09, 2013 8:24 am UTC

This comic seems like referring to xkcd What-If.
ANSWERING YOUR HYPOTHETICAL QUESTIONS WITH PHYSICS

User avatar
hwillis19
Posts: 13
Joined: Mon Oct 31, 2011 1:19 pm UTC
Location: Oxford, UK.

Re: 1158: "Rubber Sheet"

Postby hwillis19 » Wed Jan 09, 2013 8:55 am UTC

The rubber sheet is the classic model for explaining the concepts of gravitational potential, particularly of large objects like planets.

I certainly remember being taught it at school in the context of gravitational fields, many moons ago...

enwiki/Gravity_well

User avatar
Envelope Generator
Posts: 582
Joined: Sat Mar 03, 2012 8:07 am UTC
Location: pareidolia

Re: 1158: "Rubber Sheet"

Postby Envelope Generator » Wed Jan 09, 2013 9:09 am UTC

I will have none of this ballsheet.


(sad face)
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

eSOANEM wrote:If Fonzie's on the order of 100 zeptokelvin, I think he has bigger problems than difracting through doors.

User avatar
AvatarIII
Posts: 2098
Joined: Fri Apr 08, 2011 12:28 pm UTC
Location: W.Sussex, UK

Re: 1158: "Rubber Sheet"

Postby AvatarIII » Wed Jan 09, 2013 9:20 am UTC

This hypothetical always perplexed me, it's using the our ability to imagine the effects of gravity to describe how masses affect "space-time" to create gravity. so you need an understanding of one to comprehend the other.

How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda? it would be like describing blue to someone born blind.

User avatar
BAReFOOt
Posts: 179
Joined: Mon Jul 19, 2010 7:48 am UTC

Re: 1158: "Rubber Sheet"

Postby BAReFOOt » Wed Jan 09, 2013 9:32 am UTC

gormster wrote:Extra credit: If the bowling ball weighs 1000kg, and the sheet is an infinite plane of 10mm thick latex rubber, how high does the ball bounce?


It wouldn’t. The rubber sheet would rip under its own infinite weight and cause a two-dimensional big bang, while attracting the whole old universe into a giant black hole.

User avatar
BAReFOOt
Posts: 179
Joined: Mon Jul 19, 2010 7:48 am UTC

Re: 1158: "Rubber Sheet"

Postby BAReFOOt » Wed Jan 09, 2013 9:34 am UTC

AvatarIII wrote:How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda? it would be like describing blue to someone born blind.


Nonsense. You would describe it as everything pulling you into its direction at a strength depending on its mass (volume ⋅ density).

Kit.
Posts: 1117
Joined: Thu Jun 16, 2011 5:14 pm UTC

Re: 1158: "Rubber Sheet"

Postby Kit. » Wed Jan 09, 2013 9:55 am UTC

AvatarIII wrote:How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment,

Not the biggest problem, actually.

But how would you describe gravity fields to someone that was born, and will live and die in, say, Las Vegas?

leifbk
Posts: 33
Joined: Wed Nov 26, 2008 7:24 am UTC
Location: Bærum, Norway
Contact:

Re: 1158: "Rubber Sheet"

Postby leifbk » Wed Jan 09, 2013 10:00 am UTC

Quicksilver wrote:Alt Text: "It IS about physics. It ALL is."


Some of us also do stamp collecting.

hordriss
Posts: 25
Joined: Wed Dec 09, 2009 1:46 am UTC

Re: 1158: "Rubber Sheet"

Postby hordriss » Wed Jan 09, 2013 11:24 am UTC

To determine the height achieved:
First find the equilibrium point. The sheet is under tension due to the weight of the ball. Since our problem is cylindrically symmetical, the sheet can be modelled as a simple spring (F = -kx). The weight of the ball is easy to determine, given its mass; whether you use a constant acceleration g, or Newton's laws, or even Einstein's is up to you. The downwards displacement at which -kx = mg is the equilibrium point, x.
From here you can work out the energy required to pull the bowling ball down, (E = ½k(x+d)²-mgd), where d is the displacement from equilibrium, and x is the displacement at equilibrium. That energy will be transferred to the bowling ball upon the release of the rope. This energy, assuming elastic conditions, will be converted into Gravitational Potential Energy at the ball's maximum height.

(mgh = ½k(x+d)²-mgd), where x and d have already been decided. Solve for h, the maximum height above the flat surface.

uncleroy
Posts: 8
Joined: Wed Jan 09, 2013 12:22 pm UTC
Location: New York City

Re: 1158: "Rubber Sheet"

Postby uncleroy » Wed Jan 09, 2013 12:33 pm UTC

AvatarIII wrote:This hypothetical always perplexed me, it's using the our ability to imagine the effects of gravity to describe how masses affect "space-time" to create gravity. so you need an understanding of one to comprehend the other.

How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda? it would be like describing blue to someone born blind.


"And what's gravity? I forgot." The child was rubbing her eyes to stay awake. She struggled to understand but already knew she would miss the point yet another time.

"Gravity is the thing that holds the universe together. The glue, or the rivets. It pulls everything toward everything else, and it takes energy to fight it and overcome it. It feels like when we boost the ship, remember I pointed that out to you?"

"Like when everything wants to move in the same direction?"

"That's right. So we have to be careful, because we don't think about it much. We have to worry about where things are because when we boost, everything will head for the stern. People on planets have to worry about that all the time. They have to put something strong between themselves and the center of the planet, or they'll go down."


From "Lollipop and the Tar Baby" by John Varley.

Thanks for making me (a) register and (b) find my copy of The Norton Book of Science Fiction.

User avatar
cellocgw
Posts: 2067
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: 1158: "Rubber Sheet"

Postby cellocgw » Wed Jan 09, 2013 1:24 pm UTC

AvatarIII wrote:This hypothetical always perplexed me, it's using the our ability to imagine the effects of gravity to describe how masses affect "space-time" to create gravity. so you need an understanding of one to comprehend the other.

How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda? it would be like describing blue to someone born blind.

There is no such thing as zero-G. There's micro-G, but the gravity due to masses within the ship are measurable. Besides which, it's easy enough to rig up a centrifuge or something and stick said person into it.
resume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

User avatar
cellocgw
Posts: 2067
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: 1158: "Rubber Sheet"

Postby cellocgw » Wed Jan 09, 2013 1:27 pm UTC

hordriss wrote:To determine the height achieved:
First find the equilibrium point. The sheet is under tension due to the weight of the ball. Since our problem is cylindrically symmetical, the sheet can be modelled as a simple spring (F = -kx). The weight of the ball is easy to determine, given its mass; whether you use a constant acceleration g, or Newton's laws, or even Einstein's is up to you. The downwards displacement at which -kx = mg is the equilibrium point, x.
From here you can work out the energy required to pull the bowling ball down, (E = ½k(x+d)²-mgd), where d is the displacement from equilibrium, and x is the displacement at equilibrium. That energy will be transferred to the bowling ball upon the release of the rope. This energy, assuming elastic conditions, will be converted into Gravitational Potential Energy at the ball's maximum height.

(mgh = ½k(x+d)²-mgd), where x and d have already been decided. Solve for h, the maximum height above the flat surface.


Let's make it more difficult. Assume the entire setup is in a zero-G (haha contradicted my other post) environment, so the ball doesn't apply tension to the sheet. You pull on the string, and then release. Since the setup is also in a vacuum, the rubber sheet is under-damped and shoots upwards, hitting the ball. How much of the original tension (aka potential energy in the sheet) is transferred to the ball?
resume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

User avatar
Dr What
Posts: 69
Joined: Wed Dec 26, 2012 6:43 am UTC

Re: 1158: "Rubber Sheet"

Postby Dr What » Wed Jan 09, 2013 1:57 pm UTC

hordriss wrote:Since our problem is cylindrically symmetical, the sheet can be modelled as a simple spring (F = -kx).

Why? It's not correct. It's stretching the center of the sheet, so it's different. If you stretch in the middle of a spring in a direction perpendicular to the spring, it's not Hook's law. And this one is 2D problem with a force on the 3rd dimension.
So it's more complicated, but I think if we know the Young's modulus it's still solvable.

User avatar
orthogon
Posts: 3103
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1158: "Rubber Sheet"

Postby orthogon » Wed Jan 09, 2013 2:33 pm UTC

Dr What wrote:
hordriss wrote:Since our problem is cylindrically symmetical, the sheet can be modelled as a simple spring (F = -kx).

Why? It's not correct. It's stretching the center of the sheet, so it's different. If you stretch in the middle of a spring in a direction perpendicular to the spring, it's not Hook's law. And this one is 2D problem with a force on the 3rd dimension.
So it's more complicated, but I think if we know the Young's modulus it's still solvable.

If it's infinite in extent, then won't the finite downwards displacement correspond to zero strain (proportional extension) and hence zero tension in the sheet, and zero upwards force?

In fact, it seems to me to be a triple zero, since (1) the downwards movement will cause no change in the distance from the anchor point (because of the squaw on the hippopotamus) (2) any finite increase in extension is an infinitesimal proportion of the natural length, i.e. zero strain, and (3) The sheet will still be horizontal, so the vertical component of any tension is zero.

[Edit]: on re-reading I see that hordriss wasn't specifically addressing the infinite sheet.
xtifr wrote:... and orthogon merely sounds undecided.

Vroomfundel
Posts: 118
Joined: Wed Sep 29, 2010 7:36 am UTC

Re: 1158: "Rubber Sheet"

Postby Vroomfundel » Wed Jan 09, 2013 2:49 pm UTC

AvatarIII wrote:This hypothetical always perplexed me, it's using the our ability to imagine the effects of gravity to describe how masses affect "space-time" to create gravity. so you need an understanding of one to comprehend the other.

How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda? it would be like describing blue to someone born blind.


This reminds me of the famous Feynman lectures:
http://www.youtube.com/watch?v=wMFPe-DwULM

He uses the same argument to bash the flexible sheet visualization of gravity - you can't use gravity to illustrate gravity, he says, and he's right. But he uses the "linked together with a rubber band" to illustrate attraction at the sub-atomic level, when the same forces underlies the same elastic effects we observe with rubber bands. My point is, you can't visualize elementary physics concepts with everyday phenomena without committing this sin, because everything in our world is caused by the same fundamental concepts.
lexicum.net - my vocabulary learning platform

Barstro
Posts: 103
Joined: Mon Aug 13, 2012 2:34 pm UTC

Re: 1158: "Rubber Sheet"

Postby Barstro » Wed Jan 09, 2013 3:00 pm UTC

AvatarIII wrote:This hypothetical always perplexed me, it's using the our ability to imagine the effects of gravity to describe how masses affect "space-time" to create gravity. so you need an understanding of one to comprehend the other.


Is that not the process of learning? In this case, you are might not fully understand the rules behind it, but can at least observe the effects, in order to comprehend a greater abstract theory.

I am reminded of a person who was asked what it was like to be shot while wearing a bullet proof vest. I'm sure most of here have not been so shot, and have no actual idea what it is like. The person asked responded "it's like being hit in the chest with a sledgehammer". Now, I don't think anyone here has been hit in the chest with a sledgehammer either, so that shouldn't be imparting new information, but I find that concept easier to grasp, and can imagine what it is like.

AvatarIII wrote:How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment, such as someone cruising in a generation ship halfway to Andromeda?


Just take them to the revolving room and explain it with centrifugal force.

AvatarIII wrote: it would be like describing blue to someone born blind.


Green, with less yellow in it. :wink:
I think Hellen Keller had worked out a long list of adjectives to describe colors

User avatar
jc
Posts: 356
Joined: Fri May 04, 2007 5:48 pm UTC
Location: Waltham, Massachusetts, USA, Earth, Solar System, Milky Way Galaxy
Contact:

Re: 1158: "Rubber Sheet"

Postby jc » Wed Jan 09, 2013 3:09 pm UTC

gormster wrote:Extra credit: If the bowling ball weighs 1000kg, and the sheet is an infinite plane of 10mm thick latex rubber, how high does the ball bounce?
...
It bounces as high above the sheet as the rope pulled it down (ignoring the absorption of energy by the sheet itself).


Nah; if that were true, you could pull it down 1 mm, release it, and it would bounce up above the sheet to the distance it was hanging below the sheet, plus 1 mm. Somehow I suspect it wouldn't quite do that.

User avatar
Kratos Aurion
Posts: 4
Joined: Sun Aug 30, 2009 3:31 am UTC
Contact:

Re: 1158: "Rubber Sheet"

Postby Kratos Aurion » Wed Jan 09, 2013 3:35 pm UTC

I was trolled, and then un-trolled.

Thanks, Randall.

nlitchfield
Posts: 16
Joined: Mon Mar 07, 2011 1:25 pm UTC

Re: 1158: "Rubber Sheet"

Postby nlitchfield » Wed Jan 09, 2013 3:57 pm UTC

creaothceann wrote:
Randall wrote:It IS about physics. It ALL is.
Randall wrote:http://xkcd.com/435/

Mmmh...


I've always been annoyed by that one partly because it's missing the mathematics is just applied philosophy part, but mostly because it's a surprising demonstration of ignorance and reductionism for this comic.

TrueNarnian
Posts: 48
Joined: Wed Oct 26, 2011 8:49 pm UTC

Re: 1158: "Rubber Sheet"

Postby TrueNarnian » Wed Jan 09, 2013 4:02 pm UTC

I've often wondered about this. If you could somehow get a large enough mass to instantly disappear (possibly by splitting into a teardrop universe) would it cause surrounding matter to fly off the fabric of space-time?

User avatar
keithl
Posts: 662
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: 1158: "Rubber Sheet"

Postby keithl » Wed Jan 09, 2013 5:52 pm UTC

gormster wrote:Extra credit: If the bowling ball weighs 1000kg, and the sheet is an infinite plane of 10mm thick latex rubber, how high does the ball bounce?
...
Ninja edit: I just realised - I don't think any of that matters. It bounces as high above the sheet as the rope pulled it down (ignoring the absorption of energy by the sheet itself).


Nope. The sheet has mass which moves with the rising ball, so it takes some of the kinetic energy. Latex has a modulus of 1MPa, and a density of 1000kg/m3, so the longitudinal speed of propagation, sqrt(modulus/density), is 31 m/s. The transverse propagation, sqrt( tension/density), is much slower. That means that a small fraction of the stored elastic energy will reach the bowling ball during its launch. The ball will probably not lose contact with the sheet. I'd love to see a good finite element model of this.

Frankly, it sounds like a good way to get crushed between the ball and the sheet.

BTW, if it is a huge round sheet, with two dimensional symmetry, the displacement is proportional to the logarithm of the sheet diameter S divided by the ball diameter D. log(S/D). If the sheet diameter S is infinite, the logarithm is infinite. That is, put a force on it and it will just keep displacing, probably proportional to log(time). Infinite anything tends to do wonky things mathematically.

Trampolines do not use rubber sheets. They use stiffer materials under much higher tension, and connect to a rigid frame with springs. That confines the elastic energy to a small, low-mass region.

The rubber sheet gravity model may claim to help 3rd graders understand gravity and the warping of space, but it is useless for accurate calculation. I can see why Feynmann disparaged it, given the time he spent knocking it out of undergraduate heads.

User avatar
Wnderer
Posts: 640
Joined: Wed Feb 03, 2010 9:10 pm UTC

Re: 1158: "Rubber Sheet"

Postby Wnderer » Wed Jan 09, 2013 5:54 pm UTC

TrueNarnian wrote:I've often wondered about this. If you could somehow get a large enough mass to instantly disappear (possibly by splitting into a teardrop universe) would it cause surrounding matter to fly off the fabric of space-time?


I don't think so. I think a better analogy is that the bowling ball is glued to the trampoline. So when the giant mass breaks off, the fabric of space would bounce around with the gravity waves generated and the matter in space would bounce along on the waves.

User avatar
orthogon
Posts: 3103
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1158: "Rubber Sheet"

Postby orthogon » Wed Jan 09, 2013 6:04 pm UTC

Why is he asking her to imagine a ball on a rubber sheet, when he is at that very moment standing on such a ball on such a sheet? Or are we seeing the image in her mind's eye, and she has inserted beret guy into her mental picture? And then he says "imagining is fun" - is that then his imagination? Or is she imagining him saying it? Or is he saying it in real life but projected into her imagining of it?

And would the sheet really deform in that curve? I'm having doubts about my infinite-sheet claims now. What I said was true of two dimensions, i.e. a rubber band, where the band would be piecewise straight either side of the ball. But on a 2D surface I'm less sure. Maybe most of the deformation is indeed local. I fear Bessel functions will come into it. I'm this close to googling it.
xtifr wrote:... and orthogon merely sounds undecided.

User avatar
orthogon
Posts: 3103
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1158: "Rubber Sheet"

Postby orthogon » Wed Jan 09, 2013 6:16 pm UTC

keithl wrote:BTW, if it is a huge round sheet, with two dimensional symmetry, the displacement is proportional to the logarithm of the sheet diameter S divided by the ball diameter D. log(S/D). If the sheet diameter S is infinite, the logarithm is infinite. That is, put a force on it and it will just keep displacing, probably proportional to log(time). Infinite anything tends to do wonky things mathematically.

Is that assuming constant density of the ball? Where does the weight come in?
keithl wrote:Trampolines do not use rubber sheets. They use stiffer materials under much higher tension, and connect to a rigid frame with springs. That confines the elastic energy to a small, low-mass region.

So the force is mainly caused by some of the the almost-constant tension getting resolved into the vertical direction by the displacement, and the stretching of the material is second-order?
keithl wrote:The rubber sheet gravity model may claim to help 3rd graders understand gravity and the warping of space, but it is useless for accurate calculation. I can see why Feynmann disparaged it, given the time he spent knocking it out of undergraduate heads.

You do General Relativity in 3rd grade? Wow.
xtifr wrote:... and orthogon merely sounds undecided.

User avatar
Coyne
Posts: 1110
Joined: Fri Dec 18, 2009 12:07 am UTC
Location: Orlando, Florida
Contact:

Re: 1158: "Rubber Sheet"

Postby Coyne » Wed Jan 09, 2013 6:27 pm UTC

Alt Text wrote:It IS about physics. It ALL is.


No, it isn't. It's ALL about math.

Physics is so impure.
In all fairness...

User avatar
keithl
Posts: 662
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: 1158: "Rubber Sheet"

Postby keithl » Wed Jan 09, 2013 6:40 pm UTC

keithl wrote:BTW, if it is a huge round sheet, with two dimensional symmetry, the displacement is proportional to the logarithm of the sheet diameter S divided by the ball diameter D. log(S/D). If the sheet diameter S is infinite, the logarithm is infinite. That is, put a force on it and it will just keep displacing, probably proportional to log(time).
orthogon wrote:Is that assuming constant density of the ball? Where does the weight come in?

Also proportional to the ball weight, for small displacements. For big displacements, nonlinear, a workout for Mr. Computer, like most things. "Proportional to" meaning "one of many factors in a big hairy approximate equation, sorta."
keithl wrote:Trampolines do not use rubber sheets. They use stiffer materials under much higher tension, and connect to a rigid frame with springs. That confines the elastic energy to a small, low-mass region.
orthogon wrote:So the force is mainly caused by some of the the almost-constant tension getting resolved into the vertical direction by the displacement, and the stretching of the material is second-order?

Of course, a trampoline does need some displacement, and the stretch does store the energy elastically. If it is too stiff, the bounce will be too quick and the gee forces too high. But you are spot on about how the force is resolved.
keithl wrote:The rubber sheet gravity model may claim to help 3rd graders understand gravity and the warping of space, but it is useless for accurate calculation. I can see why Feynmann disparaged it, given the time he spent knocking it out of undergraduate heads.
orthogon wrote:You do General Relativity in 3rd grade? Wow.

Nope. But back in the day, we did have Disney movies purporting to popularize science, with Werner von Braun taking time off from running slaves at Nordhausen Mittelwerk to tell us about moon rockets and outer space.

User avatar
mathmannix
Posts: 1453
Joined: Fri Jul 06, 2012 2:12 pm UTC
Location: Washington, DC

Re: 1158: "Rubber Sheet"

Postby mathmannix » Wed Jan 09, 2013 7:03 pm UTC

Kit. wrote:
AvatarIII wrote:How would you describe gravity fields to someone that was born, and will live and die in a zero-G environment,

Not the biggest problem, actually.

But how would you describe gravity fields to someone that was born, and will live and die in, say, Las Vegas?


If we accept axiomatically that "what happens in Vegas, stays in Vegas", then clearly nothing can escape the gravity well of Vegas.

Therein lies, no sheet.

The force is very strong with that place.
I hear velociraptor tastes like chicken.

User avatar
ysth
Posts: 183
Joined: Wed Apr 11, 2007 7:21 pm UTC

Re: 1158: "Rubber Sheet"

Postby ysth » Wed Jan 09, 2013 7:28 pm UTC

Radical!

(I mistook the beret for a crown at first.)
A math joke: r = | |csc(θ)|+|sec(θ)| |-| |csc(θ)|-|sec(θ)| |

User avatar
mathmannix
Posts: 1453
Joined: Fri Jul 06, 2012 2:12 pm UTC
Location: Washington, DC

Re: 1158: "Rubber Sheet"

Postby mathmannix » Wed Jan 09, 2013 7:32 pm UTC

ysth wrote:Radical!


Well, Beret Guy is often irrational...
I hear velociraptor tastes like chicken.


Return to “Individual XKCD Comic Threads”

Who is online

Users browsing this forum: FOARP and 103 guests