I saw this in EE Times back in 1991 and could not believe my eyes. So I and several other engineers wasted an afternoon building it. To our surprise, it WORKED.
Problem:
You are given an ordinary can of soda (355 ml ; 12 oz), 100 feet of ordinary string, and 100 rubber bands. The red ones that wrap a newspaper.
Use a combination of rubber bands and strings to hang the can of soda from the ceiling. At equilibrium the can is X inches above the floor. Now cut one of the strings, you choose the string to cut. When you cut this string the can of soda RISES. Now at equilibrium it is (X+1) inches above the floor.
Devise a arrangement of rubber bands and strings which produces the behavior described above.
It can be done and it is not any sort of clever trickery or weird contrivance. Rubber bands and strings connected with ordinary knots. A can of soda pop. And ingenuity. Enjoy!
new material added 12 Dec 2016:
This was first described in the (quite prestigious) journal Nature , please see Figure 1:
Problem:
You are given an ordinary can of soda (355 ml ; 12 oz), 100 feet of ordinary string, and 100 rubber bands. The red ones that wrap a newspaper.
Use a combination of rubber bands and strings to hang the can of soda from the ceiling. At equilibrium the can is X inches above the floor. Now cut one of the strings, you choose the string to cut. When you cut this string the can of soda RISES. Now at equilibrium it is (X+1) inches above the floor.
Devise a arrangement of rubber bands and strings which produces the behavior described above.
It can be done and it is not any sort of clever trickery or weird contrivance. Rubber bands and strings connected with ordinary knots. A can of soda pop. And ingenuity. Enjoy!
new material added 12 Dec 2016:
This was first described in the (quite prestigious) journal Nature , please see Figure 1:
Joel Cohen and Paul Horowitz, "Paradoxical behavior of mechanical and electrical networks," Nature, Vol. 352, pp. 699-701, 22 August 1991. (link to paper)
If you think you recognize the 2nd author's name, you are right. He is the lead author of a famous book, The Art Of Electronics (amazon link)
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Is one end of each rubber band/string combination connected to the ceiling and the other end to the can in a nominally vertical arrangement?
So the strings and rubber bands are tied together? Or are there a number of each separately supporting the soda? I ask because you direct to cut a 'string', not a combo.
Tie the rubber bands to the bottom of the can.
Tie the string to the top of the can.
Pop the top of the can.
When you cut the string, the can inverts and empties.
John
Tie the string to the top of the can.
Pop the top of the can.
When you cut the string, the can inverts and empties.
John
Series a bunch of bands, twice.
attach each series a few feet apart at the ceiling, but together at the can.
Use the string to stretch the top rubber band in each string really tight. the can weight on the horizontal stretch will be very high, it will be pulled down quite a bit.
Cut the string, and it will go up because the system reverts to half weight on each top string.
Well, that's my thinking anywhoo..
John
ps..but I like my first idea better. Granted, it's messier.
attach each series a few feet apart at the ceiling, but together at the can.
Use the string to stretch the top rubber band in each string really tight. the can weight on the horizontal stretch will be very high, it will be pulled down quite a bit.
Cut the string, and it will go up because the system reverts to half weight on each top string.
Well, that's my thinking anywhoo..
John
ps..but I like my first idea better. Granted, it's messier.
Loop the rubber bands to support the can 2" above the floor. Attach the string to the can. Holding the sting above the can play out enough string so that it just can be attached to the ceiling but is not providing any support to the can. This is actually adding weight to be supported by the rubber bands. If you cut the string at the bottom the cans will rise. If you cut the string at the top it will fall to the floor and the rubber bands will now only be supporting the weight of a few inches of string.
Yes. "Can of Soda" has nothing to do with the solution; consider it a point-mass. Or better yet, a plumb-bob that attaches to a string at exactly one point. The apparatus connects to the ceiling at exactly one place and connects to the weight at exactly one place. The apparatus is vertical; the weight is directly beneath the ceiling attachment point.
Yes.
There is one attach point on the ceiling and there is one attach point on the weight. In between are a number of strings and rubber bands, tied together in some clever configuration devised by you. The weight hangs directly below the ceiling attach point.
If you find it useful you can of course tie several rubber bands "in series" to make a longer and stretchier rubber band. Similarly you can of course tie several rubber bands "in parallel" to make a stiffer rubber band that stretches less far when a force is applied. And you can have a mixture of both strings and rubber bands in your "series" and "parallel" networks, arranged howsoever you wish, if you find it useful.
I seem to recall the solution involved switching from some series combination to some parallel combination, but I can't quite come up with the actual arrangement.
Two long series of bands. Use a length of string, tie it to one series, loop it through a loop at the weight like a pulley, tie it to the second series.
At rest, each series holds half the weight.
Now, tie a second string to the weight, but take this string and tie it a little bit up one series, taught so that all the weight is supported by one band set. The vertical deflection will be more because all the weight is supported by only one set.
When you cut the string, the setup will again distribute half the weight to each series, and the weight will go up.
John
At rest, each series holds half the weight.
Now, tie a second string to the weight, but take this string and tie it a little bit up one series, taught so that all the weight is supported by one band set. The vertical deflection will be more because all the weight is supported by only one set.
When you cut the string, the setup will again distribute half the weight to each series, and the weight will go up.
John
🙂 It's just now finally occurring to me we're being challenged with this. I thought I wasn't grasping the solution you were supposedly presenting.
Oh, why not just make it easy for us? I challenge you. 🙂
Some diyAudio members only access the site once a week. I suspect that a good sized fraction of them access the site on the week-end only. Therefore I have no plans to reveal "the correct answer" before Tuesday or Wednesday at the earliest; I don't want to ruin the fun, the joy-of-discovery, of those members, prematurely. If my decision chaps your hide I recommend you initiate formal proceedings to have me thrown out. Banned. Discarded, shunned, and shamed. It might make your heart glad.
If you are able to access the archives of EE Times 1991 you could perhaps seek out the name of the scientific conference at which this result was first published. (EE Times merely reported the newsworthy papers from that conference -- I guarantee that the authors did not publish in EE Times first!). Then you can read the actual paper, in a refereed journal, containing the actual problem statement and the actual proposed solution. Your curiosity will be satisfied right away: just in case I get run over by a bus this weekend and fail to type up "the correct answer" next week. It's an option you can consider.
If you are able to access the archives of EE Times 1991 you could perhaps seek out the name of the scientific conference at which this result was first published. (EE Times merely reported the newsworthy papers from that conference -- I guarantee that the authors did not publish in EE Times first!). Then you can read the actual paper, in a refereed journal, containing the actual problem statement and the actual proposed solution. Your curiosity will be satisfied right away: just in case I get run over by a bus this weekend and fail to type up "the correct answer" next week. It's an option you can consider.
Thinking dumb:
100 *feet* of string is significant mass. And suspiciously excessive for any ceiling I want to hang from. Rig your 7 feet of string and rubber-bands from ceiling to can. Wrap-up and tie your 93 feet of leftover string down there. Measure X. Cut-off the 97 feet added string. For some values of elasticity and string weight, the new height is X+1.
100 *feet* of string is significant mass. And suspiciously excessive for any ceiling I want to hang from. Rig your 7 feet of string and rubber-bands from ceiling to can. Wrap-up and tie your 93 feet of leftover string down there. Measure X. Cut-off the 97 feet added string. For some values of elasticity and string weight, the new height is X+1.
EE Times was reporting on a paper published in a Very Prestigious refereed journal, which reported a paradox: cut a string and the weight rises.
Do you suppose such a journal would publish a paper which reported: "Suspend two masses M1 + M2 beneath a spring. Remove M1. M2 rises. It's a paradox!"
Do you suppose such a journal would publish a paper which reported: "Suspend two masses M1 + M2 beneath a spring. Remove M1. M2 rises. It's a paradox!"
As I see it there are two basic methods. The first and simplest is the loss of weight method. For a typical room with an 8' ceiling rounding that to 100" for a 1" rise you would want to loose 1% of the 12 oz weight. Just the length of string can to ceiling would weight that much so that is a simple solution. And as Mark says way to simple to be interesting.
The other solution is to increase the spring tension of the suspension. This would involve as one method using two springs attached to the can one of single looped bands and the other of dual or even triple bands.
The issue then is how to transfer the load to a shorter stiffer spring. Two approaches appear to me. When the load is on the weaker spring if you disconnect the weaker spring the can will intially bounce down and then up oscillating nicely until it reaches equilibrium. If there is a ratchet mechanism on the stiffer spring to catch the can at the peak of the swing it will end up higher.
So a simple catch hook to a stiffer spring, a piece of string, a cat's paw tube, etc.would work.
And that brings up the last approach. Weaving a cat's paw as the second spring. So cutting the string actually increases the springs pull.
Cat's paw AKA Chinese finger puzzle.
But the answer Mark wants is none of these. It is converting series springs to parallel springs.
The other solution is to increase the spring tension of the suspension. This would involve as one method using two springs attached to the can one of single looped bands and the other of dual or even triple bands.
The issue then is how to transfer the load to a shorter stiffer spring. Two approaches appear to me. When the load is on the weaker spring if you disconnect the weaker spring the can will intially bounce down and then up oscillating nicely until it reaches equilibrium. If there is a ratchet mechanism on the stiffer spring to catch the can at the peak of the swing it will end up higher.
So a simple catch hook to a stiffer spring, a piece of string, a cat's paw tube, etc.would work.
And that brings up the last approach. Weaving a cat's paw as the second spring. So cutting the string actually increases the springs pull.
Cat's paw AKA Chinese finger puzzle.
But the answer Mark wants is none of these. It is converting series springs to parallel springs.
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I remember this problem as an analogy to another problem. In a network of roads the traffic jam problem increases when one more road is added between 2 intersections.
Yes it's called Braess' Paradox and Wikipedia has an article about it, including some real world examples. Closing a road improved traffic flow.
On my daily commute frequent rock slides had the local traffic engineers reduce a four lane road to a two lane road. Traffic flow improved. So it is now one automotive lane in each direction. Same for the bicycle lanes and a paved lane with signage stating it is a rock slide zone, just in case the debri doesn't give you the hint.
Only issue was after a snow storm and some folks decided all the other folks were wrong and they could still use a passing lane. Fortunately they figured out someone coming head on with a blaring horn..
Thank you for the game!
Sorry for the quality, I have only a back of a receipt to draw on. "Fuses" are rubber bands, lines are strings. Everything are in line, I just drew them in angle to easy to see.
After cutting all forces will be G/3, so left bands become less tense, shorter. Due to stiffness of crossing strings this shortening directly arises on the hanging mass.
Sorry for the quality, I have only a back of a receipt to draw on. "Fuses" are rubber bands, lines are strings. Everything are in line, I just drew them in angle to easy to see.
After cutting all forces will be G/3, so left bands become less tense, shorter. Due to stiffness of crossing strings this shortening directly arises on the hanging mass.
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