Straw power

A forum for good logic/math puzzles.

Moderators: jestingrabbit, Moderators General, Prelates

davidogilvy
Posts: 3
Joined: Thu Sep 23, 2010 2:19 am UTC

Straw power

Postby davidogilvy » Thu Sep 23, 2010 2:23 am UTC

A heavy 300 kg sandbag one metre tall is hung from a playground swing with a rope 3 metres long so that the bottom of the sandbag just clears the ground. A bottle is then placed on the ground a metre away from the sandbag.

Explain how to to knock the bottle over with the sandbag if you are given a paper drinking straw but are not allowed to touch anything (sandbag, rope, bottle, swing) with your body or with the straw.

Edit:
Spoiler:
Just as a side note to all question askers, I do not in fact know the answer to this riddle. I found this riddle whilst stumbling the internet amongst a bunch of other more common riddles. The page did not include answers. I specifically created this account to question the Logicians on the XKCD forum. I knew from past experience on a previous long forgotten account that they were very smart, and quite frankly this question stumped me. I was hoping some intelligent mind would be able to come up with a satisfying answer.

I would post a link to the site but I have not hit 5 posts.

For a hint, the site advertises itself as a website for physics specific logic puzzles i.e. a sound knowledge in physics was needed for most of the other puzzles
Last edited by davidogilvy on Thu Sep 23, 2010 2:32 pm UTC, edited 1 time in total.

HonoreDB
Posts: 161
Joined: Tue Feb 06, 2007 4:32 pm UTC
Contact:

Re: Straw power

Postby HonoreDB » Thu Sep 23, 2010 5:51 am UTC

Getting the silly solutions out of the way, just in case:

Spoiler:
*Kick the sandbag at the bottle while wearing shoes. Shoes aren't your body.
*Or, in general, use something in the environment other than the straw as an intermediary between you and the sandbag.
* Drink Daniel Plainview's milkshake, enraging him, then bait him into charging right at you, then sidestep so he hits the sandbag instead.
* Blow through the straw at the sandbag or the swing to set it gently rocking, then continue at the appropriate moments to (achingly gradually) increase its amplitude.


Serious question:

Spoiler:
Does it matter what the swing is hanging from?

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Thu Sep 23, 2010 6:14 am UTC

I think this is the correct solution:

Spoiler:
First you must determine why the sandbag is hanging. If it is attempting suicide, this method may not work, as depressed sandbags are known to be very unresponsive. However, if the sandbag is merely having fun, you have a good chance. In this case, you must befriend the sandbag, as sandbags are known to be shy and won't want to help you if they don't know you. The straw is helpful here as a conversation-starter and is capable of making interesting noises with some effort. Once the sandbag has become more comfortable with your presence, you can get it excited by gently blowing on it through the straw. Sandbags like this. Once the sandbag is willing to help you, suggest that it come down from the rope so the two of you can knock over the bottle. If all goes well, it will agree and you can then knock over the bottle together with the sandbag, and you will have a new lifelong friend.

It is not a problem that you are not allowed to touch the sandbag, as they do not like being touched anyway.

davidogilvy
Posts: 3
Joined: Thu Sep 23, 2010 2:19 am UTC

Re: Straw power

Postby davidogilvy » Thu Sep 23, 2010 2:40 pm UTC

@ Eebster
Eebster the Great wrote:I think this is the correct solution:

Spoiler:
First you must determine why the sandbag is hanging. If it is attempting suicide, this method may not work, as depressed sandbags are known to be very unresponsive. However, if the sandbag is merely having fun, you have a good chance. In this case, you must befriend the sandbag, as sandbags are known to be shy and won't want to help you if they don't know you. The straw is helpful here as a conversation-starter and is capable of making interesting noises with some effort. Once the sandbag has become more comfortable with your presence, you can get it excited by gently blowing on it through the straw. Sandbags like this. Once the sandbag is willing to help you, suggest that it come down from the rope so the two of you can knock over the bottle. If all goes well, it will agree and you can then knock over the bottle together with the sandbag, and you will have a new lifelong friend.

It is not a problem that you are not allowed to touch the sandbag, as they do not like being touched anyway.


Please read my edited post.
For an effort toward a suitable solution however:
Spoiler:
Let us assume wording errors such as "body" instead of "shoe and body" do not count. For exciting a sort of resonate frequency through strategic puffs, I grant that is possible. However the problem states "300kg sand bag" hinting to me at least that such a method would be discouraged.

Let us assume that it does not matter that it is a swing, for easier solving purposes.


@Honore
You made me laugh. I was drinking when I read that post and milk shot out of my nose.
However
Spoiler:
I believe the correct solution should work on all sandbags regardless of emotional depression. Your restrictions on aspects of the puzzle make your answer invalid.

User avatar
SlyReaper
inflatable
Posts: 8015
Joined: Mon Dec 31, 2007 11:09 pm UTC
Location: Bristol, Old Blighty

Re: Straw power

Postby SlyReaper » Thu Sep 23, 2010 2:46 pm UTC

Spoiler:
Blow the sandbag. That will displace it a small amount. After it swigs back, blow it again and it will move a little further. Do this long enough, and the sandbag will eventually be swinging in huge arcs. No need for the straw at all.
Image
What would Baron Harkonnen do?

Moose Hole
Posts: 398
Joined: Fri Jul 09, 2010 1:34 pm UTC

Re: Straw power

Postby Moose Hole » Thu Sep 23, 2010 4:57 pm UTC

SlyReaper wrote:
Spoiler:
Blow the sandbag.
I would but my wife would get jealous.

Czhorat
Posts: 365
Joined: Fri Aug 14, 2009 12:28 pm UTC

Re: Straw power

Postby Czhorat » Fri Sep 24, 2010 1:00 pm UTC

How tall is the bottle? And can someone with more time than I have calculate how high the silly thing will be at 1m? It might be a trick question in that you'd clear the bottle in the first place.

User avatar
jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: Straw power

Postby jestingrabbit » Fri Sep 24, 2010 1:19 pm UTC

Czhorat wrote:How tall is the bottle? And can someone with more time than I have calculate how high the silly thing will be at 1m? It might be a trick question in that you'd clear the bottle in the first place.


Yeah, this was a thought I had too. The answer is it'll be at [imath]3-\sqrt{3^2-1^2} = 0.171572875[/imath] metres, or between 6 and 7 inches. There are lots of bottles that the sand bag would hit.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

User avatar
Cosmologicon
Posts: 1806
Joined: Sat Nov 25, 2006 9:47 am UTC
Location: Cambridge MA USA
Contact:

Re: Straw power

Postby Cosmologicon » Fri Sep 24, 2010 2:38 pm UTC

Right, but I think the bottom of the sandbag is actually 4m from the bar, since the bag itself is 1m tall. In that case, the bottle only needs to be 12.7cm = 5.00 inches high.

User avatar
jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: Straw power

Postby jestingrabbit » Fri Sep 24, 2010 3:12 pm UTC

Cosmologicon wrote:Right, but I think the bottom of the sandbag is actually 4m from the bar, since the bag itself is 1m tall. In that case, the bottle only needs to be 12.7cm = 5.00 inches high.


Yeah, sorry. The conclusion is a little stronger: the sandbag will definitely hit a reasonable bottle.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

redrogue
Posts: 116
Joined: Tue Dec 15, 2009 9:17 pm UTC

Re: Straw power

Postby redrogue » Fri Sep 24, 2010 3:29 pm UTC

Right, but air friction would certainly be an issue here. Blowing (straw or not) wouldn't be enough to get it started. The friction between the bag and the air would pretty much negate any effect from the tiny amout of air you can put forward... and if the bag was frictionless it wouldn't EVER go anywhere.

Since you have to knock the bottle over with the sandbag, your best bet is to...
Spoiler:
...ignore the straw. It's a red herring.

I'd use Bournoulli's principle.

Whip off your shirt. Bonus points IFF you are female and you are hot. Put your ams inside the shirt and spread them to form a sail. Wave your sail back and forth quickly in FRONT of the bag (between the bag and the bottle) to decrease air pressure there. Bournoulli's principle will cause the bag to move towards you slightly. Stop, let it swing back, repeat. You'll get it eventually.
Is 'no' your answer to this question?

User avatar
SlyReaper
inflatable
Posts: 8015
Joined: Mon Dec 31, 2007 11:09 pm UTC
Location: Bristol, Old Blighty

Re: Straw power

Postby SlyReaper » Sat Sep 25, 2010 12:06 am UTC

redrogue wrote:Right, but air friction would certainly be an issue here. Blowing (straw or not) wouldn't be enough to get it started. The friction between the bag and the air would pretty much negate any effect from the tiny amout of air you can put forward... and if the bag was frictionless it wouldn't EVER go anywhere.


Wrong. Friction is a function of velocity, and for the very low velocities you get when you're just getting it going, the friction is practically nill.
Image
What would Baron Harkonnen do?

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Sat Sep 25, 2010 6:05 am UTC

SlyReaper wrote:
redrogue wrote:Right, but air friction would certainly be an issue here. Blowing (straw or not) wouldn't be enough to get it started. The friction between the bag and the air would pretty much negate any effect from the tiny amout of air you can put forward... and if the bag was frictionless it wouldn't EVER go anywhere.


Wrong. Friction is a function of velocity, and for the very low velocities you get when you're just getting it going, the friction is practically nill.


Air resistance is a function of velocity, but it is not zero at zero velocity.

User avatar
BoomFrog
Posts: 1069
Joined: Mon Jan 15, 2007 5:59 am UTC
Location: Seattle

Re: Straw power

Postby BoomFrog » Sat Sep 25, 2010 10:14 am UTC

Eebster the Great wrote:Air resistance is a function of velocity, but it is not zero at zero velocity.

Umm... isn't it?

I think that HonoreDB's 4th silly answer (repeated by SlyReaper) is the intended solution. There's really nothing else you can do.
"Everything I need to know about parenting I learned from cooking. Don't be afraid to experiment, and eat your mistakes." - Cronos

User avatar
Cosmologicon
Posts: 1806
Joined: Sat Nov 25, 2006 9:47 am UTC
Location: Cambridge MA USA
Contact:

Re: Straw power

Postby Cosmologicon » Sat Sep 25, 2010 1:43 pm UTC

I get that air resistance is going to be on the order of 0.1N at maximum. That's not trivial, when you integrate over the back and forth of the swing. I have no idea whether it's possible to overcome that with just your breath. Could be. I can't think of an easy way to estimate the impulse you'd impart to a sandbag by blowing on it.

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Sat Sep 25, 2010 8:55 pm UTC

BoomFrog wrote:
Eebster the Great wrote:Air resistance is a function of velocity, but it is not zero at zero velocity.

Umm... isn't it?

I think that HonoreDB's 4th silly answer (repeated by SlyReaper) is the intended solution. There's really nothing else you can do.

Sorry, it's obviously zero at zero velocity (there is no net force...) but I meant it is not zero at low velocities. The point was that even a small friction force is going to be impossible to overcome with just blowing on the sandbag. And we haven't event talked about friction between the rope and the swing yet.

And clearly that solution isn't realistic at all.

bobleboffon3
Posts: 38
Joined: Fri Jul 16, 2010 7:35 am UTC

Re: Straw power

Postby bobleboffon3 » Sun Sep 26, 2010 9:10 am UTC

I don't think it's realist at all to talk about a solution like blowing the sandbag ( with or without the straw ).
You don't really even need to talk about air friction. You'd die, exhausted, way before the sandbag is even close to the bottle.

I think the fact the puzzle mention a 300KG sandbag count for something.
What if it was a 1000KG sandbag? The answer would still be "blow on the sandbag"? And if it was a 100,000KG, still the same? Was about a few million tons?

There's a limit what the human lungs can do, air friction or not ( and of course we STILL have to deal with the friction anyway ). I'm pretty sure that limit is way under 300kg, and if a solution actually exist, it's not something like that.

I'd really like to see a test happen, but I'm pretty sure blowing on that 300kg sandbag with a straw ( or without a straw ) will have the same effect as blowing on a car parked in your place, I.E. no effect at all.

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Sun Sep 26, 2010 9:13 am UTC

I hate to say there is no solution, but looking at this realistically . . . unless the solution is something really lame I don't think there is one. There is nothing useful you can do with a straw here, and you can't touch anything anyway.

gdin3d
Posts: 5
Joined: Wed Feb 10, 2010 3:03 pm UTC

Re: Straw power

Postby gdin3d » Sun Sep 26, 2010 4:58 pm UTC

Spit balls have a higher chance of rocking that sandbag :D

Can someone do the math on dat?? :P

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Sun Sep 26, 2010 5:11 pm UTC

gdin3d wrote:Spit balls have a higher chance of rocking that sandbag :D

Can someone do the math on dat?? :P

I don't even think that's true, lol.

GeorgeH
Posts: 527
Joined: Mon Aug 17, 2009 6:36 am UTC

Re: Straw power

Postby GeorgeH » Mon Sep 27, 2010 2:51 am UTC

Ridiculous thought #1:
Spoiler:
IFF the sandbag is "open" and you don't mind dirt in your mouth:

Suck the sand out of the sandbag with the straw, and pile it next to the bottle. Eventually your pile will be big enough to knock the bottle over. Technically you're not touching anything - the sand is jumping out and touching you. :P

If you're a lawyer and the sand is of an amenable consistency, you could also use the "finger over the top of the straw" trick to grab the sand (while loudly noting in the most lawyerly of tones that the problem only stipulated the sandbag - no provision was made for the sand itself.)


Ridiculous thought #2:
Spoiler:
The problem stipulated a paper straw, so I'm going to assume that it's flammable. Position the sun such that its light shines through the bottle and becomes focused, then use said light to set the straw on fire. Use your new flaming straw of death to incinerate the ropes suspending the sandbag, which will then fall down and knock the bottle over.

Of course if we're allowed to bring in external energy sources, we might as well go all out and invite a thermonuclear device to the party and have done with it...

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Mon Sep 27, 2010 3:30 am UTC

GeorgeH wrote:Ridiculous thought #2:
Spoiler:
The problem stipulated a paper straw, so I'm going to assume that it's flammable. Position the sun such that its light shines through the bottle and becomes focused, then use said light to set the straw on fire. Use your new flaming straw of death to incinerate the composer of this absurd puzzle, who will then fall down and knock the bottle over.

Fixed.

User avatar
BoomFrog
Posts: 1069
Joined: Mon Jan 15, 2007 5:59 am UTC
Location: Seattle

Re: Straw power

Postby BoomFrog » Mon Sep 27, 2010 5:50 am UTC

Actually if we're allowed to blow on things to move them we might as well just take off my shoe and throw it at the bottle. Unless we're somehow supposed to assume we are allowed to impart force indirectly via a gas but not a solid.

The puzzle is stupid and I refuse to spoiler my "answer".
"Everything I need to know about parenting I learned from cooking. Don't be afraid to experiment, and eat your mistakes." - Cronos

redrogue
Posts: 116
Joined: Tue Dec 15, 2009 9:17 pm UTC

Re: Straw power

Postby redrogue » Mon Sep 27, 2010 4:30 pm UTC

Wait a second.

A heavy 300 kg sandbag one metre tall is hung from a playground swing with a rope 3 metres...


A playground swing is typically a floppy rubber seat hung from a metal frame (with badly peeling paint) via rusted chains. At least that's what it was where I grew up. The frame often supports several swings. Nowhere in the puzzle does it say you can't touch the frame. Tip it over (angle grinder probably required).
Is 'no' your answer to this question?

Trebla
Posts: 387
Joined: Fri Apr 02, 2010 1:51 pm UTC

Re: Straw power

Postby Trebla » Mon Sep 27, 2010 6:21 pm UTC

BoomFrog wrote:Actually if we're allowed to blow on things to move them we might as well just take off my shoe and throw it at the bottle. Unless we're somehow supposed to assume we are allowed to impart force indirectly via a gas but not a solid.

The puzzle is stupid and I refuse to spoiler my "answer".


This fails to solve the riddle, even if we assume that "your detached shoe" does not count as an extension of your body. The riddle specifically states you must knock the bottle over with the sandbag. This also negates any use of the sand itself.

If we take "not allowed to touch anything with your body or the straw" at face value, then any other force could move the sandbag. If you take it to mean "no force you induce" then you could ask someone else to push the sandbag. Both of these seem to be outside the intent of the riddle though.

If it's from a physics forum, perhaps the intent was to derive the total force needed through the straw to cause the sandbag to oscillate a meter. Regardless of the intent, the riddle appears to be missing something.

User avatar
uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

Re: Straw power

Postby uncivlengr » Mon Sep 27, 2010 6:41 pm UTC

The notion that you could blow on the sandbag enough to get it swinging a meter is much like the idea that Tesla's oscillator can cause earthquakes - it neglects the fact that damping on the system (not just air resistence - friction on the rope, and swaying of the swingset frame, too) far outweighs the tiny force you can exert by blowing through a straw.

My solution:
Spoiler:
Not mentioned explicitly in the problem is the fact that the drinking straw is a meter long. Simply drop the straw between the sandbag and the bottle, and wait for a gusting wind to cause the bag to sway, tapping the straw and knocking over the bottle.

(I suspect, if there is a "real" answer, that it might have something to do with putting the straw in the bottle.)
I don't know what to do for you

qetzal
Posts: 862
Joined: Thu May 01, 2008 12:54 pm UTC

Re: Straw power

Postby qetzal » Mon Sep 27, 2010 9:21 pm UTC

Are we sure you have to knock over the bottle with the sandbag?

Spoiler:
Because if not, and if the ground below the swingset is sand or another loose, light material (like in many playgrounds), we could use the straw to blow away the sand beneath one side of the bottle.

Or maybe this is like the story of estimating the height of a building using only a barometer. In which case, tell some kid you'll give him your magic straw if he pushes the sandbag until it knocks over the bottle.


More seriously, it'd be nice to see the exact wording of the original problem. Wouldn't surprise me if it differs from the OP in some critical way. For one thing, it's not physically possible if you literally can't touch anything. Even blowing air through the straw involves the straw touching the air.

ericgrau
Posts: 92
Joined: Sat Dec 13, 2008 7:14 pm UTC

Re: Straw power

Postby ericgrau » Tue Sep 28, 2010 5:17 am UTC

On the matter of blowing on it:
Spoiler:
Sand has a specific gravity of 2.5 give or take, so the volume of the sandbag is about 300 / 2.5 = 120 liters = 0.12 cubic meters. At 1 meter tall it might be 1x0.3x0.4 for a surface area of 1x0.4=0.4 square meters. Both the drag and blowing force on the sandbag is proportional to area X velocity squared. Blowing very closely on it you might get a contact area of 0.5 cm x 0.5 cm or 0.000025 square meters.

For your blowing force to exceed the drag force:
V1^2 x 0.000025 > V2^2 x 0.4

Or taking the square root of both sides
V1 x 0.005 > 0.63 x V2
V1 > 126.49 x V2

At a height of 12.7 cm the potential energy of the sandbag is equal to 0.127 meters x mass x gravity constant or 0.127mg
At a height of 0 (and swinging at max speed) the kinetic energy is equal to 0.5 V2^2 m
0.127mg = 0.5v2^2m
0.254g=v2^2
v2^2 = 0.254m x 9.8m/s^2
v2^2= 2.49m^2/s^2
v2 = 1.58 m/s

So V1 > 126.49 x 1.58 = 200 m/s = 447 mph
The resulting air flow is 200 m/s x 0.000025 m^2 = 0.005 L/s.

So the first number is unreasonable but the second number is easy.

Let's assume you use your lips instead which have around 5 times the diameter and thus 25 times the area:
V1^2 x 0.000025 x 25> V2^2 x 0.4
Taking the square root of all that V1 is now 5 times lower or 40 m/s or 89 mph. The area is 25 times greater but V is 5 times lower so the flow is 5 times higher or 0.025 L/s.

Results: 40 m/s and 0.125 L/s in a 2.5 cm x 2.5 cm-ish mouth opening is required. A 0.5cm x 0.5 cm straw requires 200 m/s.

This study references another study where a peak velocity of 13 m/s and 0.75 L per exhalation was achieved:
http://vbn.aau.dk/files/19080650/An_Exp ... lated_Room
The straw actually hurts not helps. Like other matters of leverage and gearing and so on the straw improves speed but in exchange you lose force which is what you need to move that 300kg sand bag. You could get even more pressure by opening your mouth wider, but flow would also increase and we're already near the limit. That plus blowing on the bag constantly from both sides isn't really feasible.

User avatar
Scyrus
Posts: 124
Joined: Tue May 11, 2010 8:32 pm UTC
Location: Portugal

Re: Straw power

Postby Scyrus » Tue Sep 28, 2010 11:14 pm UTC

I have seen the site. The wording of the problem is exactly like the OP stated, word for word.
I would provide a link to it, until I discovered it has 80 of such "problems" and would be a very good source of puzzles for the xkcd forum to debate upon.
I am not sure whether providing the link will simply entertain the users or spam threads of it's puzzles here in the forum, and I do not mean to bring chaos.


Is there some way we can make use of static electricity to solve the puzzle?

User avatar
jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

Re: Straw power

Postby jestingrabbit » Tue Sep 28, 2010 11:25 pm UTC

Scyrus wrote:I have seen the site. The wording of the problem is exactly like the OP stated, word for word.
I would provide a link to it, until I discovered it has 80 of such "problems" and would be a very good source of puzzles for the xkcd forum to debate upon.
I am not sure whether providing the link will simply entertain the users or spam threads of it's puzzles here in the forum, and I do not mean to bring chaos.


I'm sure the forum will survive whatever happens.

http://www.phy.duke.edu/~hsg/physics-ch ... enges.html

Scyrus wrote:Is there some way we can make use of static electricity to solve the puzzle?


You would have to at least oscillate whatever force you apply unless its very strong. Static doesn't really lend itself to that very easily.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Wed Sep 29, 2010 2:02 am UTC

jestingrabbit wrote:I'm sure the forum will survive whatever happens.

http://www.phy.duke.edu/~hsg/physics-ch ... enges.html

I sent the guy an email. I'm really not sure how else to get an answer to this "challenge."

E: OK, so I did email Henry Greenside about the problem, and he said that blowing through the straw on the bag was the correct answer. The problem was supposed to demonstrate the strength of resonance. In particular, he noted that the formula for the resonant frequency is independent of mass.

Of course, he was using the equation for simple harmonic motion, which ignores the damping that is highly relevant when dealing with a three hundred pound bag and a drinking straw.

This was the bulk of my response (sorry about the lack of LaTex, but it was an email):

We can model blowing through the straw as a sinusoidal driving force, blowing to push the bag and sucking to pull it. Ignoring phase for the moment, the steady-state solution for a driven oscillator is x(t) = F/(m Z w) sin(wt), where x is position, t is time, F is the driving amplitude, m is the mass of the bag, Z is the impedance, and w is the frequency of oscillation (which we will assume is the resonant frequency). As we can see, the amplitude is only F/(m Z w). Since this is inversely proportional to the bag's mass, it is difficult to imagine how one could overcome the damping. Given your value of w=0.25 Hz, and assuming that is also the undamped angular frequency w_0, and for simplicity assuming the damping coefficient is 0.5, we find Z = 0.25 Hz. Given also that the mass of the bag is 300 kg (ignoring the mass of the rope) and assuming we are trying to achieve an amplitude of 1m, we can solve for the required driving amplitude F = m Z w x = 19 N.

This is of course not an exact answer. If we let the damping coefficient vary from 0.1 to 0.9, we can get solutions from 5.3 N to 48 N, and the angular frequency is also a very approximate guess. However, even a force of 5 N is unobtainable by ordinary blowing. Consider trying to suspend a 10 lb weight by blowing on it from below. We are off by at least two orders of magnitude.

The case of blowing through a straw is actually worse. This is because it restricts the air flow, so we are not able to blow as quickly. You cannot fully exhale through a straw in two seconds.


I guess then the purpose of this email was to point out that damping due to air resistance makes simply blowing on the bag unfeasible. Another poster on the forum tried a different approach, comparing the driving force to the drag force and suggesting that even with a contact area of 0.125 cm^2 -- a huge opening to blow through -- we would need to blow air at 40 m/s, or 90 mph just to reach the bottle. That's a hurricane-force wind.


We also intutively know this. While powerful winds and mythical marching soldiers may be able to take down a bridge, a small subwoofer will not.

ericgrau
Posts: 92
Joined: Sat Dec 13, 2008 7:14 pm UTC

Re: Straw power

Postby ericgrau » Wed Sep 29, 2010 8:34 am UTC

Silly physicists making overly idealized problems.

User avatar
Cosmologicon
Posts: 1806
Joined: Sat Nov 25, 2006 9:47 am UTC
Location: Cambridge MA USA
Contact:

Re: Straw power

Postby Cosmologicon » Wed Sep 29, 2010 11:39 am UTC

Eebster the Great wrote:I sent the guy an email. I'm really not sure how else to get an answer to this "challenge."

I hope you didn't tell him your idea about immolating him. Remember, if you feel the desire to kill someone for posting a physics problem you disagree with, take a few deep breaths before emailing him. :)

User avatar
uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

Re: Straw power

Postby uncivlengr » Wed Sep 29, 2010 12:38 pm UTC

resonant frequency is independent of mass.

So freaking what? The force required to move a 300kg bag a sand is entirely dependent on mass. You're not trying to get the thing to jiggle around a little bit at some frequency, you're trying to impart enough energy to get it from rest to swinging a full meter out of plumb.

That's like saying all the individual ticks of the hands of the clock on Big Ben will add up over time and overturn the whole tower... then again, maybe it's just a matter of time!
I don't know what to do for you

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Wed Sep 29, 2010 6:47 pm UTC

uncivlengr wrote:
resonant frequency is independent of mass.

So freaking what? The force required to move a 300kg bag a sand is entirely dependent on mass. You're not trying to get the thing to jiggle around a little bit at some frequency, you're trying to impart enough energy to get it from rest to swinging a full meter out of plumb.

That's like saying all the individual ticks of the hands of the clock on Big Ben will add up over time and overturn the whole tower... then again, maybe it's just a matter of time!

Clearly if you model the pendulum as an undamped oscillator, the mass is irrelevant. If you blow for long enough, it will eventually swing in a wider arc. This will admittedly take a while, but I bet it's not as long as you would think.

However, it is damped by air resistance, so mass is very relevant. He suggested that my estimates of impedance were far too high, but frankly I think there is no way this solution is possible for any reasonable value.

User avatar
Cosmologicon
Posts: 1806
Joined: Sat Nov 25, 2006 9:47 am UTC
Location: Cambridge MA USA
Contact:

Re: Straw power

Postby Cosmologicon » Wed Sep 29, 2010 7:08 pm UTC

Well, your impedance value is obviously way too big. Correct me if I'm wrong, but doesn't Z = 0.25Hz suggest that in the unforced case, the damping timescale is around 4s, ie, one swing? That seems at least an order of magnitude too much damping to me. I know we're not talking about a well-engineered Foucault's pendulum here, but don't those things run for hours?

Hmmm.... the Foucault's pendulum at the university of Copenhagen has a 145-kg weight on a 25-m string. Do you think you could displace that by 1m using only your breath?

(Incidentally, the value you're using for w is too small, by a factor of about 2pi. It should be around sqrt(10/3.5) ~ 1.7 rad/s.)

User avatar
uncivlengr
Posts: 1202
Joined: Fri Nov 14, 2008 10:35 pm UTC
Location: N 49°19.01 W 123°04.41

Re: Straw power

Postby uncivlengr » Wed Sep 29, 2010 7:54 pm UTC

Eebster the Great wrote:Clearly if you model the pendulum as an undamped oscillator, the mass is irrelevant.
That's makes no sense in this application, though - he's taking into account air resistance when it comes to blowing on the sandbag, and yet ignoring it when it dampens the motion. Either you account for something in your model, or your don't.

If he's going to play that game, let's just assume the swingset is on a frictionless surface, so that blowing on it causes the whole rig just slides into the bottle. Tada, problem solved. Or hey, let's just ignore air pressure on the side of the sandbag nearest to the bottle entirely, so the whole thing gets pushed over. Easy peasy.
I don't know what to do for you

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Wed Sep 29, 2010 10:52 pm UTC

Cosmologicon wrote:Well, your impedance value is obviously way too big. Correct me if I'm wrong, but doesn't Z = 0.25Hz suggest that in the unforced case, the damping timescale is around 4s, ie, one swing? That seems at least an order of magnitude too much damping to me. I know we're not talking about a well-engineered Foucault's pendulum here, but don't those things run for hours?


Well yeah it does, I guess it would decay by a factor of e every 4 s, which is clearly not reasonable. If we assumed instead 30 min = 1800 s, then we would have Z = 5.6 mHz which is a little more reasonable for an ordinary breath, though it is hard to estimate how reasonable it is.

Hmmm.... the Foucault's pendulum at the university of Copenhagen has a 145-kg weight on a 25-m string. Do you think you could displace that by 1m using only your breath?


Probably, if the friction is as low as you say.

(Incidentally, the value you're using for w is too small, by a factor of about 2pi. It should be around sqrt(10/3.5) ~ 1.7 rad/s.)


Maybe, I didn't spend long checking my calculations.

manapot
Posts: 1
Joined: Fri Oct 01, 2010 4:59 pm UTC

Re: Straw power

Postby manapot » Fri Oct 01, 2010 5:09 pm UTC

This may be a breach of the rules of the riddle but if you are allowed to bring a significant mass (say a giant lead sphere) and were somehow able to move it you could place the mass behind the sandbag (on the side opposite of the bottle) to get it swinging via gravity (no particles at all touching it).
Thus by quickly moving the sphere away at the back most position of the swing each cycle (much like what you spoke of with air).

User avatar
Eebster the Great
Posts: 3463
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: Straw power

Postby Eebster the Great » Mon Oct 11, 2010 1:37 pm UTC

manapot wrote:This may be a breach of the rules of the riddle but if you are allowed to bring a significant mass (say a giant lead sphere) and were somehow able to move it you could place the mass behind the sandbag (on the side opposite of the bottle) to get it swinging via gravity (no particles at all touching it).
Thus by quickly moving the sphere away at the back most position of the swing each cycle (much like what you spoke of with air).


The wind currents would be orders of magnitude more powerful than the gravitational attraction here. Cavendish only managed to deflect his small spheres 0.16 inches on his ultra-precise torsion balance with two 350 kg lead spheres. I have a suspicion that moving the gigantic sphere back and forth every four seconds would slightly outweigh that effect.


Return to “Logic Puzzles”

Who is online

Users browsing this forum: No registered users and 4 guests