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Geek Culture / puzzle: two retorts filled with water...

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mr Handy
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Posted: 29th Nov 2013 10:11
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Here is a puzzle: two retorts filled with water on scales, two objects inside (see image). Will there be balance?



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Dark Java Dude 64
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Posted: 29th Nov 2013 10:37
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AT first guess, I'd assume that the scale will tend to tilt counter clockwise from the center position. In both containers, the amount of water displaced by the ball is theoretically the same and so the mass of water in each should be identical.

Now, even though the ping pong ball is tending to float to the top and creating what would seem to be an upwards force on that side of the scale, that's only because the water there is more dense. The ping pong ball's weight is still being added to the weight of the water on the left side.

On the contrary, the weight of the steel ball on the right side is being entirely supported by an external support system, and none of its weight is being supported by the water.

Conclusion? Left side should drop.

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easter bunny
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Posted: 29th Nov 2013 11:15 Edited at: 3rd Dec 2013 01:40
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image...?
I see no image

EDIT: Firewall issues.

My answer, I definitely say it'd tip right, as the total mass in the righthand side is more than the total mass on the left.
Now to read the rest of the thread and find out...

edit2: Then again, the total displacement of either side is the same... and as the steel ball is being help up, it will push nothing down.
So my official conclusion (before I watch the video): They will theoretically be balanced, but in reality, there is more water being displaced on the left (more string submerged), so it depends if the string is more dense than the water.

edit3: never mind, I should have just stopped thinking after my initial conclusion


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Kezzla
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Posted: 29th Nov 2013 12:19 Edited at: 29th Nov 2013 15:52
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I would guess that since neither ball is adding weight and both are displacing the same amount of water there should be balance, however the metal ball seems to have slightly less string underwater so I would go with the balance tipping right due to there being slightly less water in the left glass to begin with. providing the string is less dense than the water.

PS. Damn easy to get severely double backwardsd with this puzzle

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mr Handy
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Posted: 29th Nov 2013 12:38
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Quote: "I see no image"

try this direct link

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Quik
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Posted: 29th Nov 2013 15:49
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the left ball is being held there in the water, by the water and the string, whilst the right ball is being kept from falling and not really adding anything in the forms of weight..

... that's my conclution! I literarily know nothing about physics, so I just go with what my simple brain is telling me to ~



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Seditious
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Posted: 29th Nov 2013 17:32
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I think the left side will be very slightly heavier.

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Libervurto
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Posted: 29th Nov 2013 17:35 Edited at: 29th Nov 2013 19:05
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I think the water must take some of the weight of the steel ball, so the right side would go down.


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mr Handy
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Posted: 29th Nov 2013 17:41
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I don't think that string adds any weight, I think there will be balance because of equal water volumes.

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Dark Java Dude 64
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Posted: 29th Nov 2013 21:35
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Quote: "I think the water must take some of the weight of the steel ball, so the right side would go down"
You raise an intuitive point based on buoyancy, however any weight added due to buoyancy would be due to water displaced and proportional to the amount of water displaced. Both balls are the same size, so the steel ball won't be adding any of its weight to the water relative to the ping pong ball, as far as I know. If we assume the ping ball has no weight at all, (and preferably assume the string has no weight or volume) then there should be balance. Assuming the ping pong ball does have a little tiny bit of weight though, the left side should drop.

I think we need someone very smart to set this straight.

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The Zoq2
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Posted: 29th Nov 2013 22:11
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My guess is that since the steel ball is being sustained in the air by the string, it wont apply any force to the water.

A similar problem is if you got 2 jars with insects in them and one of the insects is flying while the other one is not. Aparently both will weigh the same since the force is still applied to the bottom of the jar since there will be a counter force to the flying insect. Im guessing that that wont apply here since the steel ball is being suspended by the string like I said.

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Phaelax
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Posted: 30th Nov 2013 02:15 Edited at: 30th Nov 2013 02:17
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Quote: "however the metal ball seems to have slightly less string underwater "

That wouldn't matter because it's not adding any weight to the scale.

My first thought would be the left side would weigh more (however so slightly). But, if the pingpong ball can add enough buoyancy to pull the scale up (since it's tied to it) to counter-balance it's own weight, then by being tied to the scale it basically cancels out and therefore the two retorts would be equal.

The amount of buoyancy force would increase the further underwater it goes, right? Then we would need more details to really prove my theory, such as the size of the retorts and the length of the string. And that's assuming the picture is drawn to scale, since nowhere does it explicitly say both sides are of equal sizes or that the fulcrum is in the middle.

As a side note, displacing the water with any object will not add weight. I suppose it could technically remove weight from the retort as small water particles could rest upon the top of the ball being suspended. But I think you'd need a heck of a precise scale to measure that difference.

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Seditious
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Posted: 30th Nov 2013 07:12
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Quote: "But, if the pingpong ball can add enough buoyancy to pull the scale up (since it's tied to it)"


Wouldn't that be like one pulling oneself up by one's bootstraps?

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Dark Java Dude 64
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Posted: 30th Nov 2013 07:14 Edited at: 30th Nov 2013 08:56
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Quote: "But, if the ping pong ball can add enough buoyancy to pull the scale up (since it's tied to it) to counter-balance its own weight"
What is applying the upwards force to the ball is the water. The ball will therefore exert the same force downwards on the water, because of Newton's third law. The same force will be applied by the water downwards on the bottom of the beaker, so in the end, all of the buoyancy will cancel out. Net force of zero, no acceleration, no movement. You cannot make of container of a liquid lighter by placing something buoyant in it.

Quote: "As a side note, displacing the water with any object will not add weight."
In principle, yes it will. Say you have a cup on a scale, and this cup is full of water. Now we will take a steel ball on a string and suspend it into the water. Now, as the steel ball displaces the water, it will force the water level up against the force of gravity. Hence, buoyancy principles will begin to apply an upwards force to said steel ball. The steel ball's weight will overpower these buoyancy forces, therefore the ball would still be able to sink provided the string was released. However, because there are indeed upwards forces being applied upon the ball, the ball will apply an equal downwards force upon the body of water, which will in turn make the container 'heavier', namely from the perspective of the scale on which the container is sitting.

I think something important to point out here is that the steel ball is being supported by both the string and the water, although more so by the string than the water.

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rolfy
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Posted: 30th Nov 2013 11:42 Edited at: 30th Nov 2013 11:44
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I believe that the water still has tension even though it 'appears' that the ball is submerged so it still forces the water down and will tilt the balance to the right, however the ping pong ball is also...um...yeah, it might just balance out since they have the same volume.
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Libervurto
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Posted: 30th Nov 2013 23:16
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Is the string supporting the full weight of the steel ball?


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Dark Java Dude 64
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Posted: 30th Nov 2013 23:43
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No. If it was, the universe would surely implode into a purple hole. But really, the ball is being supported by both the string and the water. If we were to assume that it was not supporting the full weight of the steel ball, then the scale should surely tip to the left side. It should tip to the left side anyway though.

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Phaelax
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Posted: 1st Dec 2013 06:09 Edited at: 1st Dec 2013 06:10
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Quote: "In principle, yes it will. Say you have a cup on a scale, and this cup is full of water. Now we will take a steel ball on a string and suspend it into the water. Now, as the steel ball displaces the water, it will force the water level up against the force of gravity. Hence, buoyancy principles will begin to apply an upwards force to said steel ball. The steel ball's weight will overpower these buoyancy forces, therefore the ball would still be able to sink provided the string was released. However, because there are indeed upwards forces being applied upon the ball, the ball will apply an equal downwards force upon the body of water, which will in turn make the container 'heavier', namely from the perspective of the scale on which the container is sitting."


Interesting, I feel nerdier now because that makes sense to me.


So mr handy, do you have an exact answer to this puzzle that you are withholding?

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Libervurto
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Posted: 1st Dec 2013 12:13
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I think this is all part of that weird phenomenon of closed systems, like playing ping pong on a moving train, the steel ball becomes part of the right beaker system.
Now what would happen if you had a super sensitive scale and removed all the water?
Or a better example of what I'm asking is would a closed container weigh more than an open container? What if you heated them?


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mr Handy
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Posted: 1st Dec 2013 12:19
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Phaelax


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Phaelax
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Posted: 1st Dec 2013 17:36
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Interesting experiment. At first I was thinking, well he didn't actually tie the pingpong ball down so how can we really see that buoyancy has no effect? But when he dipped the steel ball in, even if the buoyancy was a factor it clearly wouldn't have made a difference.

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The Zoq2
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Posted: 1st Dec 2013 22:57
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Thats pretty interesting, but a bit sad that he dosnt explain why this happens.

Say ONE stupid thing and it ends up as a forum signature forever. - Neuro Fuzzy
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Quik
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Posted: 1st Dec 2013 23:44
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Quote: "Thats pretty interesting, but a bit sad that he dosnt explain why this happens."


this

and the bouyancy has no effect because of well - what he said, it's absolutly true what he said, while he could've tested it - I personally dont deem it necessay



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RedFlames
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Posted: 2nd Dec 2013 00:25
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Well if you think about it... if you were to measure the weight of the steel ball via the string, the string carries all the weight in air, but it'd be "lighter" when the ball is submerged, right? (Or am I thinking nonsense here?) So the water is kind of taking away some of the weight of the ball... and thus forced down.
Somehow the buoyancy of the steel ball is strangely counter-intuitive in this setup.

But I'm not good at physics anyways and suck at describing it.

(And yes, when I saw the thread I had been fooled too ^^)
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Dark Java Dude 64
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Posted: 2nd Dec 2013 02:55
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Quote: "Well if you think about it... if you were to measure the weight of the steel ball via the string, the string carries all the weight in air, but it'd be "lighter" when the ball is submerged, right? (Or am I thinking nonsense here?) So the water is kind of taking away some of the weight of the ball... and thus forced down."
Yes, you are absolutely correct! The weight you'd feel on the string would go down when you place the ball in the water. The water will then be supporting the difference.

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BatVink
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Posted: 2nd Dec 2013 13:21
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My head hurts.

So it it saying that as soon as the steel ball touches the water, it becomes part of the system, therefore it adds mass? the string on the ball is merely taking some of the burden of the mass, but not all of it.

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Dark Java Dude 64
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Posted: 3rd Dec 2013 01:14 Edited at: 3rd Dec 2013 01:19
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Pretty much. I mean I guess the way I interpret it is like this: when the steel ball is lowered into and submerged in the water, the mass of beaker and water have not changed, per se. However, some (not all) of the force that gravity imposes on the steel ball due to its mass, aka weight, adds to the weight of the beaker and water. No mass is transferred, really, but the weight is distributed between the water and string.

I think it would also be worth pointing out that whether we submerge an aluminum ball or a lead ball, the 'weight' of the container, and specifically as the scale sees it, would increase the same amount; it'd depend on the amount of water displaced, and not the weight or density of the ball. Or to get more detailed, it would depend on the amount and density of the fluid displaced, which is in this case water. Granted, if we let the ball fall completely into the water and rest on the bottom of the beaker, then the beaker would be supporting the full weight of the ball. A lead ball would in that case produce a greater difference than an aluminum ball.

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easter bunny
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Posted: 3rd Dec 2013 01:51 Edited at: 3rd Dec 2013 02:30
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That video is simply wrong.

If the ping pong ball was fully submerged, it would have displaced the same amount of water and balanced the system.

[fingers crossed]

edit: YES! I'm correct I did my own scientific [yeah right] experiment likewise:
1. Get [highly inaccurate] kitchen scales
Fill jug up about half way with water and put it in the scales.
Weight: 1.03 Kg (+-0.5 or so )
Place my pingpong ball in it (actually an empty Tupperware container)
Weight: 1.05 Kg
Push the container underwater
Weight: 1.1 Kg (as if tied to the bottom of the container)
Place my lead weight in the water (actually the Tupperware container filled with sand, so it has the same displacement, but a much higher density)
let it fall to the bottom (NOT suspended)
Weight: 1.15
Suspend it in mid-water
Weight: 1.1 (same as without sand!)

Summary: The weight of the container with the lead suspended in it is the same as the weight of the container with a body suspended in it of the same volume

The only difference is that if the ping pong ball was actually tied to the bottom, it might have made a difference...???
[As it's not actually being pushed down by an external force]

Anyways, at least I was right until someone proves me wrong (probably the next poster )


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Libervurto
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Posted: 3rd Dec 2013 16:22
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We can solve this by deduction.
If I drop a ball in an empty container it will fall to the bottom.
If I fill the container with rocks the ball will sit on top of the rocks.
....................... with sand the ball will rest slightly below the surface as it makes a divet.
....................... with mud the ball will sink further but not all the way to the bottom.
....................... with treacle the ball might make it to the bottom if it's dense enough but the treacle will slow it down.
....................... with water the ball will again sink if it's dense enough but it doesn't have to be as dense as to sink in treacle.

So what is happening? why is the ball sinking slower or stopping altogether in thicker substances? There must be a force acting upon the ball slowing it down. The substance is "pushing back" against the ball, and it's pushing back the whole way down not just at the surface.

So if we lower a ball into the container on a string the substance inside will push back. What if we fill the container around the ball? The substance still pushes back because it is trying to fill the space occupied by the ball. How much does it push back? To suspend the ball it would have to push back with a force equal to the ball's mass. But theres a limit to how much force the substance can push back with and I think that's called surface tension. As the ping pong ball floats we know there is enough force, and likely there is some to spare, but because the steel ball sinks we know it is too dense to float in water, the water pushes back as hard as it can but it is overpowered. So the water is pushing both which in turn pushes down on the containers but the one with the steel ball pushes harder so the scale drops to the right.

err? Yeah, I think.

Now what happens if we had two balls of equal density but different weight? like a hollow steel ball and a solid wooden ball for example.


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Mobiius
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Posted: 3rd Dec 2013 20:09
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Stupid internet! I didn't come here to think or learn things! lol


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BiggAdd
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Posted: 3rd Dec 2013 22:26
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Quote: "If the ping pong ball was fully submerged, it would have displaced the same amount of water and balanced the system."


Its not about water displacement though. As he said in the video, Because the ping pong ball is part of the system it doesn't actually matter if its submerged, because only the weight of the ping pong ball and the string add to the system itself.

If the ping bong ball was external to the system then it would matter if it was submerged.

Also have you not considered the external force of you pushing the Tupperware container underwater added weight into the system?

I think your experiment was a little flawed

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easter bunny
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Posted: 3rd Dec 2013 23:23 Edited at: 3rd Dec 2013 23:23
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Quote: "Also have you not considered the external force of you pushing the Tupperware container underwater added weight into the system?"

Yes it did:
Quote: "The only difference is that if the ping pong ball was actually tied to the bottom, it might have made a difference...???
[As it's not actually being pushed down by an external force]"



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BMacZero
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Posted: 4th Dec 2013 01:42
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I love these sort of physics problems. Here's one I read recently:


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easter bunny
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Posted: 4th Dec 2013 02:46 Edited at: 4th Dec 2013 05:18
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Of course not. The plane can't go anywhere, so the wings won't generate any lift.

Thinking outside the box though. Of course it CAN!!! Just turn the conveyor belt off

edit: face-palm


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Seditious
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Posted: 4th Dec 2013 03:20 Edited at: 4th Dec 2013 03:20
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Quote: "Of course not. The plane can't go anywhere, so the wings won't generate any lift."


Why not? It's moving forwards. It doesn't matter what the wheels are doing.

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Kezzla
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Posted: 4th Dec 2013 04:01
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I would have thought that the planes jet engines would ignore the conveyor belt and blast the plane forward anyway.

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Dark Java Dude 64
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Posted: 4th Dec 2013 04:20 Edited at: 4th Dec 2013 04:21
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They would indeed ignore the conveyor belt, and the plane would certainly be able to take off. If the plane was propelling itself by its wheels, then no, but the plane propels itself by something besides the wheels.

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BatVink
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Posted: 4th Dec 2013 11:30
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I think this is an impossible scenario, based on the way it is worded.

Quote: "The conveyor belt is designed to exactly match the speed of the wheels"


It's not the speed of the plane, it's the speed of the wheels.

The wheels only turn due to friction, once the plane starts moving under jet power. Assume there is no friction in the bearings of the wheels for simplicity.
As the wheels start to move the conveyor belt must speed up.
Because the conveyor belt has sped up, the wheel speed will increase. The plane is moving forward under jet power so increasing the belt speed simply rotates the wheels faster.
Thus, the belt will always be behind in speed, or if it is going to match the speed as described, it must accelerate to infinity in an instant.

Using Libervurto's approach earlier, look at it practically.

Stand backwards on a treadmill, wearing roller skates.
Hold on to your friend whilst the belt speeds up. The belt speed and wheel match in speed
Now increase your thrust by pushing against your friend stood in front of you (not touching the belt)
No matter how fast the belt is going you will move towards the front of the treadmill. The air is simply a less resistant version of your friend.

So...the plane would move forwards and take off. However the scenario is impossible because of what the belt is required to do - keep up to the wheel speed which will increase as the belt speed increases.

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Seditious
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Posted: 4th Dec 2013 12:35
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Quote: "I think this is an impossible scenario, based on the way it is worded."


True, I don't think the original problem was worded like that; it simply says that it matches the speed of the plane.

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BatVink
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Posted: 4th Dec 2013 13:47
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Quote: "it simply says that it matches the speed of the plane"


If that means that the plane is stationary (which I think it does) then it can't take off. Lift is achieved through the aerodynamics of the air passing around the wings - the air has a longer path under the wings than over creating a difference in pressure. As there is no air passing around the wings, lift cannot be achieved.

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Seditious
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Posted: 4th Dec 2013 14:01 Edited at: 4th Dec 2013 14:03
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Except, a plane's speed is its airspeed, which if stationary would be zero. If the plane is moving forwards at X speed and the conveyor belt is moving backwards by the same speed, the plane won't be stopped from taking off but the wheels will spin a lot faster (at that point the wheels are merely a 'frictionless' buffer between the ground and the craft).

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BatVink
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Posted: 4th Dec 2013 14:24
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Quote: "a plane's speed is its airspeed, which if stationary would be zero"


...which takes us back to the wording of the question again. I just checked the page it came from and the previous assumption is correct. It's a really bad physics question (or a really good one if you're trying to show that physics has limitations) because the scenario as described is a physical impossibility. In reality the whole thing would disintegrate and the plane would move forward over the rubble of what is left of the belt as it tried to match the wheel speed in no timespan.

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Posted: 4th Dec 2013 14:30
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Quote: " I just checked the page it came from and the previous assumption is correct."


Which page? It's on countless pages on the internet. I think it'd be hard to find the original page. I've always known the question to mention the speed of the plane and not the wheels though.

But yes, I agree with you regarding the way the question is worded.

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BatVink
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Posted: 4th Dec 2013 14:36
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The one that BMacZero quoted. It's not the original and it contains the conversation we're having ...

http://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

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BatVink
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Posted: 4th Dec 2013 14:39
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This is one of my favourites. There is no trick, it's purely logical, and it explains one of life's mysteries.

Why do we all feel like we usually end up in the slowest queue?

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Posted: 4th Dec 2013 14:40
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Oh, I hadn't seen that. Yes, it's certainly worded poorly there.
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mr Handy
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Posted: 4th Dec 2013 20:59
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Quote: "Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"


About plane: it will not take off.



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Dark Java Dude 64
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Posted: 4th Dec 2013 21:56
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Well assuming the conveyor belt could indeed match the exact speed of the wheels. But it couldn't.

Now, if this conveyor belt had a crap ton of force to go really fast and the plane's brakes were applied lightly, then you might be able to prevent the plane from taking off.

Real world scenario though? The plane would take off just fine.

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Indicium
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Posted: 5th Dec 2013 00:27
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Has nobody mentioned that myth busters already did this?


They see me coding, they hating. http://indi-indicium.blogspot.co.uk/
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thenerd
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Posted: 5th Dec 2013 01:39 Edited at: 5th Dec 2013 01:40
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I agree with what mostly everyone has said.

Quote: "
They would indeed ignore the conveyor belt, and the plane would certainly be able to take off. If the plane was propelling itself by its wheels, then no, but the plane propels itself by something besides the wheels.
"


The plane will take off, no matter what - because the wheels are not the mechanical force that are powering the plane to take off. A plane on the conveyor will still take off, because it is still producing the same amount of thrust. The only difference would be that the wheels would be turning twice as fast since they are travelling along the conveyor and moving forward with the plane. The only purpose of the wheels is to keep the plane off the ground, so the speed they are turning at is irrelevant.

The only way the conveyor belt would be able to stop the plane from taking off would be by somehow moving the air around the plane in the opposite direction of the thrust.

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