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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: August 14 2014 at 06:49
1) I see the tension in the string keeping the ball in equilibrium to be an important part of the analysis.

EDIT: Also mean to say, you are correct the displaced water does not factor on the left. 

EDIT Again: A google image searched turned up a solution where someone was nice enough to draw the diagram and write out the equations. So definitive answer I suppose here.


Edited by Equality 7-2521 - August 14 2014 at 06:57
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 5154 		Direct Link To This Post Posted: August 14 2014 at 06:33
Originally posted by Dean Dean wrote:

Looking at the hidden answers Pat gave the same explanation, his last sentence (the left side would be lighter) may have given the wrong impression.
His conclusion was correct, the scale will tip to the right, but I'd say that the reasoning was not correct:


"Assuming the strings are mass less, I would imagine that the right hand side would fall. It should be independent on the weight of the two balls, only depending on their volume and the fact that the left hand side will float while the right hand side will not. Essentially what's pressing on the scales on both sides is the weight of the water and the pressure of the displaced water by the balls. However, on the left we will have an opposing contribution due to the tension in the string since it is connected to the scale. The left hand side should be lighter. "

1-it is not the fact that one ball floats and the other not which is relevant, as I said the ping pong ball would balance the scale if it was pushed submerged from outside, having exactly the same tendency to float.
2-the displaced water does not contribute to the weight of the left, only on the right. If it did, the scale would stay balanced.
3-the tension in the string does not "reduce the weight of the left side" since they for part of the same system. No matter how big a bag full of air you would submerge (tied to the bottom of the container) it will never lift up its own container.


Edited by Gerinski - August 14 2014 at 06:42
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Dean View Drop Down
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Points: 37575 		Direct Link To This Post Posted: August 14 2014 at 05:41
Originally posted by Gerinski Gerinski wrote:

 
Notice that if the ping pong ball was being pushed and kept submerged from the top from outside the container, say by a wire rod with a small cupped end at the bottom, then the scale would stay balanced. 

Yes, exactly. You could replace the steel ball and string with a ping pong ball and rigid rod and the right-side will still go down.
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Points: 37575 		Direct Link To This Post Posted: August 14 2014 at 05:38
Looking at the hidden answers Pat gave the same explanation, his last sentence (the left side would be lighter) may have given the wrong impression.
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Points: 5154 		Direct Link To This Post Posted: August 14 2014 at 05:22
^^ OK so here is what I believe is the correct answer, which was also Dean's.
The left container forms an isolated system, with no external forces acting on it (other than gravity of course). The left scale plate holds the mass of the container, the mass of the water and the mass of the ping pong ball.
On the right side the steel ball is held hanging from outside the container system so its mass is not supported by the scale plate. The scale plate holds the mass of the container, the mass of the water and the buoyant force of the ball, which Archimedes told us is equivalent to the volume of water displaced by the ball. Since a ball of water is heavier than the ping pong ball, the scale will tip to the right.
Notice that if the ping pong ball was being pushed and kept submerged from the top from outside the container, say by a wire rod with a small cupped end at the bottom, then the scale would stay balanced. 

Incidentally, it is incorrect to think that the ping pong ball will exert a force upwards on its container due to its tendency to float. They form part of the same system and as they say, you can not lift yourself up by pulling from your bootstraps.


Edited by Gerinski - August 14 2014 at 05:25
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Points: 5154 		Direct Link To This Post Posted: August 13 2014 at 11:53
This is becoming "the invisible ink thread" LOL
OK I leave some more time for our friends in other time-zones, tomorrow we can be more explicit about it.
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Points: 5319 		Direct Link To This Post Posted: August 13 2014 at 11:50
The scale should balance
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: August 13 2014 at 11:14
Originally posted by someone_else someone_else wrote:

I am not sure either, so I give my comment in background color. Anyone who is interested can select the text (i.e. by pressing Ctrl-A) to read it:

On the right hand side, the steel ball and the string that suspends it, do not add weight to the scale because the gravitational force is neutralized. On the left hand scale, the weight of the string and the air inside the ball add a little weight (but there is an upward force inside the ball because its density is less than the density of water), so I guess the left hand side will go down.


This in particular ignores the reciprocal buoyancy force at work on the water.
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 37575 		Direct Link To This Post Posted: August 13 2014 at 09:45
Originally posted by Gerinski Gerinski wrote:

Originally posted by Dean Dean wrote:

In the interest of fairness I'll not read the hidden explanations until other people have "voted", but I'll simply state: "right-side goes down" and leave it at that for now.
It would be however nice to know the reasoning behind the opinions.
I'll give my reasons when more people have answered, I don't want to sway anyone's thinking (which is also why I haven't peaked at Pat and Robert's explanations).
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Points: 5154 		Direct Link To This Post Posted: August 13 2014 at 09:43
Originally posted by Dean Dean wrote:

In the interest of fairness I'll not read the hidden explanations until other people have "voted", but I'll simply state: "right-side goes down" and leave it at that for now.
It would be however nice to know the reasoning behind the opinions.
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Points: 37575 		Direct Link To This Post Posted: August 13 2014 at 08:22
In the interest of fairness I'll not read the hidden explanations until other people have "voted", but I'll simply state: "right-side goes down" and leave it at that for now.
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Points: 5154 		Direct Link To This Post Posted: August 13 2014 at 08:08
^ let's add that we can neglect the mass of the strings themselves.
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Points: 24639 		Direct Link To This Post Posted: August 13 2014 at 07:28
I am not sure either, so I give my comment in background color. Anyone who is interested can select the text (i.e. by pressing Ctrl-A) to read it:

On the right hand side, the steel ball and the string that suspends it, do not add weight to the scale because the gravitational force is neutralized. On the left hand scale, the weight of the string and the air inside the ball add a little weight (but there is an upward force inside the ball because its density is less than the density of water), so I guess the left hand side will go down.
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Points: 5154 		Direct Link To This Post Posted: August 13 2014 at 07:22
^ it was meant as a puzzle. I found it somewhere and I have to admit that although I think I know the answer, I do not know it for sure. I will for the moment refrain from commenting on your solution to see if others have interesting input, I would say that your outcome seems correct to me but not the reasoning.
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: August 13 2014 at 07:11
I'm not sure if you're asking or this is supposed to be a puzzle. So my answer is in white text below:


Assuming the strings are mass less, I would imagine that the right hand side would fall. It should be independent on the weight of the two balls, only depending on their volume and the fact that the left hand side will float while the right hand side will not. Essentially what's pressing on the scales on both sides is the weight of the water and the pressure of the displaced water by the balls. However, on the left we will have an opposing contribution due to the tension in the string since it is connected to the scale. The left hand side should be lighter.
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 5154 		Direct Link To This Post Posted: August 13 2014 at 06:15
What will happen?
Obviously the two containers are exactly the same, with exactly the same volume of water, and the two balls have exactly the same volume.
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: August 06 2014 at 19:28
The Miracle Space Drive that Wasn't
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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Points: 16892 		Direct Link To This Post Posted: July 20 2014 at 19:53
This is quote old news, but bionic arms, legs and other body parts are on the market!

Maybe we'll see R2D2 in our lifetimes!



Edited by King of Loss - July 20 2014 at 20:09
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Points: 16892 		Direct Link To This Post Posted: May 21 2014 at 21:11
Originally posted by Equality 7-2521 Equality 7-2521 wrote:

Cool model of a geometric vanish puzzle



That is very cool! Clap
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Equality 7-2521 View Drop Down
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Points: 15784 		Direct Link To This Post Posted: May 21 2014 at 10:20
Need for Replication Is Not Censorship; It's Science
"One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall. "
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