Physics question involving a beaker, water, cork, glue and water
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 | 12 votes (27.27%) | ||
| | 8 votes (18.18%) | ||
| | 24 votes (54.54%) |
44 members have voted
June 4th, 2012 at 1:54:55 PM
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First put a beaker on a scale. Then glue a cork to the bottom of the inside of a beaker. Wait for glue to dry. Then fill it with water.
The glue is water-soluable. Eventually it will loosen and the cork will rise to the top.
At the moment the cork breaks free from the bottom of the beeker, will the scale register more, less, or equal weight?
Please put your answer in "spoiler" tags if you're confident you got the answer right (Doc), and don't want to spoil it for others, unless they choose to click on the spoiler button. This suggestion applies to any kind of math/physics/trivia question.
The glue is water-soluable. Eventually it will loosen and the cork will rise to the top.
At the moment the cork breaks free from the bottom of the beeker, will the scale register more, less, or equal weight?
Please put your answer in "spoiler" tags if you're confident you got the answer right (Doc), and don't want to spoil it for others, unless they choose to click on the spoiler button. This suggestion applies to any kind of math/physics/trivia question.
Have a nice day.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2012 at 2:08:07 PM
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Quote: WizardFirst put a beaker on a scale. Then glue a cork to the bottom of the inside of a beaker. Wait for glue to dry. Then fill it with water.
The glue is water-soluable. Eventually it will loosen and the cork will rise to the top.
At the moment the cork breaks free from the bottom of the beeker, will the scale register more, less, or equal weight?
Please put your answer in "spoiler" tags if you're confident you got the answer right (Doc), and don't want to spoil it for others, unless they choose to click on the spoiler button. This suggestion applies to any kind of math/physics/trivia question.Have a nice day.
My answer:
Per my limited knowledge of chemistry/physics, the law of conservation of matter should apply - basically, The mass of an isolated system cannot be changed as a result of processes acting inside the system. Therefore, will remain "SAME".
June 4th, 2012 at 2:14:12 PM
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equal.
A falling knife has no handle.
June 4th, 2012 at 2:22:47 PM
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Less. I go against the crowd.
June 4th, 2012 at 2:32:32 PM
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Very interesting and intriguing. It's got my gears turning. And here's what I came up with:
"Logic" dictates that at that moment, things change causing the beaker's weight to change. However, conventional logic is wrong.
The weight of the contents remains constant. When the cork breaks free, water displaces it, forcing it to float, causing people to assume the total weight has changed.
The other "conventional" logic is that the mere disturbance of the cork breaking free causes motion, which causes the scale to register changes.
However, according to Newton's law of actions having an equal and opposite reaction, the scale registers no change.
Bottom line: Assuming the bond is strong enough to hold the cork long enough for the scale to 'settle' before breaking free, the scale will remain unchanged.
The weight of the contents remains constant. When the cork breaks free, water displaces it, forcing it to float, causing people to assume the total weight has changed.
The other "conventional" logic is that the mere disturbance of the cork breaking free causes motion, which causes the scale to register changes.
However, according to Newton's law of actions having an equal and opposite reaction, the scale registers no change.
Bottom line: Assuming the bond is strong enough to hold the cork long enough for the scale to 'settle' before breaking free, the scale will remain unchanged.
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June 4th, 2012 at 2:41:38 PM
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If asked last year, I'd probably gnaw on this question for quite awhile, and I'm sure my brain would have split into opposing sides and waged war. But a year ago I asked a similar question about fish in a cooler, and Doc and Mosca set me straight. This question is close enough to that one for me to say
it'll weigh the same
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June 4th, 2012 at 3:10:08 PM
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Quote: WizardPlease put your answer in "spoiler" tags if you're confident you got the answer right (Doc), and don't want to spoil it for others, unless they choose to click on the spoiler button.
Well, if you're going to call me out by name on such a thing, I guess I'll have to toss in a bit of a twist. Now I just know that everyone is clicking on the "Show Spoiler" buttons right off the bat, but why not think for a sec about what possible twist I could come up with?
O.K., in an equilibrium state, with the cork glued to the bottom or floating on the surface, the scale will (should anyway) read the same thing.
On the other hand (Twist #1), the Wizard asked "At the moment the cork breaks free...." This may be interpreted as the transient problem as the cork accelerates upward and water accelerates downward below the cork, followed by the cork and water slowing down toward the final equilibrium state. During that transient, the scale reading should remain, on average, the same as before, but it could vary up and down erratically. Visualize this as if you are standing on the scale and shaking all over, up and down. You don't expect the scale reading to remain steady do you?
Taking this to an extreme, it is possible that the cork will pop out of the water and be free-flying in the air for a very brief period (Twist #2). It might even splash some water droplets into the air with it. If the scale is responsive enough to be able to record that instant, it should display a value less than the original one, followed by a higher-than-original value as the cork splashes back down. Analogy: you're standing on the scale and jump into the air.
Yep, one of those "less" votes is mine, just to be contrary. But I assure you that if you are considering equilibrium states, then "equal" is the right answer, and the average value during the transient period should be the same, too.
On the other hand (Twist #1), the Wizard asked "At the moment the cork breaks free...." This may be interpreted as the transient problem as the cork accelerates upward and water accelerates downward below the cork, followed by the cork and water slowing down toward the final equilibrium state. During that transient, the scale reading should remain, on average, the same as before, but it could vary up and down erratically. Visualize this as if you are standing on the scale and shaking all over, up and down. You don't expect the scale reading to remain steady do you?
Taking this to an extreme, it is possible that the cork will pop out of the water and be free-flying in the air for a very brief period (Twist #2). It might even splash some water droplets into the air with it. If the scale is responsive enough to be able to record that instant, it should display a value less than the original one, followed by a higher-than-original value as the cork splashes back down. Analogy: you're standing on the scale and jump into the air.
Yep, one of those "less" votes is mine, just to be contrary. But I assure you that if you are considering equilibrium states, then "equal" is the right answer, and the average value during the transient period should be the same, too.
June 4th, 2012 at 3:36:50 PM
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Didn't they do a similar thing on Mythbusters where everybody
in an elevator had to jump up at the same time and the myth
said their weight in the elevator would disappear. As I recall,
it still weighed the same when they were all suspended in the
air because their mass was still in the elevator. Maybe the cork
thing is different, I get all my knowledge from TV and cereal
boxes.
in an elevator had to jump up at the same time and the myth
said their weight in the elevator would disappear. As I recall,
it still weighed the same when they were all suspended in the
air because their mass was still in the elevator. Maybe the cork
thing is different, I get all my knowledge from TV and cereal
boxes.
"It's not called gambling if the math is on your side."
June 4th, 2012 at 3:41:45 PM
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In the interests of discussion, let's allow a few days to submit answers before discussing the solution openly.
Based on some hidden comments, let me emphasize that I'm asking about the effect on the scale the exact moment the cork breaks free. Your instruments are delicate enough to measure this. Let me also rule out the issue of the cork rising up the air and possibily splashing water out of the beaker, because even if these events happened they would be after the cork broke free of the bottom. However, if you wish to discuss the whole timeline in your answer, assume the cork is never airborne and no water splashes out.
Based on some hidden comments, let me emphasize that I'm asking about the effect on the scale the exact moment the cork breaks free. Your instruments are delicate enough to measure this. Let me also rule out the issue of the cork rising up the air and possibily splashing water out of the beaker, because even if these events happened they would be after the cork broke free of the bottom. However, if you wish to discuss the whole timeline in your answer, assume the cork is never airborne and no water splashes out.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2012 at 3:54:42 PM
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Less. As the cork is moving upwards, it is providing an additional support force to the water above it. The amount of force that the scale is pushing upwards on the beaker to support is decreased by the amount of force that the cork exerts on the water above it as flies upward through the water. Ignore the fact that the cork will splash some water above what was the surface of the water. The total amount of upward force exerted by both the cork and the scale's support force (read: weight) have an inverse relationship. It is the same principal as tying a balloon to a brick.
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June 4th, 2012 at 4:00:02 PM
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Quote: EvenBobI get all my knowledge from TV and cereal
boxes.
HAHAHA. Thanks for that one.
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June 4th, 2012 at 4:11:10 PM
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more. The cork when it is glued to the bottom of the beaker is exerting a force in the opposite direction of the water and beaker. The moment the cork breaks free this opposite force is zero and the beaker is heavier
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June 4th, 2012 at 4:28:09 PM
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I had ignored that part. The cork provides a constant upward pressure on the system until it reaches the surface and settles, then?
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June 4th, 2012 at 5:29:49 PM
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Quote: WizardBased on some hidden comments, let me emphasize that I'm asking about the effect on the scale the exact moment the cork breaks free.
In my earlier post, hidden (Ha!) by the spoiler button, I raised the issue of equilibrium or steady-state conditions versus transient conditions. I am now interpreting your clarification to mean that you are, indeed, interested in the transient problem and that you are specifically interested in the very first change (if there is one at all) that occurs as the cork ceases to be attached, without regard for any subsequent change(s) that might occur in the opposite (or same) direction. Is that correct?
June 4th, 2012 at 5:45:17 PM
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The correct answer is that the scale will register increased weight at the moment the cork starts flowing up.
An easy way to see it is to realize that the cork is accelerating upwards, and its weight increases due to acceleration (like the increase in weight you feel in an elevator when it starts moving up).
Another way to think about this is that the beaker and the cork comprise an isolated system. The center of mass has to stay put. If the cork is moving up, something (of equivalent mass) must be moving down, increasing the pressure on the scale.
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June 4th, 2012 at 6:57:35 PM
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Force has a time component; this is an instant, which I took to mean no time. At the instant of release, nothing. However, I will gladly try to understand why I am wrong, if so, rather than defend a wrong answer.
A falling knife has no handle.
June 4th, 2012 at 7:16:32 PM
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Quote: MoscaForce has a time component; this is an instant, which I took to mean no time. At the instant of release, nothing. However, I will gladly try to understand why I am wrong, if so, rather than defend a wrong answer.
Consider a simpler system in which a mass is accelerating and the rate of acceleration is increasing due to a uniformly increasing force being applied. At a single instant during that period, there is a force, and the force is changing. The amount of change over zero time cannot be finite unless there is an infinite rate of change, but I think it is reasonable to discuss either an infinitesimal, non-zero time period or to discuss something that is continuously changing at an instant of time just after the cork is free.
Ruling out the question is similar to saying that you can't possibly be falling at the instant right after stepping off a cliff.
June 4th, 2012 at 7:28:13 PM
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I am not confident in my answer so I will not put it in a spoiler tag.
I think the answer is 'Same'. Although the cork is now moving up through the water the displaced water is also moving down through the beaker thereby cancelling each others momentum out. There is potential energy being turned into kinetic energy but I think the weight change would be negligible.
I think the answer is 'Same'. Although the cork is now moving up through the water the displaced water is also moving down through the beaker thereby cancelling each others momentum out. There is potential energy being turned into kinetic energy but I think the weight change would be negligible.
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June 4th, 2012 at 7:59:22 PM
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Quote: MoscaForce has a time component; this is an instant, which I took to mean no time. At the instant of release, nothing.
Shall we say, 0.001 seconds after the cork is released, will the scale register (more/less/same) weight than before it was released?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 4th, 2012 at 10:01:37 PM
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I'm also not confident of my answer so I won't bother with spoilers, but I tried to analogize. If I'm standing on an analog (mechanical) bathroom scale holding a 5lb dumbbell, the scale shows my weight + 5lbs. If I then throw the dumbbell straight up in the air, the scale will show an increased weight before settling on my weight. Similarly, if I jump up and off a scale, the scale shows an increase before it settles on zero. I think, but am not sure, that the same thing is going on here.
There is an easier way to replicate the experiment, I think, by using a beaker, water, a balloon, some steel ball bearings, and an electromagnet. Put a few BBs in the balloon and then blow it up to a size that will be able to rise in the beaker if pushed to the bottom and then let go. In other words, don't fill up the balloon with BBs, just enough to allow the balloon to stay in place at the bottom of a water-filled beaker when the electromagnet is placed underneath the beaker and electrified. Then take the whole contraption - water-filled beaker with balloon with air/BBs attracted to the bottom by the electromagnet on the outside - to your local grocer's produce department and put it on the produce scale. After the needle stabilizes on the actual weight of the experiment, turn off the power to the electromagnet and watch what happens...
There is an easier way to replicate the experiment, I think, by using a beaker, water, a balloon, some steel ball bearings, and an electromagnet. Put a few BBs in the balloon and then blow it up to a size that will be able to rise in the beaker if pushed to the bottom and then let go. In other words, don't fill up the balloon with BBs, just enough to allow the balloon to stay in place at the bottom of a water-filled beaker when the electromagnet is placed underneath the beaker and electrified. Then take the whole contraption - water-filled beaker with balloon with air/BBs attracted to the bottom by the electromagnet on the outside - to your local grocer's produce department and put it on the produce scale. After the needle stabilizes on the actual weight of the experiment, turn off the power to the electromagnet and watch what happens...
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June 5th, 2012 at 12:13:16 AM
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Same. It is a contained system.
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June 5th, 2012 at 4:55:20 AM
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Stage 1: Cork is glued to the bottom.
Stage 2: Cork is in transit from the bottom of the beaker to the top.
Stage 3: Cork is at the top and the system is in equilibrium.
I assume we're talking about the weight of the system during stage 2.
We all agree that the weight of stages 1 & 3 are the same. On the other hand, nobody has talked about the shift in center of mass. When the cork is at the bottom and that displaced water is towards the top of the beaker, the center of mass is higher (further away from the ground) than when the cork floats to the top and the displaced water goes back to its place (closer to the ground). So during stage two, the center of mass is moving downward. This change in center of mass requires a net force, therefore "equal" cannot be the correct answer.
The most simple real life example of a center of mass going downward is falling down. Right now, if you wanted to fall down how would you do it? The same way people faint, by pushing on the ground with less force. So, during the process of lowering your center of mass you would be pushing on the ground less hard and weigh less until you physically need to support your weight again.
Therefore, since in the problem you provided the center of mass goes downward during stage 2... my vote is for "less".
Well, not really. In haste I voted "more" earlier so I revoke that vote and now say "less".
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
June 5th, 2012 at 5:10:45 AM
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Quote: ahiromu
Therefore, since in the problem you provided the center of mass goes downward during stage 2... my vote is for "less".
Well, not really. In haste I voted "more" earlier so I revoke that vote and now say "less".
Your first vote was correct. Your line of reasoning (center of mass) is almost right. One thing you are missing is the realization that in a closed system the center of mass can never move. If the cork is moving up, something must be moving down, pushing the scale.
Try jumping on a scale for example. Or holding something in your hand and throwing it up.
"When two people always agree one of them is unnecessary"
June 5th, 2012 at 5:12:40 AM
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Quote: EvenBobDidn't they do a similar thing on Mythbusters where everybody
in an elevator had to jump up at the same time and the myth
said their weight in the elevator would disappear. As I recall,
it still weighed the same when they were all suspended in the
air because their mass was still in the elevator. Maybe the cork
thing is different, I get all my knowledge from TV and cereal
boxes.
Ahhhh college. There were about a dozen of us in a dorm elevator all drunk. For some reason we thought it would be hilarious to jump at the exact same time... let's just say we never did that again.
Are you talking about 2004 Episode 9? I haven't seen it, but the question is whether or not you can survive a falling elevator by jumping at the last second. The answer is no, a full and unequivocal no. If you jump in an elevator (or jump at anytime) then you are creating a large force pushing yourself up and a large force coming back down. So let's say the maximum occupancy for an elevator is 3000 pounds, if you have 2000 pounds of people that all decide to jump it's very easy to go above 3000 for a moment.
Don't jump in an elevator, I'm talking with experience.
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June 5th, 2012 at 5:34:53 AM
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I'm guessing my rationale is too obvious (or stupid) to be correct, but here goes...
I say the scale registers MORE weight, because the air in the cork provides a lifting force on the bottom of the beaker and once that force is removed, the beaker will be subject to a slight, temporary increase in gravitational force. However, since the cork is not being removed from the beaker, the inertial effect will only be temporary and the weight will quickly equalize to its original reading.
June 5th, 2012 at 6:36:39 AM
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I am not at all convinced I am correct in my answer so I will not add a spoiler, but I am envisioning a scenario where the scale's needle might vibrate kind of like when you initially drop a bag of fruit or vegetables on the scale at your local grocery store. I still submit that while there might be temporary fluctuations in the needle due to the cork rising that the weight of what is contained in the beaker will not change.
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June 5th, 2012 at 6:40:43 AM
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The answer is less. The weight sharply decreases when the cork breaks free, then stays more or less the same as the cork floats up, and then, when it gets to the top, it increases sharply, probably overshooting the original weight before oscillating a little and settling on the original weight when it reaches equilibrium.
This is analogous to a box with a ball attached the top and then dropped. While the ball is falling, it is not contributing to the box's weight. This is entirely unlike the situation of a bird hovering in a box because the bird is exerting enough force downward to maintain itself in place. A falling object is inherently not exerting enough force to remain in place, if any.
Instead of a ball, we have water moving downward to displace the cork that is not contributing its full amount to the box's weight as it is moving downward.
Also, ahiromu gives another way of looking at it and nails it.
This is analogous to a box with a ball attached the top and then dropped. While the ball is falling, it is not contributing to the box's weight. This is entirely unlike the situation of a bird hovering in a box because the bird is exerting enough force downward to maintain itself in place. A falling object is inherently not exerting enough force to remain in place, if any.
Instead of a ball, we have water moving downward to displace the cork that is not contributing its full amount to the box's weight as it is moving downward.
Also, ahiromu gives another way of looking at it and nails it.
June 5th, 2012 at 7:18:36 AM
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Quote: Gabes22I am not at all convinced I am correct in my answer so I will not add a spoiler, but I am envisioning a scenario where the scale's needle might vibrate kind of like when you initially drop a bag of fruit or vegetables on the scale at your local grocery store.
The question is what is the initial movement of the needle on the scale? Remember we assume he have instruments delicate enough to tell.
Quote:... that the weight of what is contained in the beaker will not change.
I don't think anyone would dispute that the scale is measuring force applied against it, which can come from forces besides gravity.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 5th, 2012 at 11:18:05 AM
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Now that I'm thinking it through, since every action has an equal and opposite reaction, the force pushing up on the cork is also pushing down on the scale. I change my vote from 'same' to 'heavier'.
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June 5th, 2012 at 12:01:16 PM
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Every action has an equal and opposite reaction, yes. But the cork has potential energy when it is at the bottom of the water. it is not pushing off anything to move up through the water, I am afraid of being very wrong and sounding very ignorant here... I think it the weight actually remains the same the whole time.
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June 5th, 2012 at 12:07:06 PM
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Quote: bigfoot66I think it the weight actually remains the same the whole time.
That may be true, but isn't the question at hand. The question is the effect on the scale. As I wrote earlier, the scale measures force applied against the scale, which may be different than just the weight of the object on it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 5th, 2012 at 12:22:30 PM
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Quote: WizardThat may be true, but isn't the question at hand. The question is the effect on the scale. As I wrote earlier, the scale measures force applied against the scale, which may be more than just the weight of the object on it.
ARRGGG! This is a great question, I have been wrestling with it a fair amount and at various points been confident thatthe answer is more, less, and the same. Thanks for giving me this challenge! I go back to my original answer. As the cork breaks free, the scale will register less weight because the weight of the cork and some of the water will stop being measured while the cork is traveling towards the surface of the water.
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June 5th, 2012 at 4:09:40 PM
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As a side note, any time there is a discussion of gravity, masses, and acceleration, weaselman and I disagree – we don't even agree on the definition of weight.
I have been continuing to ponder whether I even understand the question correctly. I think the Wizard's clarifications have indicated that we are particularly interested in the transient responses and not the steady-state, equilibrium conditions. I agree with bigfoot66 that this is a very good question, depending on the level at which one wishes to try to analyze it.
Here is my current analysis, which runs on quite a bit:
I have been continuing to ponder whether I even understand the question correctly. I think the Wizard's clarifications have indicated that we are particularly interested in the transient responses and not the steady-state, equilibrium conditions. I agree with bigfoot66 that this is a very good question, depending on the level at which one wishes to try to analyze it.
Here is my current analysis, which runs on quite a bit:
I believe that from the time the cork ceases to be bound to the beaker until the time that it is floating steady on the surface and all currents in the water have died out, there will be numerous factors that cause temporary changes in the force against the scale, all of which average out over that period as equal to the original force.
My current thinking is that while there may be lots of erratic variation in the reading of the scale, the question asks us which direction the needle twitches first. I suspect that if there were a group of highly knowledgeable people discussing this openly, they would have trouble reaching agreement on which would be the very first effect.
So, I am trying to consider that very first instant, before the upper surface of the cork has risen a detectable amount, before any water has dropped a nanometer, and before any water has managed to seep between the cork and the beaker. What factor could have presented itself at that point that could affect the force on the scale?
The one that I currently suspect would arise first is a release of tensions that have been created due to the buoyancy of the cork. While it is still attached to the beaker, the cork is being stretched vertically by the lifting forces of the water. Granted, the elastic limit of cork in tension is quite small, but the cork is stretched some minor amount. Also, the glue and even the bottom surface of the beaker are stretched a very tiny bit by these same tension forces.
When the glue connection fails, all of this tension within the cork, glue, and glass can no longer be supported. I believe that the semi-elastic contraction of the cork will be much more sudden than even the beginning of its rise through the water. Similarly, the residual glue will snap to a relaxed mode, some against the bottom of the cork and some against the glass. The glass bottom itself will relax from its elongation or other distortion from the pre-break stresses.
The upward motion of the cork and any attached glue cannot convey a change in forces to the scale except through the water, likely involving a time delay because actual bulk movement of the cork would be necessary. On the other hand, I think the downward motion of the glass bottom of the beaker (and any attached glue) can be transmitted directly and more quickly to the scale.
Based on this reasoning, I anticipate that the very first twitch will be in the direction of a higher/heavier reading on the scale, but it's duration will be exceedingly brief and its magnitude rather small.
I will be interested in hearing an explanation of any answer that someone believes they can actually prove is the first force to act.
My current thinking is that while there may be lots of erratic variation in the reading of the scale, the question asks us which direction the needle twitches first. I suspect that if there were a group of highly knowledgeable people discussing this openly, they would have trouble reaching agreement on which would be the very first effect.
So, I am trying to consider that very first instant, before the upper surface of the cork has risen a detectable amount, before any water has dropped a nanometer, and before any water has managed to seep between the cork and the beaker. What factor could have presented itself at that point that could affect the force on the scale?
The one that I currently suspect would arise first is a release of tensions that have been created due to the buoyancy of the cork. While it is still attached to the beaker, the cork is being stretched vertically by the lifting forces of the water. Granted, the elastic limit of cork in tension is quite small, but the cork is stretched some minor amount. Also, the glue and even the bottom surface of the beaker are stretched a very tiny bit by these same tension forces.
When the glue connection fails, all of this tension within the cork, glue, and glass can no longer be supported. I believe that the semi-elastic contraction of the cork will be much more sudden than even the beginning of its rise through the water. Similarly, the residual glue will snap to a relaxed mode, some against the bottom of the cork and some against the glass. The glass bottom itself will relax from its elongation or other distortion from the pre-break stresses.
The upward motion of the cork and any attached glue cannot convey a change in forces to the scale except through the water, likely involving a time delay because actual bulk movement of the cork would be necessary. On the other hand, I think the downward motion of the glass bottom of the beaker (and any attached glue) can be transmitted directly and more quickly to the scale.
Based on this reasoning, I anticipate that the very first twitch will be in the direction of a higher/heavier reading on the scale, but it's duration will be exceedingly brief and its magnitude rather small.
I will be interested in hearing an explanation of any answer that someone believes they can actually prove is the first force to act.
June 5th, 2012 at 4:30:56 PM
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For the purposes of this discussion, I would like to focus on just the effect of the movement of the water and the cork in the beaker. I think that any change in form of the cork, glue, and beaker are neglibible and can be ignored for purposes of discussion.
Let's also think of the scale as being perfectly accurate.
Let's also think of the scale as being perfectly accurate.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 5th, 2012 at 4:43:10 PM
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I keep thinking about this problem, I can't get it off my mind. I am eager to hear the answer. However I am convincing myself more and more that my original analysis is correct. While the cork is being held at the bottom of the water, it has potential energy. When it breaks free the potential energy becomes kinetic energy which is ultimately dissipated in the water but until the cork surfaces, the kinetice energy of its upward motion bears some of the load of the weight of the water. Therefore the total weight the scale is supporting is reduced and the needle moves closer to zero
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June 5th, 2012 at 4:44:31 PM
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Well, it seems that the question keeps evolving. And if some force changes are "negligible", I don't know why you would want/need a scale that is "perfectly accurate". I take it now that rather than looking for the first change that could be detected by a perfect scale, we should be willing to wait for one that is not negligible to someone who has in mind a bigger change that occurs later. What if someone considered that change "negligible"?
I think I will opt out of further speculation on which answer is the preferred one.
I think I will opt out of further speculation on which answer is the preferred one.
June 5th, 2012 at 5:07:49 PM
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Quote: DocWell, it seems that the question keeps evolving. And if some force changes are "negligible", I don't know why you would want/need a scale that is "perfectly accurate". I take it now that rather than looking for the first change that could be detected by a perfect scale, we should be willing to wait for one that is not negligible to someone who has in mind a bigger change that occurs later. What if someone considered that change "negligible"?
I think I will opt out of further speculation on which answer is the preferred one.
If you think the expansion of the beaker and or cork are not negligible then you should argue that point when we throw this wide open. However, I think they are, and discussion of those effects only confuses the issue.
There seems to be a lot of comments in the spoilers about the needle in the scale having a pendulum effect, which is true on cheap scales. For example, after you step off a cheap bathroom scale it will wobble above and below 0 for a second. Let's assume the scale in question is a digital scale. I don't say it is perfectly accurate to confuse you, but to nix discussion about any inaccuracy in the scale.
I think the way the question was originally phrased is fine, and I'm only trying to address questions and issues I've seen in the comments. As far as I know, nobody else is having such a hard time with the way the question was framed.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 6th, 2012 at 11:09:24 AM
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We are on day 3, how much longer are you going to tease me here before we get the answer?
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June 6th, 2012 at 1:03:29 PM
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I originally voted for same but now I think I must change my mind.
Looking at the big picture, when the cork is released there is clearly an increase in the kenetic energy within the beaker. The masses of water and cork are in motion due to acceleration. This energy has to come from somewhere so the potential energy of the beaker must drop during the acceleration. The mass of the beaker is not changing so the only way for the potential energy to change is for the acceleration on the beaker to decrease. This will make the beaker lighter during the acceleration so the needle will initially move down.
June 6th, 2012 at 1:10:10 PM
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jml24: Without revealing or discussing your entire answer, I will just comment about your concern that "This energy has to come from somewhere...." The energy is stored (from one perspective) as potential energy of the cork being held below the surface of the water or (from the counter perspective) from the potential energy of the water being held at a higher elevation due to the presence of the cork.
June 6th, 2012 at 1:21:24 PM
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Quote: bigfoot66We are on day 3, how much longer are you going to tease me here before we get the answer?
How about now! Please have at reading all the spoilers.
I claim that the answer is LESS. Some spoilers have identified the reason. The way I would put it is the center of gravity is shifting downward as the cork moves upward, because water is denser than cork. The scale is measuring force applied against it. As the center of gravity moves down, force is being released, thus less is applied against the scale.
I would also like the record to show that at the time of this post the results were:
More: 8
Less: 7
Equal: 19
So what I believe to be the correct answer, which Doc agree wish, came in last.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 6th, 2012 at 1:26:41 PM
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Thinking about it that way, it makes perfect sense. The water being displaced by the cork contains potential energy. When that energy is dissipated, it must go somewhere.
What is the energy source of gravity though? That's something I have never understood. And does the force of gravity travel at the speed of light or what?
What is the energy source of gravity though? That's something I have never understood. And does the force of gravity travel at the speed of light or what?
June 6th, 2012 at 2:00:20 PM
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Quote: QuadDeucesWhat is the energy source of gravity though? That's something I have never understood. And does the force of gravity travel at the speed of light or what?
This is something I've wondered about off and on for at 30 years. My college astronomy teacher said all objects emit particals called gravitons. Somehow, other objects are attracted to them. However, as far as I know, the existence of gravitons is not proven and they are more of a placeholder theory until a better idea comes along.
I sometimes wonder if string theory is much the same -- a way to explain things we don't understand, although we can't actually observe it.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 6th, 2012 at 2:04:47 PM
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Quote: QuadDeucesWhat is the energy source of gravity though? That's something I have never understood. And does the force of gravity travel at the speed of light or what?
As to the first question, it's either the distortion caused by mass on space-time, or you can get a Nobel prize if you figure it out. As to the second, you can get a Nobel prize if you figure it out.
Donald Trump is a fucking criminal
June 6th, 2012 at 2:34:22 PM
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Quote: WizardSo what I believe to be the correct answer, which Doc agree wish, came in last.
To be honest about it, I probably never really answered the question you had in mind. Instead, I went off discussing two silly tangents, one in which the cork popped out of the water (giving an answer of "less") and one looking at the very instant of glue failure when I considered the very brief "twitch" of the scale as the cork, glue, and glass relaxed their distortions -- that would result in the "negligible" and very brief force that would give an answer of "more".
For that time interval during which the cork is rising, I agree with the Wizard that the center of mass of the system is dropping and that the force would be less. I was in error in my previous comments that the average force during the transient problem would be the same as the steady force in the equilibrium conditions. Ignoring the truly minor effects, the force should be less during the entire transient problem, with the exception of the brief period when the cork may pop above its final position and then sink back -- as it sinks back, the water will be lifted again, resulting in "more".
June 6th, 2012 at 3:05:03 PM
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Quote: Doc...For that time interval during which the cork is rising, I agree with the Wizard that the center of mass of the system is dropping and that the force would be less.
Ooops! In an effort to be agreeable, I misspoke once again. It is not so important that the center of mass is dropping but that the center of mass is accelerating. While the cork is accelerating upward (and the water accelerating downward), the center of mass is accelerating downward and the force on the scale is less. If/when the cork reaches a constant upward velocity due to viscous forces, the force on the scale will return to its original value. When the cork breaks the surface and decelerates (or accelerates downward), meaning the downward velocity of the water also is decreasing, then the force on the scale is "more" than the original value.
June 6th, 2012 at 3:16:28 PM
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Quote: QuadDeucesThinking about it that way, it makes perfect sense. The water being displaced by the cork contains potential energy. When that energy is dissipated, it must go somewhere.
What is the energy source of gravity though? That's something I have never understood. And does the force of gravity travel at the speed of light or what?
Without going into speculative theories like gravitrons, I'll just say that gravitational attraction is a force, not an energy. Systems obtain potential energy (or have their potential energy increased) by doing work on them -- you move them a distance against the force of the gravitational field.
When the cork floats upward, the gravitational potential energy of the cork increases (it is being lifted) but the gravitational potential energy of the water is reduced even more as it drops. This net amount of potential energy that is given up as the materials move is indeed dissipated, as you said. For the most part, it is dissipated through viscous interactions within the water and at the water-cork interface. The final destination of the energy is in the form of internal energy of the water and the cork, which both will tend to be at very slightly higher temperatures than before.
June 6th, 2012 at 3:31:30 PM
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While the wizards answer (less) may or may not be correct. I still believe that it will weigh more. I do not agree with the logic concerning the shifting of the center of gravity. The force on the scale is made up numerous components, which are not all working in the same direction. The mass of the beaker, water and cork provides a downward force on the scale while the buoyancy of the cork provides a force in the opposite direction.
At the instant the cork breaks free, the buoyancy force on the scale is zero thus, I still believe that the scale will register more. The force which causes the shift in the center of gravity is the buoyant force or lack of buoyant force when the cork beaks free.
At the instant the cork breaks free, the buoyancy force on the scale is zero thus, I still believe that the scale will register more. The force which causes the shift in the center of gravity is the buoyant force or lack of buoyant force when the cork beaks free.
new motto for the left: “I don't know if I received bad information, but I think I suspected there was more than there actually was,” (John Brennan Mar 25, 2019)
