Buoyancy
What explains the motion of the hourglass?
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18 solutions
Dear Blake, Your explanation doesn't explain why in the original animation, after the apparatus was turned over there was a 3 or 4 second pause before the hour glass started to rise. Please explain why there was a pause or why the animation was changed. Many of us were trying to explain the pause. Thanks Tony Burch
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This initial pause in the beginning of the animation is addressed in the section of my solution: the initial motion :
To explain the first few seconds, we have to consider forces other than gravity and buoyancy. When the hourglass starts on the bottom in the original GIF, you might be able to notice that it's at a slight angle, and leaning against the side of the cylinder. This is because with all the sand in the top of the hourglass, it's top-heavy, meaning the density of the top is higher than the density of the bottom. So in this case the buoyant force of the bottom of the cylinder ( F b ) is greater than the buoyant force on the top ( F t ), which causes a torque around the center of the hourglass, rotating it against the side of the cylinder.
This pushing against the cylinder creates friction , the third force F f that explains why the hourglass stays initially at rest. The force of stationary friction between the leaning top-heavy hourglass and the cylinder is enough to counteract the constant, upwards buoyant force on the hourglass. So for the first few seconds of this GIF, the hourglass remains at rest. The force of friction balances with the upwards buoyant force until the sand distributes more evenly so the hourglass isn't top heavy, and isn't leaning against the cylinder anymore. At this point the buoyant force accelerates the hourglass up as we've already discussed.
Since this initial motion can't be explained just using the force of gravity and the buoyant force, we did accept the answer "None of the above" as correct for those who answered the problem earlier in the week.
The hourglass moves upwards as a consequence of the work done by the falling sand, practically a reaction phenomenon. Should the sand flow stop, the hourglass sinks.
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How much work do you estimate is being done by the falling sand, and how do you think it would compare to the work required to move the whole hourglass? Understanding the motion of the hourglass is a matter of force balance, not any work done by the sand.
The total upwards force of buoyancy on the hourglass doesn't depend at all on the position of the sand and whether or not it's falling. All that matters for this force is the density of the hourglass, and whether it weighs more than the water it displaces.
Well, initially the trickling of the sand seemed to somehow correlate with the buoyancy of the hourglass (clever little trick this!), so I thought perhaps the sand was invisibly reacting to something, and some of the contents were assuming a gaseous state thereby reducing the mass but that was folly. I then questioned how the hourglass was seemingly starting from a stationary position and was rising slowly and I resolved it must be lighter than the body of water but by a small margin so they probably inverted the cylinder and immediately began shooting. And there, the answer lay. The hourglass simply weighs less than the water it displaces, but the motion of the sand and degree of buoyance (speed of ascension) are matched to confuse you hahaha!
I believe you are right but by another simple matter I think that the hourglass does not rise immediately because the center of gravity in the hourglass is high making it want to flip and because the buoyancy is so low for the first few seconds of it being flipped are spent wedged within the small tube. You can see evidence of this when the hourglass is about halfway up the cylinder and it begins to shake around as the center of gravity shifts lower and it comes off the sides of the tube.
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Exactly what I was thinking. When the lower part is empty there is a torque around the center of mass. The hourglass touches the cylinder creating a friction force which is strong enough to hold the hourglass at the bottom. When the upper part is empty the system is stable, no more significant friction and the hourglass rises. I think the answer should also include an explanation why the hourglass stays still for a while at the bottom.
Don’t think so as it takes quite some time after the turn for the hourglass to move. Watch the sand build up in the bottom before it moves. I think the hour glass is top heavy and rests on the side of the glass until the c of g shifts and it releases and rises. Yes it is lighter but friction holds it at first
Buoancy alone does not explain the observation, and I'm sorry that answer is marked as the correct one. I do prefer the Greg/Lucas theory of friction holding it for the early times, because of the higher gravity center of the hour glass creating a torque that forces it to rotate and lean against the glass tube wall. As the sand runs down the gravity center lowers, allowind the hour glass to be vertical, stop touching the wall, and start rising.
in my case, I kept waiting for the hourglass to do something, but it simply sat at the bottom of the column of water
I kept on clicking on the picture to try to get it to do something, and nothing would happen
since the entire hourglass + sand was sitting at bottom of column of water, I had no indication that this was supposed to be the starting position for the movie, so I concluded that the hourglass plus sand weighed more than the water it displaced
I suspect that this is actually correct for a system where the hourglass is simply sitting at the bottom of the column of water
however, as soon as I pressed the answer button, I got the indication that the answer was wrong, and the hourglass started immediately rising - clearly indicating that my answer was in fact wrong
this it turned out that there was some buggy code present where (at least for me, on an iPhone 7, with the latest iOS) the animation did not work correctly, thus leading to the wrong answer
oh well, c’est la vie
The anwer would have been intuitive if your video had shown that the enclosed cloumn of fluid had actually been turned end on end befoe each ascent. The buoyancy of the enclosed hour galss and it's sand dosen't change by the position of the sand and air. This isn't so much a physics question as it's a 'magic' trick. It warbles becaue of the change in center of gravity. But keep them coming.
The real answer is that you can't tell from the video- it could be neutrally buoyant or positively buoyant. If it positively buoyant then why is it near the bottom at the start.
Looks like it weighed less than the water. But then it would just be a trick, and that it should've been shown just floating near the top. So, it's none of the above and instead, changing barametric pressure or temperature as evidenced by https://en.m.wikipedia.org/wiki/Galileo_thermometer
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The hourglass is buoyant and so rises, but only when enough sand falls from the top and it stops leaning on the cylinder (ie no friction).
A separate question. Would the speed of ascent be the same in open water, I wonder? Could the fact that the cylinder is only slightly larger than the hourglass be slowing the rate that the water can move around it, thereby slowing it's ascent?
Once again, Brilliant is relying on information not provided. In this case, that information is the assumed state prior to the start of the video. We must assume that the larger cylinder has just been inverted. No other solution is possible since the buoyancy of the hourglass cannot change as long as it remains fully submerged. The form of the question is designed to create a false assumption that something more complex is happening than an object floating in water.
This is the stupidest "problem" to date...
A just as likely solution is that the larger glass is suspended upside-down (from our perspective) and a string suspending smaller at the top has been released. Or magic! When.you have to dig outside of factual data, you merely disprove common theories (like displacement); however, claiming disproof of competing theories does not work to prove another theory unless the set of solutions is bounded...and these bounds are consistent with.what we can know. In short, inadequate responses to an incomplete question.
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Brilliant is a basically a riddle problem site so it has a very narrow view of problems- it is not brilliant. Brilliant would require thinking outside the forced bounds. The same thinking in math problems all other the place.
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I have REALLY tried to give this site another shot. Looks like I won't be making that mistake again.
Relevant wiki: Fluid Mechanics
The upward force exerted on a body by the liquid in which it is submerged is called Upthrust or Buoyant Force ( F B )
Buoyant Force is nothing but an upward force exerted on the body when placed in a liquid .
W = weight of the body
Case 1 :
F B < W
The body will sink .
Case 2 :
F B = W or F B > W
The body will float .
The buoyant force applied on the hourglass by the water is more than the weight of the hourglass .
Therefore, the hourglass rises in the water column .
The above picture demonstrates that if buoyant force is more than the weight of the body the body floats. But if it is less then the weight of the body the body sinks .
Note : This might be also one of the reason .
I think a more clear reason would probably this :
The sand flows from the upper section to lower section that means the upper section gets emptied while the lower section gets filled with sand . So, the air in the lower section moves and gets filled in the upper section . We know that air is less dense than water . As a result the air in the upper section forces the whole hourglass to rise in the water level .
This is the reason why an emptied water bottle floats in seas and rivers .
It's good but I would suggest to include more explanation as why this happens?Why the weight comparison matters?
I was trying to think on more of a gravitational point thinking this was actually upside down and we were being made to think it was floating
So this has nothing to do with the movement of the sand?
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Apparently nothing at all. The sand moving was to throw our reasoning off by adding an action that has no effect on the buoyancy. :-)
It does not explain why the hour glass sinks when the top is filled, but floats as the top empties into the bottom!!!!!!
To me, the question was why doesn't the hourglass rise until a percentage of sand runs into the lower chamber. The answer is friction: when all of the sand is above the air, it tries to rotate the hourglass; wedging it in-place. Once enough air migrates to the upper chamber the rotational force decreases to the point that the buoyancy is able to override the friction.
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Yeah, how is this a question about flotation? There is a clearly unique phenomenon of friction causing the hourglass movement to change as the sand changes. Weird one, brilliant.
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exactly. It was obvious about the buoyant force. The interesting part is to understand why it takes time to start floating.
I think the exact reason would probably this :
The sand flows from the upper section to lower section that means the upper section gets emptied while the lower section gets filled with sand . So, the air in the lower section moves and gets filled in the upper section . We know that air is less dense than water . As a result the air in the upper section forces the whole hourglass to rise in the water level .
This is the reason why an emptied water bottle floats in seas and rivers .
@Ram Mohith , I think there is a thrust force acting in direction opposite to the relative velocity of ejection of mass( here sand). As mass is decreasing (moving downlward) , a thrust force acts on the system which makes it flow up against the gravity in air.
By the way, is the outside surrounding of sand-dial filled with air or water?
Because in the question it is not mentioned whether sand dial is floating in air or water??
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or oil? While the sand is falling, those grains are not supported by the hourglass. If the hourglass and it's contents are almost buoyant, then while the sand is falling it could float upward, but once the entire sand load is static again, it would not, and would sink again. I doubt they thought about this possibility, and the system was merely filmed after the outer container was inverted, and it is mostly fluid viscosity against its significant buoyancy that slows its ascent.
The mass of the sand falling creates an equal and opposite upward force (Newton). The hourglass has a near-neutral buoyancy, and the small reaction force of the sand is sufficient to cause it to float, as long as the sand is falling.
So it does have to do with the distribution of the sand in the hourglass which was marked wrong! I don't always agree with the solutions to these problems/
Another factor that needs to be considered is the Center of Buoyancy vs. the Center of Gravity of the hourglass. The shape of the water displaced is constant and symmetrical, so the CoB is always at the neck of the hourglass. But the CoG will move as the sand flows. When it is initially flipped, the CoG is in the top bulb, above the CoB, so the whole hourglass is being twisted and wedged against the side of the tube, and friction holds it in place. But as the sand flows, the CoG moves down, and when it is below the CoB, the hourglass self rights, freeing it from the side, allowing it to float. So the answer they wanted is only partially correct.
The air movement doesn't affect the system because the air in the system is constant. Whether the sand is at the top part of the hourglass or at the bottom part of the hourglass, mass of the system is the same hence same weight.
The movement of the sand is not relevant to the buoyancy of the hourglass.
The hourglass is immersed in a mixture of two colourless liquids with different densities: one denser than the hourglass, and one less dense. When the assembly is inverted, the denser liquid finds itself at the top of the tube, above the less dense liquid - an unstable situation. The two liquids eventually change place. Because the hourglass is less dense than the denser liquid, as the heavier liquid pools at the bottom of the tube, the hourglass will begin to float upwards. It continues to rise until the denser liquid is all at the bottom of the tube, and the less-dense liquid is at the top.
The shape of the hourglass slows down the flow of the liquids.
To minimise the opportunity for observers to see the boundaries between the liquids, the two liquids should have similar refractive indices.
Wowsers, that's quite an interesting answer! Very well thought-out and definitely out-of-the-box logic! Good going :)
John -- where do you get the facts for that idea ?
So you agree that it has to do with the distribution of the sand?
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No, the distribution of the sand does not affect the buoyancy of the hourglass. The (net) buoyancy is affected by the volume of the hourglass and its weight. Neither of these quantities changes throughout the experiment. In particular, the motion of the sand affects neither the volume nor the weight.
The buoyancy of the hourglass is analogical to the swim bladder of a fish.
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From wikipedia Swim Bladder: "By adjusting the gas pressurising organ using the gas gland or oval window the fish can obtain neutral buoyancy and ascend and descend to a large range of depths." There is no way that the hourglass density can change. The glass is rigid, and no air or sand can enter or leave.
Positive buoyancy is the obvious part. But why the delay in ascent after flipping? I'd guess there is some friction between the hourglass and cylinder. The, at first, top-heavy hourglass leaned on the cylinder until enough sand fell reduced friction.
Correct, Farron. https://youtu.be/kctdo6rQZbY
I had the same idea for the answer. Firstly the time, secondly surface of the sand at the beginning was not flat.
Thank you @Frederic Friedel ! I was going to post that video if no one else had.
Easy, this is due to Buoyancy or Upthrust. When a body floats on a liquid, then the displaced part of the liquid is equal to the weight of the body. If the body is submerged with the help of an external force, the water displaced weighs more than the body, thus increasing the force upwards and the body regains its original position. The hourglass comes up since it is displacing more water than it actually weighs.
when the sand drops to the lower portion it loses potential energy so the glass moves up to increase its potential energy the same amount.
so, why doesn't the hourglass rise until a percentage of sand runs into the lower chamber?
there were no external forces involved here, hourglass first drowns of its own weight stays at momentary rest , then after a certain fraction of sand is dripped down , it rises up . what you explained is a case where mass of the body remains unchanged , at the point of application of force, like that of a small ball .
The hourglass is a closed system. No matter what action it happened inside, the total mass are the same. It floats if it is lighter, sink if it is heavier.
Why was it stuck in the beginning? Surface tension?
Maybe temperature is a factor.
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Amedeo asked the right question... Why was it (i.e. the hour glass and the sand in it) stuck in the beginning?
We know It floats to the top simply because it is lighter than the water it displaces BUT.... why did it not float to the top at the beginning, that's the question.
I don't think the delay in rising to the top is to do with surface tension of temperature because they don't change.
Is it to do with the downwards force of the sand impacting on the lower bulb cancelling out the upwards buoyancy force at the beginning? If so, then why does it start to rise whilst the sand is still falling?
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It's highly doubtful that the hourglass is stuck (there is no friction). If you look at both the movement of the hourglass and that of the sand, you will see what is most likely a 'jump' in the picture frames; the frame holds steady at the initial condition - then jumps to several frames later where you see the sand in the hourglass has already descended a bit and the hourglass has already ascended a bit. It is a matter of the camera - not friction or being 'stuck'.
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@Jesse Otis – Update: They have changed the video on that; now the cylinder is not turned over and video is played in a loop; the picture frame sequence does not 'jump'. As such, a pictorial suggestion of a stuck hourglass has been eliminated.
So they can mislead you into getting it wrong by tricking you into thinking the sand flowing is correlated with the rising when it’s not.
Hi @Amedeo Amato, good observation. This clip is from a longer video. Before the hourglass starts to rise, it's leaning slightly against the glass wall, which provides some friction, in addition to its weight, that keeps it down. As the sand falls into the bottom, the hourglass straightens out and stops leaning against the wall, at which point it starts to rise. We wanted to focus on what's happening after it begins to rise. Unfortunately, we left that small section at the beginning where the hourglass is still leaning for a moment. I've updated the animation to show only the rise.
What if there was no water, just air and what if there was a perfect seal between the hour glass and the chamber and what if the hour glass did still rise? Would a solution still exist!
Could the sand contain a nuclear isotope that generated heat and caused the air below to expand as the air above contacted as the heat source moved from top to bottom....might that have been a more interesting question?
I had a bit of a hard time figuring out what this hourglass does.
It's actually got two actions. At the end of its cycle, the sand is in the bottom of the normal sandglass and the sandglass has floated to the top of the outer tube. TO RESET THE HOURGLASS, FLIP THE ENTIRE OUTER TUBE OVER.
Now the sand flows to the bottom of the sandglass and the sandglass floats to the top of the outer tube. So the liquid is denser than the whole sandglass with sand and air in it. The sand's position doesn't effect the sandglaass's mass, which is constant. The sandglass moves up slowly because because the liquid is moving through tight gaps between the widest parts of the sandglass and the inner wall of the tube. The two actions have nothing to do with each other.
Lol I first saw the viDeo of the hourglass descending downward. My thought would be to try the experiment myself. To rule out temperature playing a role or the air emptying from the top is pulling towards the surrounding air. I’m going to study what this buoyancy law is.
An interesting extension question is how the motion of the sand affects the motion of the hourglass (if at all.) In other words, if all the sand started at the bottom, would it rise faster, slower, or same?
Do not discuss in this space. I think Matin should submit as a separate problem.
I got that it was because of buoyancy. But I have a question. If the hourglass was not flowing, or if it were another container with equal volume, the same amount of sand, and the same amount of glass, would it still float or does it depend on the flow of sand? I would assume that it would still float as the relative density would be the same. Am I mistaken or does the floating hinge on the sand?
The cause of the hourglass floating is the fact that there is want in the tube and air in the glass the sand is light weight and with the air inside of the hour glass causes it to float
Thanks! That really helped. Would it float without the flow of sand, though?
Something that I have noticed in the illustration above that the hourglass neither rises from its's initial position and somewhere sticks to the bottom of the glass unless it gets filled with certain amount of sand in the lower bulb and so when it reaches the upper layer of the tube it again sticks when the lower bulb is heavy with the sand and the upper bulb is light.In the former case the bulb stick to the bottom because of the heavy weight of the upper bulb and at the top it sticks because of the light upper bulb.So the main crux of the situation lies with the upper glass bulb as the * upper bulb keeps displacing the water in order to rise * .If we carefully notice that the upper hourglass is at play and it rises by dripping all the sand in the lower glass bulb hence rising in the water tube due to buoyancy.
Hi @erica phillips , you're right that there was something more going on in the animation you saw. This clip is from a longer video. The way this contraption works is that when the sand is in the top, it's top heavy and leans slightly against the glass wall. That provides some friction, in addition to its weight. The force of friction plus the pull of gravity exceeds the buoyant force from the water.
As the sand falls, the center of mass of the hourglass gets lower, and the hourglass straightens out, stops leaning against the wall. Without that friction, the buoyant force is greater than its weight, and the hourglass it starts to rise. We wanted to focus on what's happening after it begins to rise. Unfortunately, we left that small section at the beginning where the hourglass is still leaning for a moment. I've updated the animation to show only the rise.
Ohhh I thought so. Yay. Lol.
I think it's just like the glitter in those tubes. If you put them upside down it will float to the upper end :)
The mean density of polymer glass, sand and air of hourglass is less than density of water.
According to the principles of Archimedes and flotation a body displaces its own weight of th fluid in which it is placed.Therefore the weight of the hourglass in water is counterbalanced by upthrust. So its weight is less than that of water so it rises.the distribution of sand will act the same in whatever position as weight acts downwards
The motion of the sand inside the hourglass was just a simple diversion to fool our minds. Furthermore the speed of the rising hourglass doesn't depend on the rate of shifting sand. Just a simple application of fluid mechanics. The video must have been shoot after inverting the hourglass .
It isn't actually the weight of the hourglass but rather it's density.
This problem has proved divisive in the solution comments, but the answer that most accurately explains the motion of the hourglass is the hourglass weighs less than the water it displaces .
What's going on here?
In this GIF we can see that the hourglass is floating from the bottom of the cylinder to the top. The important implicit assumption here is that the cylinder was likely just inverted , which is why the hourglass starts on the bottom, even though it clearly floats.
The forces in play
The basic idea when analyzing whether or not an object like an hourglass floats is looking at the interplay between two forces: The buoyant force is equal to the weight of the water displaced by an object, and the force of gravity is equal to the weight of an object. These two forces act in opposite directions: the weight of an object pulls it downwards (towards the Earth), and the buoyant force pushes it upwards. The total force on the object will be the sum of these two forces.
If the object is less dense than water, then the weight of water it displaces (the buoyant force) will be greater than its own weight (the force of gravity). The total force will then be in the upwards direction since the buoyant force is greater than gravity's pull. Similarly, if the object is more dense than water, then the total force will be in the downwards direction.
What does the GIF show?
The GIF shows the hourglass accelerating in the upwards direction, meaning the total force acting on the hourglass must also be in the upwards direction. Simply stated, the hourglass is floating , so the buoyant force is overcoming the force of gravity. This means that the hourglass must weigh less than the water it displaces.
But what's going on with the sand??
In the GIF we've been looking at so far, the movement of the sand is not relevant to the motion of the hourglass. Whether or not the hourglass as a whole floats depends only on its density, which is unchanged whether the sand is in the top or the bottom.
This is a different GIF, which was shown briefly earlier in the week during editing of the problem (sorry everyone!).
In this case, the hourglass appears to sit at rest on the bottom of the cylinder until a certain amount of sand moves from the top to the bottom, at which point it begins to accelerate upwards thanks to the buoyant force. We've already stated that the buoyant force must be the same no matter the arrangement of sand, so what's going on here?
The initial motion
To understand this initial motion , we have to consider forces other than gravity and buoyancy. When the hourglass starts on the bottom in the second GIF, you might be able to notice that it's at a slight angle, and leaning against the side of the cylinder. This is because with all the sand in the top of the hourglass, it's top-heavy, meaning the density of the top is higher than the density of the bottom. So in this case the buoyant force of the bottom of the cylinder ( F b ) is greater than the buoyant force on the top ( F t ), which causes a torque around the center of the hourglass, rotating it against the side of the cylinder.
This pushing against the cylinder creates friction , the third force F f that explains why the hourglass stays initially at rest. The force of stationary friction between the leaning top-heavy hourglass and the cylinder is enough to counteract the constant, upwards buoyant force on the hourglass. So for the first few seconds of this GIF, the hourglass remains at rest. The force of friction balances with the upwards buoyant force until the sand distributes more evenly so the hourglass isn't top heavy, and isn't leaning against the cylinder anymore. At this point the buoyant force accelerates the hourglass up as we've already discussed.
Since this initial motion can't be explained just using the force of gravity and the buoyant force, we did accept the answer "None of the above" as correct for those who answered the problem earlier in the week.