Does Buoyant Force Demonstrate Newton's Third Law?

[MRose]

Would it be accurate to explain to 8th grade students that buoyant force illustrates Newton's third law in that gravity exerts a downward force on a fluid and the fluid, in turn, exerts an equal and opposite force on earth? Further explaining that since it is a fluid, that the reactive force occurs not just downward but in all directions including upward. I need to make a strong connection between gravity and buoyancy without getting too heavily into formulas. I know that pressure and depth are part of this system but am not sure that I need to integrate these variables in the introductory portion of the topic.

Thank you for any insight that you can provide.

 

[Chen]

I would explain it with different pressures at different depths. If you have a box of height H submerged into liquid, the pressure on its top side is different than the pressure on its bottom side. This is what causes buoyancy, and you can probably explain it to your students in 45 minutes or less. You would have to start off by explaining the meaning of pressure, continue by showing what the pressure is inside a liquid and how it changes as you go deeper and deeper into the liquid. From there it's easy enough to show how the different pressures can describe the buoyancy force.

 

[arildno]

No, you should not make reference to Newton's third law.
The best way to illustrate buoancy without a lot of maths, is Stevin's method:
1. Imagine a portion of the fluid at rest (placed somewhere in the fluid)
This fluid part is acted upon by gravity, but all the same, it remains at rest.
By Newton's 2.law, it has to exist some other force to effect this situation; we call this force the force of buoyancy.

2.What is the object that produce the force of buoyancy?
Surely, it must be the water surrounding the portion you are looking at (there's no other "objects" around..).

3. What happens if we submerge an object into water?
Surely, the surrounding water couldn't care less if that object consists of water or anything else.
Hence, on any object submerged (in a fluid at rest), the buoancy force must equal the weight of the displaced water volume, acting upwards.

I don't know if this is too difficult for 8'th graders to follow, but I hope this was helpful for developing your own ideas.

 

[ZapperZ]

Would it be accurate to explain to 8th grade students that buoyant force illustrates Newton's third law in that gravity exerts a downward force on a fluid and the fluid, in turn, exerts an equal and opposite force on earth? Further explaining that since it is a fluid, that the reactive force occurs not just downward but in all directions including upward. I need to make a strong connection between gravity and buoyancy without getting too heavily into formulas. I know that pressure and depth are part of this system but am not sure that I need to integrate these variables in the introductory portion of the topic.

Thank you for any insight that you can provide.

I would explain it with different pressures at different depths. If you have a box of height H submerged into liquid, the pressure on its top side is different than the pressure on its bottom side. This is what causes buoyancy, and you can probably explain it to your students in 45 minutes or less. You would have to start off by explaining the meaning of pressure, continue by showing what the pressure is inside a liquid and how it changes as you go deeper and deeper into the liquid. From there it's easy enough to show how the different pressures can describe the buoyancy force.

I'm afraid that I will have to disagree with Chen on this. Telling the students of a pressure differential doesn't explain why the boat floats. And since the elementary calculation of buoyancy itself involves only the volume of displaced fluid (and nothing on pressure differentials), I don't see how this will aid in their understanding.

What you initially wanted to do sounds reasonable. Just tell the students

"Look, boat floats on water. Boat is not sinking even though it has a weight or a force pulling it downards. There must be something "supporting" it or pushing it upwards by the same amount as its weight. Since the only thing boat is in contact with is the water, then the only source of this supporting force comes from the water. We call this supporting force the buoyant force."

If those brats complain that this is just way too superficial, throw at them a copy of Halliday and Resnick. :)

Zz.

 

[Chen]

ZapperZ, but if you forcibly submerge the boat into the water and let it go, why does it float up? The calculation of buoyancy actually does represent the different in pressure, because the volume of the submerged object depends on its height, which in turns changes the pressure difference.

 

[ZapperZ]

ZapperZ, but if you forcibly submerge the boat into the water and let it go, why does it float up? The calculation of buoyancy actually does represent the different in pressure, because the volume of the submerged object depends on its height, which in turns changes the pressure difference.

It floats up because the amount of displaced fluid (the TOTAL volume of the object) produces at NET upward force. When it reaches the top, the amount of displaced fluid is no longer the total volume of the object, but rather the volume BELOW the water line.

If you happen to have an object that barely float at the surface when the top surface is at the same level as the water level, then it will float even under water without having to force it. The difference in pressure isn't as significant here until you have a noticeable difference in the DENSITY of the fluid itself due to the weight of the volume of water above it.

Zz.

 

[MRose]

All of replies have been very helpful. Thank you. Perhaps I did not ask the question as clearly as I could have. What I would like to do is tie the students' developing understanding of gravity's influence on matter with the concept of why fluids have this property called buoyancy. I'm not so much going to try to explain why a boat floats, just yet. I was hoping to build on what they know about gravity, motion, and density and move toward a discussion of buoyancy and pressure. What do you think? They will be doing a hands-on activity using a spring scale and mass suspended in water to observe the apparent change in weight of an object before and as it is suspended in water. The activity will be used to illustrate the concept of gravity's effect on an object in air and how that buoyancy changes the observed effect.

 

[ZapperZ]

All of replies have been very helpful. Thank you. Perhaps I did not ask the question as clearly as I could have. What I would like to do is tie the students' developing understanding of gravity's influence on matter with the concept of why fluids have this property called buoyancy. I'm not so much going to try to explain why a boat floats, just yet. I was hoping to build on what they know about gravity, motion, and density and move toward a discussion of buoyancy and pressure. What do you think? They will be doing a hands-on activity using a spring scale and mass suspended in water to observe the apparent change in weight of an object before and as it is suspended in water. The activity will be used to illustrate the concept of gravity's effect on an object in air and how that buoyancy changes the observed effect.

So you'll have the kids do an experiment resembling these:?

http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/dens.html
http://www.seed.slb.com/en/lab/buoyancy/

Sounds like a worthwhile exercise. The change in weight should tell them something.

Zz.

 

[MRose]

Yes. They already have some experience with density by doing an experiment similar to the water displacement activity described in the first link. And they will be performing the activity described in the second link. I'm trying to develop my understanding of these concepts to be able to communicate the connection between gravity and bouyancy in a way that my students will understand.

 

[Chen]

It floats up because the amount of displaced fluid (the TOTAL volume of the object) produces at NET upward force. When it reaches the top, the amount of displaced fluid is no longer the total volume of the object, but rather the volume BELOW the water line.

Yes, I know all of that, but how are you going to explain it to the kids? "That's just how it works" is not going to cut it. Why does "the amount of displaced fluid (the TOTAL volume of the object) produces at NET upward force"? I always believed that when explaining something you need to build it from the ground up, otherwise the students' understanding of the issue is shaky. Just look at the homework forum here! A good and thorough explanation is required, so if someone asks the student how it works, he can reply with an intelligent answer rather than "That's what I've been told, God knows why it works like that."

 

[Chen]

Yes. They already have some experience with density by doing an experiment similar to the water displacement activity described in the first link. And they will be performing the activity described in the second link. I'm trying to develop my understanding of these concepts to be able to communicate the connection between gravity and bouyancy in a way that my students will understand.

MRose, you can begin by explaining how gravity affects the water. Maybe use some real-life analogy the students can relate to more easily. For example, imagine a high tower of kids standing on one another. The kid at the top will not feel any force, because there's nothing above him. The 2nd kid will feel the weight of one kid, and 3rd kid will feel the weight of two kids, etc. The kid at the very bottom will feel the biggest force, since all of the other kids are above him.

So now that they understand how gravity affects the molecules in water, they should be able to understand the forces that every water molecule is feeling inside the container. You also need to make a point, that all water molecules at the same level will feel the same force. Now you can introduce the concept of pressure, which is pretty easy to explain. Finally, throw in a plastic cube into the container, and explain to them what forces each side of the cube experiences (most important are the top and bottom sides; you can ignore the others, or just say that the forces there cancel thanks to symmetry).

I don't know, seems pretty simple for me. With good examples they should be able to understand it in a couple of lessons.

 

[Doc Al]

It floats up because the amount of displaced fluid (the TOTAL volume of the object) produces at NET upward force. When it reaches the top, the amount of displaced fluid is no longer the total volume of the object, but rather the volume BELOW the water line.

I will side with Chen on this one. The buoyant force equalling the weight of displaced fluid is a result, not a fundamental reason. After all, how can "displaced fluid" mysteriously exert an influence on a submerged body?

The fundamental reason for buoyant force is the difference in pressure.

If you happen to have an object that barely float at the surface when the top surface is at the same level as the water level, then it will float even under water without having to force it. The difference in pressure isn't as significant here until you have a noticeable difference in the DENSITY of the fluid itself due to the weight of the volume of water above it.

I don't know why you say the difference in pressure is not significant in this case: That's the only thing creating the buoyant force! The fluid pushes all sides of the object--that net force is the buoyant force. (If the top is exposed to air, that just means that the object is really submerged in two fluids, but the same ideas hold.)

Note: As I write this I see that Chen has expanded his answer.

 

[ZapperZ]

I will side with Chen on this one. The buoyant force equalling the weight of displaced fluid is a result, not a fundamental reason. After all, how can "displaced fluid" mysteriously exert an influence on a submerged body?

The fundamental reason for buoyant force is the difference in pressure.


I don't know why you say the difference in pressure is not significant in this case: That's the only thing creating the buoyant force! The fluid pushes all sides of the object--that net force is the buoyant force. (If the top is exposed to air, that just means that the object is really submerged in two fluids, but the same ideas hold.)

Note: As I write this I see that Chen has expanded his answer.

In my original response to this, I wrote:

"And since the elementary calculation of buoyancy itself involves only the volume of displaced fluid (and nothing on pressure differentials), I don't see how this will aid in their understanding."

Note that I said ELEMENTARY calculation of buoyancy. Even at the Halliday-Resnick level of intro physics, there are no calculation of buoyancy that involves pressure differentials. I didn't say fluid pressure plays zero part in the outcome of buoyancy. However, look at all the typical problem given in questions such as this. I do not recall ever seeing that you need to consider pressure difference as a necessary step in such calculations. Thus, if you only need to consider the fluid density, and the displaced volume as the ONLY criteria in describing the buoyant force, introducing "pressure differentials" at this particular stage is an uncessary complication. I do not see why it has to be introduced here. Where does it come in when I calculate the buoyant force?

Yes, I know all of that, but how are you going to explain it to the kids? "That's just how it works" is not going to cut it. Why does "the amount of displaced fluid (the TOTAL volume of the object) produces at NET upward force"? I always believed that when explaining something you need to build it from the ground up, otherwise the students' understanding of the issue is shaky. Just look at the homework forum here! A good and thorough explanation is required, so if someone asks the student how it works, he can reply with an intelligent answer rather than "That's what I've been told, God knows why it works like that."

When you "displace" the fluid, as in submerging it in a column of water, that volume is displaced "vertically". You can easily explain that this is the same as "lifting" that volume upwards. It is this weight you are displacing that provides the necessary counter force. There isn't any need to invoke "pressure differentials" here.

Look, as a physicist, I like nothing more than having as deep of an explanation as we can get. But unless I miss completely the whole issue here, this thing is meant for what.. grade 8 kids? I can bet you that when they calculate buoyant force at this stage, you will NOT see any "pressure differentials" involved in either the calculation, or explanation. It is because of that that I question the need to introduce pressure differentials as the explanation for the existence of buoyant force. If we want to complicate things, why just stop there? Why not invoke the whole of thermodynamics (pressure is a thermo state variable, after all) along with it if we want a "complete" explanation.

Zz.

 

[jdavel]

MRose

Here's what I'd do.

Get a transparent plastic tube (about 2 feet long and about about 2 inches in diameter) and glue a plastic cover over one end (the bottom). Then drill two rows of finger-sized holes along opposite sides from the bottom to the top. Also drill one up through the cover you glued on the bottom. Next glue pieces of balloon rubber over each hole (don't stretch the rubber, but be sure the glue joint is good and strong, especially on ones near the bottom!).

Now fill the tube with water and have the students press the balloon diaphragms in with their finger to see which ones require more or less force This should show them that pressure increases with depth, and doesn't depend on whether it's applied from the right or the left. In particular have them compare the side holes very near the bottom, with the hole that's really on the bottom by lifting the tube up so they can push on this one too. This should show them that pressure exerts the same force in all directions, even vertically.

Finally, show them a picture of a submerged cube with force arrows representing pressure on the left, right, top and bottom sides. Have them tell you the relative magnitudes (strength) of each force. Then ask them whether the net force from all the pressure arrows is up or down. Then ask them what would have to be true about the weight of the cube for it to float up? For it to sink?



The problem with explaining all this with the diplaced volume method is that all you can do is draw a force arrow pushing up on the bottom of the object and then say "this force comes from a thin layer of water spread over the entire surface of the body of water that the object is in. So if an object is in the ocean, some of the displaced water that's "causing" this force is thousands of miles away; that's hard to explain! Don't get me wrong; the answer works out the same, but I don't thing they'd understand it.

 

[Chen]

...of course, don't call it a diaphragm in front of the kids! God knows they will go home that day and tell their family about it: "Mommy mommy, today the teacher showed us diaphragms! And we touched them too! It was so cool."

 

[Doc Al]

Sorry if I seem to want to beat this horse to death, but I can't help myself.

"And since the elementary calculation of buoyancy itself involves only the volume of displaced fluid (and nothing on pressure differentials), I don't see how this will aid in their understanding."

Note that I said ELEMENTARY calculation of buoyancy. Even at the Halliday-Resnick level of intro physics, there are no calculation of buoyancy that involves pressure differentials. I didn't say fluid pressure plays zero part in the outcome of buoyancy. However, look at all the typical problem given in questions such as this. I do not recall ever seeing that you need to consider pressure difference as a necessary step in such calculations. Thus, if you only need to consider the fluid density, and the displaced volume as the ONLY criteria in describing the buoyant force, introducing "pressure differentials" at this particular stage is an uncessary complication. I do not see why it has to be introduced here. Where does it come in when I calculate the buoyant force?

If all you want to do is calculate buoyant force, then you are of course correct. But if you want to understand buoyant force, you must first understand the concepts of force and pressure. I have an old copy of H-R right in front of me. When they introduce Archimedes principle they make it very clear that buoyant force is due to pressure differences. And they give a simple argument to show that the resultant force due to these pressure differences is equal to the weight of displaced fluid. Of course, once Archimedes principle is derived one is free to use it without having to derive it each time.

I strongly doubt that 8th graders will be able to understand these arguments. I also wonder what the point is of teaching them to calculate something that they won't really understand. (But I have to admit that I was able to calculate many things long before I understood them!)

When you "displace" the fluid, as in submerging it in a column of water, that volume is displaced "vertically". You can easily explain that this is the same as "lifting" that volume upwards. It is this weight you are displacing that provides the necessary counter force.

Hmmm... so when I put the rock in the water, the rock pushes the water up. Thus the water must push the rock down! Ah... so buoyant force is negative!

Just kidding!

 

[ZapperZ]

Hmmm... so when I put the rock in the water, the rock pushes the water up. Thus the water must push the rock down! Ah... so buoyant force is negative!

Just kidding!

Oy vey... I'd rather teach the kids about diaphrams! :)

Zz.

 

[jdavel]

...of course, don't call it a diaphragm in front of the kids! God knows they will go home that day and tell their family about it: "Mommy mommy, today the teacher showed us diaphragms! And we touched them too! It was so cool."

...and Joey poked one so hard it broke, and water went all over the floor!

 

[Chen]

...and Joey poked one so hard it broke, and water went all over the floor!

...but we weren't done yet, so at the absence of rubber we poked the hole with our bare finger to see what it feels like inside!

 

[LURCH]

MRose,
Have you had your class yet? If so, how did it go? If not, I think Zapperz's explanation of bouyancy is your best shot for 8^th graders, and certainly the most direct link between gravity and bouyancy. They alerady know Archemede's principle (displacement), yes? Put something in water, and the water rises. Gravity is pulling down on both the object and the water. Whichever is heaviest (the object or the water it displaces) will sink to the bottom, and the other will rest on top. A cc of wood displaces a cc of water; the cc of water weighs a gram, a cc of wood is lighter than that, so the water is pulled down and the wood forced up to rest on top. A cc block of iron weighs more than a gram, so it falls to the bottom and the water rests on top of it. It's just gravity pulling on two things at once, and these two weights work against each other.

 

[MRose]

MRose,
Have you had your class yet? If so, how did it go? If not, I think Zapperz's explanation of bouyancy is your best shot for 8^th graders, and certainly the most direct link between gravity and bouyancy. They alerady know Archemede's principle (displacement), yes? Put something in water, and the water rises. Gravity is pulling down on both the object and the water. Whichever is heaviest (the object or the water it displaces) will sink to the bottom, and the other will rest on top. A cc of wood displaces a cc of water; the cc of water weighs a gram, a cc of wood is lighter than that, so the water is pulled down and the wood forced up to rest on top. A cc block of iron weighs more than a gram, so it falls to the bottom and the water rests on top of it. It's just gravity pulling on two things at once, and these two weights work against each other.

I cannot thank you all enough for helping sort through this. I haven't taught it just yet as the kids are just coming back from their Easter breaks. However, your insights and humor have made the synthesis a whole lot easier. Many thanks to you all.

 

[Integral]

The pressure differential buoyant force would be very easy to test, even in an 8th grade class room. Simply take a rectangular piece of wood, measure the buoyant force in different orientations. Is there a measurable difference? If you use say a .25m length of 2X4 I would think that if pressure differential was a significant factor you should be able to observe it.

 

[Doc Al]

The pressure differential buoyant force would be very easy to test, even in an 8th grade class room. Simply take a rectangular piece of wood, measure the buoyant force in different orientations. Is there a measurable difference? If you use say a .25m length of 2X4 I would think that if pressure differential was a significant factor you should be able to observe it.

I'm not sure what you mean by "pressure differential" buoyant force. Unless my understanding of buoyant force is waaay off, all buoyant force is due to differences in pressure.

 

[Integral]

I am simply proposing an experiment to measure the difference. 3 hooks in a .25m long section of 2X4 one centered on each axis of symmetry. Find the mass that gives the block neutral buoyancy in each axis. There should be a significant difference between the force when submerged in the long direction vs the shortest.

Is this what determines the equilibrium position?

 

[Doc Al]

There should be a significant difference between the force when submerged in the long direction vs the shortest.

The buoyant force should be exactly the same whatever the orientation. (Of course the stability of the floating object depends on the orientation.)

 

[avin]

what happens when a tin box of same average density as of a liquid is immersed in the liquid. will the tin box remain suspended at that depth or will come up to the surface?

 

[JohnDubYa]

Systems (such as the combined boat and water) want to minimize potential energy, which means that systems like to evolve so that heavier objects are lower to the ground.

Now consider a boat floating on the water. If this same boat was submerged, than a corresponding amount of water would have to rise above it to fill in the hole that it originally displaced. But since this water weighs more than the boat, that would represent a system of high potential energy. But systems want to LOWER potential energy. So the boat doesn't sink.

 

[Doc Al]

neutral buoyancy

what happens when a tin box of same average density as of a liquid is immersed in the liquid. will the tin box remain suspended at that depth or will come up to the surface?

Since the net force on the tin box will equal zero (its weight is exactly balanced by the buoyant force) it will remain suspended. This is called neutral buoyancy.

 

[avin]

Since the net force on the tin box will equal zero (its weight is exactly balanced by the buoyant force) it will remain suspended. This is called neutral buoyancy.

Doc, this is the logical answer as per the Archemedies principle. However, few books give the answer that the tin box would rise to the surface. The explanation for the same is not given in those books.

 

[Doc Al]

Doc, this is the logical answer as per the Archemedies principle. However, few books give the answer that the tin box would rise to the surface. The explanation for the same is not given in those books.

You can't believe everything you read.

Can you give me an example of a book claiming this?