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Archimedes' principle

Bottom Feeder

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#1
Waaaaay back in 2009 I demonstrated the Archimedes' principle of determining density. About a month after that post we had the April Fool’s Day reset. Four or five hours of work gone in an instant. I'm sure I was not the only one disappointed by that move. Now I’m retired and have a bit more time on my hands so I thought maybe I would try it again (hope we don’t go TU again after this) with silver this time instead of a gold maple leaf.

I purchased this pretty little dog a couple years ago and I decided to check it’s density to see if was indeed 925 sterling.

Dog Silver R.jpg

First I calculated what it should come out to; the dog weighs 76.5 grams. The density of silver is 10.49 gm/cm³ — So the dog must be around 7.3 cm³ of silver. Therefore, suspended in water, it should displace 7.3 cc of water, which weighs 7.3 grams. If it displaces 8 grams of water, then it is 8 cc in volume and 8 times 10.49 gm/cm³ will get you what that 8 cc of silver should weigh or 83.92 grams, which would indicate that it wasn't silver.

The setup
1 - setup.jpg

Dog, plastic cup of water, scale and support device​
The dog's weight
2 - dog weight.jpg

76.50 grams of whatever...​
Then weigh and tare the cup of water

3 - Water.jpg

The dog needs to be suspended with a small thread to immerse it in the water

4 - Dog Suspended.jpg

The dog suspended above the water

5 - Ready.jpg
now I lower it into the cup

6 - Dog Immersed.jpg

And read the resulting increase in weight: 7.43 grams. This is the result of the displacement of 7.43 cc of water (density of water 1 gm/cm³). Therefore the total volume of the dog is 7.43 cc. I know for some of you science deniers out there won't be able to get your head around this but, trust me — it's correct.

The dog comes in at 10.3 gm/cm³ Since 925 sterling is 10.37 gm/cm³ I would say that the dog is 925

Because lead density is 11.3 gm/cm³, if the dog was silver plated lead the volume of 7.43 would weigh 83.96 grams (which it don’t). As well, as lead is much softer than 925 you could easily bend, say, a leg (which I can’t with my fingers) further identifying it. One of the closest look-alikes for silver is Nickel Silver (AKA German Silver) but since it has a density of 8.69 gm/cm³ it would make the measured volume of the dog weigh around 64.57 grams (which it don’t).

My balance has a limited capacity of 200 grams, but it was the best I could afford that had resolution down to 0.01 grams. So It has some limits. The temperature and physical makeup of the water has some small diversions in in but I would not recommend using other stuff for testing, such as:

Everclear.jpg

Throws the density off somewhat :Happy::Happy:

BF
 

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#2
Now try that with a 1964 quarter and a 2017 quarter, we will need to test silver coins if TSHTF.
 

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Now try that with a 1964 quarter and a 2017 quarter, we will need to test silver coins if TSHTF.
A silver quarter = 6.25 grams
Since 1965 they weigh 5.670 grams

So if it looks like a quarter, rat, just weigh the damn thing, it shouldn't be that tough to tell.
However, if you try to check density on a 6.25 gram chunk of silver all I can say is "Good luck."

BF
 

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You didn't account for the thread holding up the dog. That displaced some liquid.

Accuracy matters in these things... :judge
 

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You didn't account for the thread holding up the dog. That displaced some liquid.

Accuracy matters in these things... :judge
Believe it or not boss, but I used the thinnest thread and cut the bitter end off at the knott to reduce the error. But a little silver polish in between the toes will throw it off just as much as that tiny-assed thread would. :Happy:

And ya gotta limit the results to your original measurement accuracy (0.01), none of this divide by four to get 0.0025 accuracy in the results, ya know. So, all in all, with the resolution on my scale the thread don't account for diddily.
BF
 

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Waaaaay back in 2009 I demonstrated the Archimedes' principle of determining density. About a month after that post we had the April Fool’s Day reset. Four or five hours of work gone in an instant. I'm sure I was not the only one disappointed by that move. Now I’m retired and have a bit more time on my hands so I thought maybe I would try it again (hope we don’t go TU again after this) with silver this time instead of a gold maple leaf.

I purchased this pretty little dog a couple years ago and I decided to check it’s density to see if was indeed 925 sterling.


First I calculated what it should come out to; the dog weighs 76.5 grams. The density of silver is 10.49 gm/cm³ — So the dog must be around 7.3 cm³ of silver. Therefore, suspended in water, it should displace 7.3 cc of water, which weighs 7.3 grams. If it displaces 8 grams of water, then it is 8 cc in volume and 8 times 10.49 gm/cm³ will get you what that 8 cc of silver should weigh or 83.92 grams, which would indicate that it wasn't silver.

The setup
View attachment 116320
Dog, plastic cup of water, scale and support device​
The dog's weight
View attachment 116321
76.50 grams of whatever...​
Then weigh and tare the cup of water


The dog needs to be suspended with a small thread to immerse it in the water


The dog suspended above the water

now I lower it into the cup


And read the resulting increase in weight: 7.43 grams. This is the result of the displacement of 7.43 cc of water (density of water 1 gm/cm³). Therefore the total volume of the dog is 7.43 cc. I know for some of you science deniers out there won't be able to get your head around this but, trust me — it's correct.

The dog comes in at 10.3 gm/cm³ Since 925 sterling is 10.37 gm/cm³ I would say that the dog is 925

Because lead density is 11.3 gm/cm³, if the dog was silver plated lead the volume of 7.43 would weigh 83.96 grams (which it don’t). As well, as lead is much softer than 925 you could easily bend, say, a leg (which I can’t with my fingers) further identifying it. One of the closest look-alikes for silver is Nickel Silver (AKA German Silver) but since it has a density of 8.69 gm/cm³ it would make the measured volume of the dog weigh around 64.57 grams (which it don’t).

My balance has a limited capacity of 200 grams, but it was the best I could afford that had resolution down to 0.01 grams. So It has some limits. The temperature and physical makeup of the water has some small diversions in in but I would not recommend using other stuff for testing, such as:


Throws the density off somewhat :Happy::Happy:

BF
Cute pooch!
 

michael59

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#9
So BF I am just not getting it. You are going on displaced water correct? Then where is your graduated cylinder?

Remember you are weighing the displaced water so you have to know how much water has been displaced. Knowing the volume displace it is calculated the mass of water in the volume that is the determining factor.

I would think that the glass should be full and the doggie dropped in and then then all the water that is displaced by the doggie will be on the glass and on the scale then if the glass with the doggie still in it is removed the water still on the scale is very representative of said displace water.
 

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Look at it like this, michael; the dog is trying to 'float' in the water (you know it would sink to the bottom and that's why you suspend it). It is actually pressing down on the balance with 7½ grams of pressure trying to 'float'. To actually be able to float, an item of that volume (7½ cc) would have to weigh a tiny bit less than 7½ grams. And when you dropped that in the water the balance would indicate you have added an extra (about) 7½ grams of 'something' to the cup of water.

Does that help out any?

BF
 

michael59

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#11
Nope, not at all. You are measuring buoyancy of the doggie. What you are looking for is displacement.....ummmm kind of like tonnage on a ship is determined. How much water the ship displaces while loaded is the tonnage it is carrying and how much it is not displacing is its tonnage when running empty.

You need a graduated cylinder or just a cylinder and measure the height of the water. Drop the doggie into it and measure the height of the water level. Subtract the first height from the second and this is the displacement. The water displacement it what is used in the calculation of density in the ratio of silver density, cant go wrong on it.
 

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#13
So, basically, what you're saying is that this 2500 year old method is in the same realm as the flat earth and 'we've never been to the moon', right?

OK mikey, try it and see if you can gauge correctly the increase in the volume in the graduated cylinder accurately enough to calculate it.

:inspector:
BF
 

michael59

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#14
you don't have to be so mean ya know. Density of silver is x grains per volume of water? correct? volume of water determines volume of metal. IF grams/mass does not meet the density of the metal compared to what its volume is then there is a big question to be answered as to why.

We are both talking about the same thing sept I am saying you do not have to choke the doggie while suspended in water. I guess I am saying I dispense with that step edited to add: I don't suspend the doggie I would just drowned it.
 
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Bottom Feeder

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<he> sorry, mike, I didn't mean to be snarky. I've used this (very infrequently) to determine the density of an unknown mineral in order to try to identify it (density, among other things). It gets the density in the ballpark which helps eliminate some possibilities of what it might be.

If you try the displacement method you will discover that you need a special graduated cylinder to accurately measure the volume increase. But, of course, if the object you're trying to find the density of is large (say 3 or 4 thousand cubic centimeters) the margin of error in reading the graduated cylinder will be less than with a small object like this. You are correct, you can drop the big thing in water, measure the increase on the graduations, use that with the weight and determine the density of that object, but it only (sort of) functions on a larger scale, but not in the one ounce coin realm.

BF
 

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#16
So, basically, what you're saying is that this 2500 year old method is in the same realm as the flat earth and 'we've never been to the moon', right?

OK mikey, try it and see if you can gauge correctly the increase in the volume in the graduated cylinder accurately enough to calculate it.

:inspector:
BF
And, I have. I took a cylinder which was graduated aka had marks denoting 1cc's and multiples of 10cc's and we dropped rocks in them. Yes the rocks were ment to be gold. We dropped each rock separately and noted each water volume increase. We then dried the rocks and weighed them. And yes we should have weighed them first but there was a crowed around the scales. We then determined that the volume displaced did not meet the requirements of the volume that would be displaced by gold.

So you see we both are doing the same thing.
 

Joe King

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#18
the dog is trying to 'float' in the water (you know it would sink to the bottom and that's why you suspend it). It is actually pressing down on the balance with 7½ grams of pressure trying to 'float'. To actually be able to float, an item of that volume (7½ cc) would have to weigh a tiny bit less than 7½ grams. And when you dropped that in the water the balance would indicate you have added an extra (about) 7½ grams of 'something' to the cup of water.
Yea, but until you demonstrate this while on a helicopter flying West, none of it's valid!
 

michael59

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Look at it like this, michael; the dog is trying to 'float' in the water (you know it would sink to the bottom and that's why you suspend it). It is actually pressing down on the balance with 7½ grams of pressure trying to 'float'. To actually be able to float, an item of that volume (7½ cc) would have to weigh a tiny bit less than 7½ grams. And when you dropped that in the water the balance would indicate you have added an extra (about) 7½ grams of 'something' to the cup of water.

Does that help out any?

BF
K, here we go to the east in the helicopter while being chased by bigfooty flying a kite with hooks in it.

first you weigh the container: Note weight
second you place object in container: Note weight
third you cover object with water to a known gradient point: Note weight of water

Sum up all weights and subtract out container subtract object to get water weight. Convert weight of water to volume of water. extrapolate out if density of object equates with density of supposed object as a true representation of object using the extrapolated water volume.

Then fly north or south do a left or right turn and as the world turns bigfooty will come into view and lay him out with that 31mm cannon and dodge the kite.
 

michael59

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I learned to trust the atomic mass in the periodic table by doing the rock water thingy...….Sorry I am laughing too dam much to think of how to do the rock, paper, scissors joke....mainly cus I am snickering too much from putting bigfooty in there.
 

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#24
Ya lost me here.
Let me cogitate on yer method for a bit...
gradient point: weight of water or spot on cylinder where water covers object......

this way is really fast and you do not have to be that accurate unless One! you might generate massive amounts of heat causing an explosion or you are dealing with massive amounts of monies.
 

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#25
One of the problems with the graduated cylinder is the meniscus. The meniscus is the curve seen at the top of a liquid in response to its container. The meniscus can be either concave or convex, depending on the surface tension of the liquid and adhesion to the wall of the container. In our case, water, the meniscus is always concave.
Meniscus.jpg
Notice that the graduated cylinder above is graduated in 0.1 cc increments. Incorrectly reading the meniscus will introduce errors in your calculations (BTW, did you keep any of those gold-not rocks?)

If you think about the volume occupied by one cubic centimeter you will realize that the larger around your measurement flask is, the closer together the graduations will have to be. So, with the above graduated cylinder (about an inch around) you will have a tough time stuffing that dog down it's throat. Examples of chemistry liquid measurement equipment:

322px-Beakers.jpg

That's your graduated cylinder on the right. The red liquid beaker on the left is probably the smallest I could get the dog in. With that said, I can only say that I have never seen a graduated beaker, cylinder, or volumetric flask that was graduated in hundredths of a cc. So even with a good graduated cylinder (graduations at 0.1 cc) you would not be able to achieve the level of accuracy to required to accurately determine density of smaller objects.

BF
 
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#27
You're both right, and are both proposing ways of measuring the same thing (weight of displaced water) in different ways (net forces vs. displaced volume).

Feeder's method is a measurement of the buoyant force on the dog. This is, simplistically, the difference in total force on the object due to the change in pressure with height. It doesn't matter if you're 50 feet deep in the ocean or 50 feet down a vertical pipe full of water: the pressure is determined by the weight of the column of water directly above. Buoyancy is the result of the downward force on the top of the statue being slightly less than the upward force on the bottom of the statue, resulting in a net upward force on it. Equal and opposite reaction: the water exerts that same difference in force DOWNWARD to it's bottom, into the scale, while the tension in the string holding the statue up decreases by the same amount (so if he were measuring the weight of the dog from the top of the string, he would see the apparent weight decrease by that amount). Turns out, after you do the math, this force is equal to the weight of displaced water.

Ships float because they weigh less than the amount of water that they displace, so the only force that the feel is from below. (We're ignoring atmospheric pressure, here, to keep things simple).

Michael's method is a direct measure of the displaced volume of water. Again, both methods ultimately rely on the displaced weight of water, it's just how you measure that volume. Either direct measurement of volume, or indirectly due to its effects.



Confirmation measurement:

Make your tare cup of water as before. Weigh it; this is your tare weight. Make a mark on the side of the glass at the water level.

Drop or suspend the statue fully in the water. Mark the new water height.

Remove the statue. Fill the water to the second height. Measure this new weight. The difference between this weight and the tare weight is the weight of water displaced by the statue.





Sources of error:

Temperature and atmospheric pressure both affect the density of water. Not by much, and you probably don't care about 0.000001% accuracy, but FWIW, pure water has a density of 1 g / cm^3 at 4.0 degrees C and 1 standard atmosphere external pressure. Air pressure will also effect the total pressure in the water. If you want, perform both experiments one right after the other (minimize changes in atmospheric pressure), using the same pitcher of water for both (minimizing potential changes in temperature).

Measuring height of the water. Use a glass that only barely fits the statue. This will maximize the change in water height, and make your markings of the change in height more accurate, percentage-wise. Also, make your markings as fine as possible: use a pencil, not a paintbrush.

Your scale. It looks like you're using a scale rated to 200 g. You've got a tare weight of 177 grams right off the bat, that's pushing you to the top-end of the range. I don't know the details of that particular scale, but many instruments start to deviate from a good measurement as you approach the top-end of their range, especially consumer-grade ones. Use as little water as you can, give yourself some headroom to work with.




EDIT: spelling, clarity.
 
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michael59

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#28
You're both right, and are both proposing ways of measuring the same thing (weight of displaced water) in different ways (net forces vs. displaced volume).

Feeder's method is a measurement of the buoyant force on the dog. This is, simplistically, the difference in total force on the object due to the change in pressure with height. It doesn't matter if you're 50 feet deep in the ocean or 50 feet down a vertical pipe full of water: the pressure is determined by the weight of the column of water directly above. Buoyancy is the result of the downward force on the top of the statue being slightly less than the upward force on the bottom of the statue, resulting in a net upward force on it. Equal and opposite reaction: the water exerts that same difference in force DOWNWARD to it's bottom, into the scale, while the tension in the string holding the statue up decreases by the same amount (so if he were measuring the weight of the dog from the top of the string, he would see the apparent weight decrease by that amount). Turns out, after you do the math, this force is equal to the weight of displaced water.

Ships float because they weigh less than the amount of water that they displace, so the only force that the feel is from below. (We're ignoring atmospheric pressure, here, to keep things simple).

Michael's method is a direct measure of the displaced volume of water. Again, both methods ultimately rely on the displaced weight of water, it's just how you measure that volume. Either direct measurement of volume, or indirectly due to its effects.



Confirmation measurement:

Make your tare cup of water as before. Weigh it; this is your tare weight. Make a mark on the side of the glass at the water level.

Drop or suspend the statue fully in the water. Mark the new water height.

Remove the statue. Fill the water to the second height. Measure this new weight. The difference between this weight and the tare weight is the weight of water displaced by the statue.





Sources of error:

Temperature and atmospheric pressure both affect the density of water. Not by much, and you probably don't care about 0.000001% accuracy, but FWIW, pure water has a density of 1 g / cm^3 at 4.0 degrees C and 1 standard atmosphere external pressure. Air pressure will also effect the total pressure in the water. If you want, perform both experiments one right after the other (minimize changes in atmospheric pressure), using the same pitcher of water for both (minimizing potential changes in temperature).

Measuring height of the water. Use a glass that only barely fits the statue. This will maximize the change in water height, and make your markings of the change in height more accurate, percentage-wise. Also, make your markings as fine as possible: use a pencil, not a paintbrush.

Your scale. It looks like you're using a scale rated to 200 g. You've got a tare weight of 177 grams right off the bat, that's pushing you to the top-end of the range. I don't know the details of that particular scale, but many instruments start to deviate from a good measurement as you approach the top-end of their range, especially consumer-grade ones. Use as little water as you can, give yourself some headroom to work with.




EDIT: spelling, clarity.
K, bud....I am a bit too f'n drunk to understand er comprehend...yep I'm blasted....so I favorited ur post....

kind of got dixed on it
 

AgBar

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#29
K, bud....I am a bit too f'n drunk to understand er comprehend...yep I'm blasted....so I favorited ur post....

kind of got dixed on it

Ha! No worries. I had a long day on not enough sleep and a few drinks myself before I wrote that, so it may be all sorts of jargony gobbelty-gook. Sort it out tomorrow. :beer:
 

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#30
Nice demonstration of this method. As you know I have a rock to do this with. Hard to say when I will get around to it though. It does seem like a good winter activity when cabin fever sets in. :)
 

Joe King

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#33
It don't.
Unless yer doin it in a helicopter flyin east
(or was that west?)
Anyhow it will cause cold one way and heat the other.
Probably North and South, but then with the spin of the Earth it'd just spin ya off in a spiral. You're f'ed no matter which way your helicopter flies, f'ed I say!
 

Unca Walt

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#35
Waaaaay back in 2009 I demonstrated the Archimedes' principle of determining density. About a month after that post we had the April Fool’s Day reset. Four or five hours of work gone in an instant. I'm sure I was not the only one disappointed by that move. Now I’m retired and have a bit more time on my hands so I thought maybe I would try it again (hope we don’t go TU again after this) with silver this time instead of a gold maple leaf.

I purchased this pretty little dog a couple years ago and I decided to check it’s density to see if was indeed 925 sterling.


First I calculated what it should come out to; the dog weighs 76.5 grams. The density of silver is 10.49 gm/cm³ — So the dog must be around 7.3 cm³ of silver. Therefore, suspended in water, it should displace 7.3 cc of water, which weighs 7.3 grams. If it displaces 8 grams of water, then it is 8 cc in volume and 8 times 10.49 gm/cm³ will get you what that 8 cc of silver should weigh or 83.92 grams, which would indicate that it wasn't silver.

The setup
View attachment 116320
Dog, plastic cup of water, scale and support device​
The dog's weight
View attachment 116321
76.50 grams of whatever...​
Then weigh and tare the cup of water


The dog needs to be suspended with a small thread to immerse it in the water


The dog suspended above the water

now I lower it into the cup


And read the resulting increase in weight: 7.43 grams. This is the result of the displacement of 7.43 cc of water (density of water 1 gm/cm³). Therefore the total volume of the dog is 7.43 cc. I know for some of you science deniers out there won't be able to get your head around this but, trust me — it's correct.

The dog comes in at 10.3 gm/cm³ Since 925 sterling is 10.37 gm/cm³ I would say that the dog is 925

Because lead density is 11.3 gm/cm³, if the dog was silver plated lead the volume of 7.43 would weigh 83.96 grams (which it don’t). As well, as lead is much softer than 925 you could easily bend, say, a leg (which I can’t with my fingers) further identifying it. One of the closest look-alikes for silver is Nickel Silver (AKA German Silver) but since it has a density of 8.69 gm/cm³ it would make the measured volume of the dog weigh around 64.57 grams (which it don’t).

My balance has a limited capacity of 200 grams, but it was the best I could afford that had resolution down to 0.01 grams. So It has some limits. The temperature and physical makeup of the water has some small diversions in in but I would not recommend using other stuff for testing, such as:


Throws the density off somewhat :Happy::Happy:

BF
YOU DROWNDED THAT PORE LI'L FARGIN DOGGIE!!!!
 

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#36
Probably North and South, but then with the spin of the Earth it'd just spin ya off in a spiral. You're f'ed no matter which way your helicopter flies, f'ed I say!
Just as long as you don't lose my dog.
How does it affect it?? Dramatically!!! Send lots of money to Al Gore and the UN right now!!
Hey, look, don't tell anybody but I'm pilin up silver just because of this little factoid. Ya see, when they discover we can cure climate change with seeding the atmosphere with tons of atomized silver I'll make a friggin fortune.
YOU DROWNDED THAT PORE LI'L FARGIN DOGGIE!!!!
Naw, walter, he was pretty much dead already. I haven't seen him move in years. years...

BF