So how unusual is it to stay up way past midnight together with your teenager, when BOTH of you have to get up early for work

trying to figure out WHY the displacement is proportional to the mass of the object, not it's volume?

Triggered by this story The Golden Crown Mystery was a mystery about the king sending a certain amount of gold to the goldsmith for a new crown. When the crown was returned finished, the king thought that not all the gold that was sent to the goldsmith was in his crown. The night of this the king told Archimedes of his problem. When Archimedes went home he discovered what is now known as the Law of Hydrostatics (buoyancy). The Law of Hydrostatics is any object immersed in fluid, is buoyed up by a force equal to the weight of the fluid displayed by the object. Archimedes did this by filling up his tub to the top, and got in. When he got in Archimedes realized that the mass of the water that fell out of the tub was equal that of the mass of his body. The next day he did the same thing with the crown, and the amount of gold supposed to be in the crown. Archimedes found that the gold had more mass than the crown, thus not all the gold was in the crown

DISCLAIMER: He (DS) started it! :lol:

PS. The sucky part is not the fact that both of us are grumpy from lack of sleep today. The sucky part is - we STILL don't know why :shake:

Wouldn't it be because the weight/mass is what causes displacement? Volume/space is size and it's mostly gravity that pulls a mass into the water, displacing it? ouch, now my brain hurts. :o :hahaha:

Personally, I think it's much cooler to contemplate your ability to get your teen to stay up and talk to you, and your ability to stay up with him. :bow:

sounds like a great memory building, bonding moment!! and if you figure out the answer be sure to let us know, unless someone here knows? anyone?

i don't know either but i wanted to say how cool to do this with your teen...
i have a 13 year old and he is way cool:)

I went searching for better understanding and found these definitions.
I think I get it now, but don't think I could explain it well.

What is mass: "Generally, mass is defined as the measure of how much matter an object or body contains -- the total number of subatomic particles (electrons, protons and neutrons) in the object." Quoted from this site: http://science.howstuffworks.com/fpte1.htm

Volume is a quantification of how much space an object occupies.

I think it's great that you and your son could spend time learning together. Those are such wonderful moments.

Volume is a quantification of how much space an object occupies.



Yes, but that's just it! So if two objects (lets say two crowns) are identical in size, how come one of them will displace more water than the other? They take the same "space", right? So they should displace the same amount of water... we think...

Ugh - any physicist mamas here who can explain it in "layman's" terms? :help:

Yes, but that's just it! So if two objects (lets say two crowns) are identical in size, how come one of them will displace more water than the other? They take the same "space", right? So they should displace the same amount of water... we think...

Ugh - any physicist mamas here who can explain it in "layman's" terms? :help:

I am not sure if I have it figured out. I just went reading on that website I linked. There were more pages that went into force, acceleration, and other factors that apply to mass. I'll try to explain what was goin on in my head after reading.

Picture two kid's boats. One small empty plastic one, and another one the same size, but with rocks in it (both are enclosed). Both of them have the same volume or take up the same amount of space, but one has more mass. If you multiply the mass of each item, by the pull of Earth's gravity, you get the weight of each item. Obviously one of the boats weighs more due to the rocks.
Force is proportional to your mass. If you have more mass, the Earth exerts a greater force on you. More force would mean more water being displaced, I'm thinking.

Here's the stuff on Force:
http://science.howstuffworks.com/fpte2.htm

I really don't have a clue. Just trying to make sense of stuff I was reading. Now you've got me hooked on knowing the answer. We need a physicist mama to explain!

Hey, I have a partner in discussion! Yay :)

We frequent HowStuffWorks, and others. Google is my friend :lol:

But see, in your example with boats, one boat is less immersed in water because it is floating. So floating object make sense to me too.

But too solid object that both sink and are the same size... I am still going to search :P

Hey, I have a partner in discussion! Yay :)

We frequent HowStuffWorks, and others. Google is my friend :lol:

But see, in your example with boats, one boat is less immersed in water because it is floating. So floating object make sense to me too.

But too solid object that both sink and are the same size... I am still going to search :P

I would guess that a heavier object would sink lower in the water and exert more force, than an object that also sunk, but didn't weigh as much.

Really, where are the other mamas that are supposed to be helping us out! LOL
Maybe retitle your post "Science/physics question, help us solve it"

I love doing this stuff. Even if I never figure it out, it sure is fun trying.

Good idea, I am going to retitle it right now :D

But see, in your example with boats, one boat is less immersed in water because it is floating. So floating object make sense to me too.

But too solid object that both sink and are the same size... I am still going to search :P
Well, the plastic boat is floating because it has less mass. They both have the same volume.

A freshly felled tree will float down the river. A steel rod of the same size will sink. Same volume, different mass.

Conversely, the same mass can occupy different volumes. Fill two identical glasses exactly half full with water. Place one in the freezer. Water expands as it freezes, and the level will rise in the glass, even though the mass is the same.

Well, the plastic boat is floating because it has less mass. They both have the same volume..
True, the boat is floating because it has less mass in this example and the idea of "mass proportional to displacement" sits right with me IN THIS CASE.

But when both objects of the same size and both are on the bottom of the pool - don't they take up the same "amount of space" in the water? And the volume of the water in that "amount of space" is the same for both objects?

I'll get it eventually, I know I will :smirk:

I now see what you are saying. If one crown was made of lead, and the other of gold, they would both sink. The gravity of lead is like 11 and that of gold around 19, but they'd both be sitting on the bottom of whatever was containing the water. In this case, I see the perplexity of the question. It's almost like at the point where the gravity of the object is greater than that of water, it's no longer an issue of mass, but volume. But, um, that can't be, right? Interesting, very interesting.

Where's RocketScientist? Seems like she would know! lol

Okay, I found the answer:

If the object is less dense than water (if it floats on water), it
displaces a weight of water equal to the weight of the object. If the
object sinks in water, it simply displaces a volume of water equal to the
volume of the object.

This is known as the Principle of Archimedes.


Richard Barrans Jr., Ph.D.

From here:
http://www.newton.dep.anl.gov/askasci/phy99/phy99x34.htm

Somehow, it was more fun to ponder it. . . .

I would guess that a heavier object would sink lower in the water and exert more force, than an object that also sunk, but didn't weigh as much.


Not exactly.
The total weight is actually irrelevant. The density is the key (unit mass per unit volume). As mentioned above, two items of the same volume (the wooden log and the steel rod) which have different densities will have different masses.

Note: It is not always true that the mass of the displaced water will equal that of the submerged object. If the density of the object is greater than the density of water. the object will sink completely, and the mass of the water displaced will equal the mass of water of the same volume as the object, but no more.
The mass of displaced water equals the mass of the object only when the object floats, at least partially.
In other words, 1 cubic centimeter of Gold completely submerged in water will displace 1 cubic centimeter of water. In this case, the gold has a mass of about 19 grams and the displaced water has a mass of 1 gram.

Of course, by using different shapes, you can make materials with a greater density than water float (Steel ships are a good example), but this becomes a bouyancy problem rather than a more simple weight/density/mass/volume problem. :)

I could explain more.. this is just the tip of the iceberg... lol

~Dan (amey's DH)

If the density of the object is greater than the density of water. the object will sink completely, and the mass of the water displaced will equal the mass of water of the same volume as the object, but no more.
But in the example in the first post - Archimedes was able to determine which of the crowns (that both sunk) was golden and which was not.

So that was my thinking exacly that both displaced the mass of water of the same VOLUME as the object. And both crowns were of the same VOLUME. Then how come the golden crown diplaces more water than iron crown of the same VOLUME?

I could explain more.. this is just the tip of the iceberg... lol
~Dan (amey's DH)

Please please do!

Okay, I found the answer:

If the object is less dense than water (if it floats on water), it
displaces a weight of water equal to the weight of the object. If the
object sinks in water, it simply displaces a volume of water equal to the
volume of the object.

This is known as the Principle of Archimedes.


Richard Barrans Jr., Ph.D.

From here:
http://www.newton.dep.anl.gov/askasci/phy99/phy99x34.htm

Somehow, it was more fun to ponder it. . . .

Yes, that's what I/we thought too! But what about the "legend" that I quoted in the first post...

But in the example in the first post - Archimedes was able to determine which of the crowns (that both sunk) was golden and which was not.

So that was my thinking exacly that both displaced the mass of water of the same VOLUME as the object. And both crowns were of the same VOLUME. Then how come the golden crown diplaces more water than iron crown of the same VOLUME?

The myth is not quite correctly described.
This link explains the myth more thoroughly, and why it is likely just a myth:
http://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html

The idea is that Archimedes knew that the weight was correct, and he used the amount of displaced water to determine the volume of the new crown. Greater volume of the new crown meant less dense materials, so he deduced that some gold had been replaced with less dense (and cheaper) silver.


My "tip of the iceberg" comment was referring to the principles of bouyancy, and how objects made of materials more dense than water can be constructed to float in water. I was really just working the iceberg angle because that is itself an example of bouyancy principles in action. The density of ice is very slightly less than the density of water (I think this is due to some amount of air trapped in the frozen ice, but I cannot remember for sure), so ice floats, but just barely. The reason the "tip of the iceberg" means what it does is because only a tiny portion of an iceberg will be visible above the surface of the water. The iceberg will displace a volume of water almost equal to its own volume. The portion of the iceberg above the water surface represents the small difference in volume between the ice and the water of the same mass.

Bouyancy quiz: a 50-pound steel brick sinks like (what else?) a brick. If I take that same steel brick and melt it down and shape it into a boat, it would float. How is this true? (Assume no chemical changes to the metal and no other materials used in making the boat.) :p


-Dan (Amey's DH)

Apparently, our friends at howstuffworks.com have answered my question!

http://science.howstuffworks.com/question254.htm

-Dan (Amey's DH)

EUREKA !!! :D

THIS is what made a click for me he replaced some of the gold given to him by an equal weight of silver

So he did NOT make crowns identical in SIZE, but identical in WEIGHT. Which of course makes the "fake" one bigger in SIZE.

I was under ASSumption (hee-hee) that the SIZE was the same :rolleyes:

Dan, thank you very very much! Thank you Marina and thank you Amey and thank you Charity and thank you Phunkymama!


Oh, and we like HowStuffWorks too :) Yesterday it was Integrals and Derivatives :thumbsup: Yes, I studied it umpteen years ago and yes, I successfully forgot.