So, we all know about water displacement. You know, you have water in a container, and if you put a heavy object in the container, the water level rises. Simple enough concept.
I remember an old episode of Clarissa Explains It All where she had a class assignment to invent a way to help the environment. She had this lame idea to have people put a cinderblock in their bathtub with them (a “Bath Brick” as she called it) so the water level would rise and they wouldn’t have to use so much water.
And it made me remember back to some middle school science class, where the teacher told us that matter from a neutron star, or whatever you call those tiny dead stars, was extremely dense and heavy. Like, a particle the size of a grain of sand would weigh a couple of tons.
So then I had this idea. What if a tiny particle of this dense matter was put in a bathtub? How much water would it take to fill the tub? A cup? A teaspoon? The same ammount?
If a tiny particle was put in a bathtub, you’d need the same amount of water minus the size of the tiny particle. The condition on density is just so the object doesn’t float; broadly speaking, if it weighs more than the weight of water it would displace, it sinks, and this means you want something dense so that it will sink. Once it sinks, you want something big so it’ll displace a large amount of water.
Yes, but a pound of gold will displace more water than an equal ammout of say, silver. So why wouldn’t an extremely dense grain of sand displace more water than an ordinary grain?
(assuming that the material is denser than water, of course; if it is less dense than water it will displace less because it will not be fully immersed (unless you push it down))
Oops, actually wrong way around; a pound of silver will displace more water than a pound of gold (or, say iridium); the more dense a material, the smaller a pound of it will be and the less water that pound will displace.
A pound of gold will displace less water than a pound of silver because gold is more dense. A pound of gold is smaller than a pound of silver. Density, by the way, is defined as mass (or weight) per unit volume, i.e. pounds per cubic inch.
A cubic inch of gold will displace the same amount of water as a cubic inch of silver but the cubic inch of gold will weigh more. This is what is analagous to the grains of sand.
You can use this priciple to determine the density of an object of known weight but unknown volume. The volume of an object will be very difficult to measure if it is elaborately shaped. You can place the object in a full container of water and catch all of the water that is displaced. If you weigh this water and devide the weight by the known density of water, you get the volume of the water displaced. This will be the same volume of the object. Divide this volume by the weight of the object and you get the object’s density.
You need to be more specific with that statement. Do you mean that a pound of gold will displace more than an equal mass of silver, or an equal volume of silver?
If you focus on mass, then the pound of silver will displace more than the pound of gold, since you need a larger volume of silver to achieve the same mass.
If you’re making their volumes equal, then they’ll displace the same amount of water.
“The volume of fluid displaced by an object immersed in the fulid is equal to the volume of the object”
That’s exactly how my grade 11 chemistry notes had it worded, and somehow I still remember it that way 5 years later.
So if you know the density of an object, and it displaces a certain amount of fluid, then you can determine it’s weight. Or more practically, if you know its weight and amount of fluid displaced, then you can determine it’s density, which in the case of Archimedes and the crown, supposedly allowed him to determine whether the crown was pure gold or tainted with silver…
I just came up with a nice thought experiment that should make this whole thing clear to the OP.
Imagine that you have an empty, sealed container, filled with air. There is a small hose attached to the container so that you can fill it with a liquid if you wish. Now, submerge the container in a bath tub (use magnets or an extra weight on top to keep it from floating), with the hose running up and out of the tub. Notice that the water level has risen.
Now, use the hose to fill the container with some nice, heavy mercury. It’s obvious that the water level will remain constant even though you’re increasing the density of the submerged container.
An object that is less dense than water (and is allowed to float) will sink only to the point where it has displaced an amount of water equal in mass to itself.
So placing a 5 kilogram pine block in a bath that is brimming full, will cause 5 kilograms of water to spill over the rim; this water is equal in mass to the entire block but equal in volume to only the submerged portion.
If I may pick your brain, and hijack this thread for a moment, I have a related question. My co-workers and I were having a conversation along these lines last week. If you take the USS H.S. Truman, for example, she’s listed as displacing 96,000 tons. I was under the impression that her displacement equals her actual weight. Most people disagreed, or weren’t sure. Internet searches on definitions revealed that displacement is expressed in several ways, but the question remains: Does the H.S.T. actually weigh 96,000 tons if that’s what she displaces?
that is correct. Archimede’s principle states that a body immersed in a fluid is buoyed up with a force equal to the weight of the displaced fluid. For a body that floats, the weight of the displaced fluid is equal to the weight of the body itself. For a body that sinks, the weight of the displaced fluid is less than the weight of the body.
Sure it’d work! What do you think would happen if you took super-condensed matter from a neutron star and sudenly removed it from the star and dropped it in your bath tub (or anywhere else for that matter)?
BOOM! :eek:
Without the extreme, unbelievable pressure that was holding it together, it would expand quickly and violently. I don’t think you’d ever have to worry about bathing again, and thus water is conserved.
No, a pound of gold would displace less water than a pound of silver. Gold is denser, so a pound of it is smaller…
To be precise, a pound of gold is 0.373 kg (Troyes pounds for precious metals, right?). And the density of gold is 19 700 kg/m^3, so the pound has a volume of 0.000 018 9 m^3, or 18.9 ml. It will displace 18.9 ml of water (about 0.666 fluid ounces).
A pound of silver is also 0.373 kg (though a pound of lead or feathers is 0.454 kg owing to the complexities of the Mediaeval System of weights and measures used in the USA), and the density of silver is 10 500 kg/m^3, so the volume of a pound of silver is 0.000 035 5 m^3. A pound of silver will displace 35.5 ml of water (about 1.25 fluid ounces).
The story here is that an object immersed in a fluid will be subject to a buoyancy force (from inequalities of fluid pressure) equal to weight of the fluid displaced. So an object that is denser than the medium it is immersed in will experience a buoyancy force that is less than its volume, and will sink. On the other hand an object that is less dense than the medium will experience a buoyancy force that is greater than its weight, and will float up until part of it breaks the surface of the fluid (or until it enters a part of the fluid that is less dense). Then it will be displacing less [weight of] fluid and the buoyancy force will diminish. This will continue until the floating object is displacing fluid with weight equal to its own or until it is otherwise restrained (eg. by tension in an anchor-chain, or contact forces from bumping into the top of a container).
Remember the story of Archimedes in the bath? Hiero of Syracuse had given a goldsmith some gold to make a piece of jewelry (tradition says a crown, but I suspect that that is an anachronism). And he suspected that the goldsmith had replaced some of the gold with an equal mass of base metal, pocketing the gold in addition to his agreed fee. Archimedes had been asked by his tyrant to try to work out whether this was the case, and so was set the problem of accurately determining the volume of a golden crown of complicated shape without melting it down. While observing the behaviour of the water level as he entered his bath he suddenly understood the principle of displacement, and worked out a solution to the problem.
Note well that if the crown displaced its own weight of water that would have been no use. Archimedes (and Hiero) already had a way of determining the mass of the crown by weighing it with a pair of accurate scales. What they needed (to determine its density, and therefore tell whether it was still pure gold) was a way to accurately measure its volume. So if gold displaced its own weight of water (as a floating object does) there would be no point to the story.
