Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Quantumcat on 25/11/2003 13:31:01
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I don't know what the -exact- translation is in english, probably Archimedes' Force or something. Apparently if a body is suspended in water, it pushes the body upwards. We were working with it in physics class, but I still don't know exactly how it happens or how it works.
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I thought Archimedes claim to fame was the issue of buoyancy - an object feels a force (upthrust) equivalent to the weight of the water it displaces ?
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Of course but why?
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The bouyancy of an object in a liquid is a function of the volume of the object. More correctly, it's a function of the surface area of the bottom of the object. For instance, take 2 cylinders of equal volume, one that is wide and short and one that is tall and narrow...the wide one will experience more bouyant force in water than the other.
First a little background:
The molecules of a liquid are mobile, much like that of a gas. However, due to various intermolecular forces, they are attracted to each other enough that they don't escape from the mass very easily. The strong the attractive forces, the more dense the liquid. Water, which engages in hydrogen bonding between water molecules, is rather dense for a liquid. Hydrocarbons (oils, alkanes, and the like) have only Van der Waals forces to hold them together (which are weaker than H bonds), so they tend to be less dense. Very short hydrocarbons have so little attractive force that they are gaseous at room temperature...like methane, ethane, propane, and butane. Methanol is only one oxygen atom away from being methane but yet it is a liquid at room temp...that's how powerful hydrogen bonding can be. Larger hydrocarbons have stronger Van der Waals forces (there are more atoms to attrack to each other) and so are less volatile at room temp.
With that background information in mind, it is the same molecular motion of a liquid that causes an object to be bouyant. One of Newton's laws states that the net force an object experiences is the vector sum of all forces acting upon the object. Current not withstanding, all sides of an object in a liquid are going to experience an equal force because it the net force of the liquid's atoms striking from each side cancel out. However a floating object experiences an upward force from the liquid molecules striking the bottom. Since pressure is a function of surface area (Force * area) the greater the surface area of the bottom, the greater the upward force. As long as the downward force due to gravity does not exceed this upward bouyant force, the object floats.
that help?
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Brilliant explanation - beautifully done. Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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That's what I said to the teacher, I thought maybe because the molecules slapped into the object with the object's head poking out of the water the net force'd be up. But he said I was wrong, and I could see I was wrong, because there was still Archimedes happening when it was fully submerged!!! if it's fully submerged then pressure'd be zero. It's something else from what you've explained, I think.
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So what you're getting at is submerged rather than floating things...I see where you're coming from on this now. You need to look at the net density for the object in water: its total mass divided by its total volume. If this net density is greater than that of water, it sinks. If not, it rises to the surface. Why? Well, if there were no water, it would fall due to gravity. Keep in mind that water is also affected by gravity. So, you have this object, affected by gravity, sitting in a fluid that is held in its container (lake bed, pool, what have you) by gravity. There is a net downward force for any given sample of this water. There is a net downward force on the object.
Newton's first law gives us an equation that says the force an object (or system of objects ie water molecules) experiences is the product of its mass and its acceleration. In this case, acceleration is the same for both the water and the object. So, the difference lies in the mass...but since we're dealing with fluids and things with volume, we have to look at mass over an area, which is density. In a nutshell, the more dense of the two will experience a greater downward force due to gravity. If the water displaced is more dense than the object, ALL the water is more dense than the object, hence the water experiences greater downward force, causing the effect of the object rising to the surface.
This same principle is how a hot air balloon works. Air is a fluid too, just much less viscous than liquids. The air in the balloon expands according to your gas law of choice (for simplicity's sake, PV=nRT) and the hot air inside slowly becomse less dense due to its volume increasing. It experiences a bouyant force similar to that a floating object experiences.
So, basically, gravity is your culprit.
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Cannibinoid, you are getting way too technical and leading yourself off in the weeds.
Bouancy is caused by a density gradient. When an object is the same density as the liquid it is submerged in it won't float up (or sink). When the density is different, the liquid (and a gas behaves the same way) will flow around the object in order to come to a lower potential energy in the gradient. This puts more liquid on one side than on the other and it experiences a force, which may make it accelerate if no other force (like a rope) is acting on it.
When a body is on the surface of a liquid, it will displace it's own weight in the liquid and come to equilibrium.
If you have objects of different densities in zero gravity, no bouancy force occurs. I've seen films of astronauts putting a sphere of water in front of them and then blowing a bubble of air into the water. It stays put! If they touch the water and move it a little the air rushes out the "front" of the water.
I hope this helps. I'm a little scattered tonight.
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John
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I think I was so technical because I was sorting it out in my own mind...I actually had to stop and think to myself "Why DO things of different densities separate the way they do." Besides, I'm a chemsist, I look at materials questions like this in terms of atoms and molecules rather than holistically. I can't help it. =)
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Looking at atoms and molecules is good, but sometimes you can't see the "forest for all the trees".
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John
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Hey cannabinoid, what is your AIM name?
Also the teacher gave us a formula, and explained why it happens, but it was in french and too difficult to understand. I don't remember if he mentioned density but probably i just didn't recognise the letter in the equation for it. I don't have my physics book here but I will post it next time.
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Cannabinoid - I'd like to talk on the radio show about the barrel / raft question we were discussing a while back - would you be willing to appear on the programme to talk about it ?
Chris
"I never forget a face, but in your case I'll make an exception"
- Groucho Marx
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Tweener: But without the trees, there is no forest. ;)
Quantum: AIM name is jtm420spam The symbol used for density is lowercase greek rho (i think)
Chris,
Sure, what do I need to do? email me...the address should be in my profile.
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PA = curvy P V G
The curvy P is called mass volumetrique, so I suppose it's the same as density?
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Yep, that "curvy P" is the greek symbol I'm thinking of. Pretty sure it's lowercase rho. My french isnt so good but mass volumetrique sure sounds like density to me, considering density is mass per unit volume.
What equation is that you put in the last post? It seems weird they'd have density and volume as factors in the same side of the equation since their product is mass...easier to just have 1 variable.
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Mass volumique is in kg/m3 eg water is 1000 kg/m3. V is volume of liquid. G is gravitational force, 9.8 or so for earth.
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