Calling All Angels: Questions on Gold, Buoyancy & More

[holly]

Okay, let me solidify something. I have thought on this until I am dizzy.

Is it true that you just can't fake the density of a pure element? That if, for example, you have a 10 gram piece of what is supposed to be gold, pure gold, in a cube shape, could you not secretly adulterate it? Could not a person take a drill, drill a little cylinder in the cube, place other base materials in it to exactly equal the weight, if not the density, of what was removed, seal the top of the little cylinder made when it was drilled with a thin sheet of gold (under a vacuum), and then have it fulfill the correct displacement for pure gold? I must be missing something, something vital...

And finally, one last buoyancy remark, and I'm DONE with that evil subject: When an object is sitting on the BOTTOM of a lake or ocean, and it is firmly sitting there, sunk in the mud, would not the upward buoyancy, at that point, be zero? And finally, the downward force would be greater than the upward one?

Thanking you in advance.

 

[cookiemonster]

Well, D = m/V. Now if you have the same m and the same V...

The buoyant force isn't zero, but it's certainly less than the gravitational force. Once it hits the bottom, the ground has an upward force equal to the sum of the buoyant and gravitational forces, so the total force on the object is zero (or else it'd magically float up or magically fall through the earth!).

cookiemonster

 

[holly]

Oh cookiemonster, I knew you'd help me! Well, I hoped, anyway!

But then how did Archimedes know the crown was really gold? I guess it will be a mystery if it really was or if it wasn't. Wish I had me a time machine to go back and see.

Thank you, I will now also lay Buoyancy to rest in Davy Jones' Locker.

 

[cookiemonster]

Well, you'd have to find something with exactly the same density as gold. I'm no analytical chemist (I don't much care for chemistry in general, for that matter), so I don't know if there's something like that, but...

cookiemonster

 

[Palpatine]

Concerning that buoyancy issue, I think what holly meant was what if the object is completely smooth and pinned to the bottom so that no water (or anything else) comes between the object and the bottom. If this is the case then there would be no upward buoyancy force. The water pressure will push it downward.

 

[cookiemonster]

That's true, but that's an awfully harsh restriction on the shape of an object. It is a good point to make, though, that there must be an underside, and that that underside must have a certain amount of area relative to the top (which depends on the depth of the object), of the object exposed to water in order for there to be an upward buoyant force.

cookiemonster

 

[Doc Al]

Originally posted by holly
And finally, one last buoyancy remark, and I'm DONE with that evil subject: When an object is sitting on the BOTTOM of a lake or ocean, and it is firmly sitting there, sunk in the mud, would not the upward buoyancy, at that point, be zero? And finally, the downward force would be greater than the upward one?

It depends on the shape of the object. Just for fun, let's take a sealed box-shaped obect and stick it firmly into the mud at the bottom of the lake. The box is upright (not tilted).

The bouyant force is the net force due to the water pressure on all sides. Since it's stuck firmly into the mud, it will be the downward pressure that will exert the bouyant force. (The forces on the sides cancel; the bottom is not touching water, so no water pressure there.) So, in this case, the bouyant force actually acts downward.

The forces on the object are these:
- bouyant force pushing down (agent = water)
- weight pulling down (agent = the entire earth)
- normal force pushing up (agent = surface of earth/mud)

These forces are in equilibrium.

For your amusement, check out this thread: https://www.physicsforums.com/showthread.php?s=&threadid=11531&highlight=puzzler