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Mon 11 Apr, 2005 03:31 pm
With reference to the famous test by Archemedes, I would like to settle a debate on the displacement of water.
It was my understanding, that the way Archemedes could determine whether a crown was pure gold was by both weighing the object, AND seeing how much water it displaced, and then seeing if an equal weight in gold displaced as much water.
That is how I understand the reasoning, and I believe that would certainly work. Here's the problem, my friends say that you would not need to weigh the crown. You can determine its density by water displacement (or volume) alone. They say that a cubic foot of lead will displace a different amount of water than a cubic foot of gold. I say that is impossible. They say I am wrong.
Normally I wouldn't bother asking, but they tend to be more intelligent than me, especially in regards to math.
So, who's right?
A cubic foot is a cubic foot, weather it is gold, lead, wood or water. The weight of the cubic foot of material will be different and each material will have a different density (weight per unit volume).
Rap
Are they thinking that the amount of water displaced will give the weight? This is how the weight of boats is determined, but this will only work if the density of the object is less than the density of water. And it still won't tell you the density of the object.
I had them clarify, and they were saying that equal volumes of different materials can displace different amounts of water. I said that was impossible since water displacement is based on volume. But they said volume is not the only factor in water displacement.
The only exception I can think of is if the material in the water somehow affected the molecular structure of the water, for example, an extremely cold metal would displace more water than an extremely hot metal. They argued that lead actually does affect the water, somehow making it more dense or less dense.
I tried arguing with them, but they just smiled and shook their heads.
The amount of water displaced is a function of the surface area of the matter displacin' the water. regardless of their own intrinsic weight, items with equal surface area, if equally submerged, will displace an equal amount of water.
As long as the object sinks then your method for determining density is correct and your friend is wrong.
Hi SCoats: Perhaps your friends are thinking of floating objects which displace less than their volumn in water. Either floating or totally submerged, surface properties change the amount of water displaced by a few parts per million. In my opinion your understanding is correct unless someone wants to nit pick. Neil
Archimedes discovered that you could easily determine the volume of an item by completely submerging it in water (weighing things was as easy as a balance).
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