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Q & A: using submerged weight to calculate density

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Most recent answer: 06/15/2013
Q:
Hey, I am trying to compute rock density values for a bunch of individual rock samples. I know the standard methods but have question about a possible different approach. I can buy a completly submergable digital scale. My question is this "can I determind an accurate wet weight of the samples by submerging the scale in pure water, zeroing the scale and then adding the rock sample to the scale. The rock would be completely submerged as well. I could then do standard dry weights and compute the densities. I can find no refernce to anyone doing density calculations this way so am thinking it must be a flawed approach. But, even with my 3 semesters of physics back in the day, I cannot figure out why it would not work. Any reply would much appreciated. Thanks, Bob Marvin Reno, Nevada
- Robert (age 52)
Reno, Nevada
A:

This is a very cool idea. With any stone, you have two things you don't know, the volume (V) and the weight (W). You want the density W/V. The standard way to measure these is via a scale to measure W and by displacing water from a container to measure V. You've got a different way, which just needs some algebra to complete.

Let's call the known density of water R (it's 1 gm/cm3, but I want to keep this in general form until we're done.) The submerged weight you'll measure is just Ws=W-VR. So RV=W-Ws.
Now W/V = R*W/RV = RW/(W-Ws), and you're done. 

Mike W.


(published on 06/15/2013)

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