Solid Brass
Posted in Candle Holders & Accessories on 01/18/2004 07:31 am by admin
a solid brass statue weighs 190 N in air. what is its volume?
the statue is suspended from a rope and totally immersed in water. what is the tension in the rope (the apparent weight of the statue in water)?
Use Archimedes Principal to answer this question:
"The buoyant force is equal to the weight of the displaced fluid."
Thus, in air, the net force is equal to the statue's true weight minus the buoyant force.
190 N = W - Fb
The statue's weight, W, is simply the density of the brass times its volume times gravity, and the buoyant force is equal to the density of the air times the statue's volume times gravity:
190 N = d-brass * g * V - d-air * g * V
Re-writing this expression provides the volume:
V = 190 N / (d-brass * g - d-air * g)
From Google, I found that the following typical densities (air is assumed to be taken at sea-level):
d-brass = 8400 kg/m^3
d-air = 1.2255 kg/m^3
d-water = 1000 kg/m^3
Substituting these values provides:
V = 190 N / (8400 * 9.8 - 1.2255 * 9.8)
V = .00231 m^3
When the statue is submerged in water, we again use Archimedes Principal to find its apparent weight:
W = d-brass * g * V - d-water * g * V
W = (.0231)*(9.8)(8400 - 1000)
W = 167.4 N
Good Luck 
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