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zfgibbs · Apr 26, 2009, 11:40 AM

Ok my question is:
A sample of unknown material appears to weigh 270 N in air and 155 N when immersed in alcohol of specific gravity 0.700.
(a) What is the volume of the material? m^3

(b) What is the density of the material? Kg/m^3

Ok I have done this problem at least 7 times and keep coming up with the same answer but webassign keeps saying my answer is incorrect. Could someone help me with the formula?

Perito · Apr 26, 2009, 12:45 PM

Originally Posted by zfgibbs

A sample of unknown material appears to weigh 270 N in air and 155 N when immersed in alcohol of specific gravity 0.700.

(a) What is the volume of the material? m^3

(b) What is the density of the material? kg/m^3

Ok I have done this problem at least 7 times and keep coming up with the same answer but webassign keeps saying my answer is incorrect. Could someone help me with the formula?

Newtons is a measure of force, not of mass. That may be where you're going wrong. (You could also be making a simple math mistake).

The first thing to do is to convert force to mass:

$270\,N- 155\,N = 115\,N$ newtons of buoyancy

$115\,N\,=\,115 \, \frac {Kg \, m}{sec^2}$

$115 \, \frac {Kg \, m}{sec^2} \div 9.80665\, \frac {m}{sec^2}\,=\, 11.727\, Kg$

The specific gravity of the liquid is given as 0.700. The definition of specific gravity is the mass relative to the mass of water. We'll assume, as is often done, that the mass of water is 1 Kg/L (1 g/mL) so the mass of water is 1000 Kg / cubic meter. Therefore, the mass of alcohol must be 700 Kg/cubic meter

$11.727\, Kg\, \div \, 700\, \frac {Kg}{m^3}\,=\,1.196\,m^3$

To find the density, we need to convert 270 N to Kg

$270 \div 9.80665=27.53\, Kg$

and the density is

$\frac {27.53\,Kg}{1.196\,m^3}\,=\,23.024\,\frac {Kg}{m^3}$