DATA and OBSERVATIONS

Determination of Specific Gravity Using Archimedes' Principle

Material	mass, dry	mass, apparent	mass difference	SG, observed	SG, listed	error
Aluminum	88.15 ± 0.01 g	55.62 ± 0.01 g	32.53 ± 0.02 g	2.710 ± 0.001	2.7 to 2.8	0%
Brass	273.49 ± 0.01 g	241.21 ± 0.01 g	32.28 ± 0.02 g	8.472 ± 0.004	8.47	0%

Material	mass, dry	mass, dry cork & submerged sinker	mass, cork & sinker submerged	mass difference	SG, observed	SG, listed	error
Cork	2.24 ± 0.01 g	41.47 ± 0.01 g	25.69 ± 0.01 g	15.78 ± 0.01 g	0.142 ± 0.001	0.16	-11%

The mass of the dry cork sample was reported as the average of two measurements.

In weighing the cork and sinker, it was found that the sinker was not heavy enough to submerge the cork. Therefore, for cork and sinker, the first set of weight readings was discarded and a second set obtained.

Before weighing the dry samples of Aluminum and Brass, the balance was not calibrated. Therefore, a second weight was obtained for the empty pan, and the weight difference was taken as the dry sample mass. A maximum error (± 0.005 g) was estimated for weighing the empty pan's offset from zero. Estimated errors for the sample and empty-pan mass measurements were used to calculate probable error (± 0.015 g) for the value of mass difference due to buoyant force. The probable error was reported as 0.02 g, maintaining the 2-decimal precision of the mass while reflecting additional uncertainty introduced by the second weighing.

The Aluminum and Brass samples had the same physical dimensions, so the mass difference due to buoyant force (hydrostatic pressure per unit volume of water displaced) was about 32 grams for both samples. Thus, the relative error for this derived quantity was about 1 in 2400 (0.15 compared with 32). This was the greatest contributor in calculation of probable error for specific gravity for both metals. Therefore, the relative error in specific gravity was located at about 1 in 2700 for Aluminum, and about 1 in 2100 for Brass (yielding 4 significant figures ± 3 decimal places).

Published values for specific gravity of Aluminum alloy and Yellow Brass were taken from CRC Handbook of Chemistry and Physics, 64^th Edition. The value for specific gravity of ground cork shown above was taken from the internet site www.reade.com/Particle_Briefings/spec_gra2.html.