ARCHIMEDES' PRINCIPLE
PURPOSE:
To measure the specific gravity of lead and tin samples as well as an alloy sample consisting of an
unknown mixture of lead and tin. The percentage of lead and tin in the sample will be determined.
APPARATUS:
Centigram balance with water container platform
Small beaker of water
Lead, tin, and alloy sample
Small suspending string
METHOD:
The specific gravity (s. g.) of any substance is defined as the density, ρ, of the substance divided
by the density of water, ρW
Archimedes' principle states that the buoyant force, B, on an object submerged in a fluid, is equal to the
weight of the displaced fluid. For water
where V is the volume of water displaced and g is the acceleration due to gravity. By applying Newton's
laws to the sample suspended in water and substituting equations (1) and (2), the specific gravity of the
sample becomes:
where m is the mass of the sample in air and m′ is
the mass of the sample in water. The combination of
equation (3) for the three samples leads to the
following expression for the fraction of tin and lead in
the alloy sample:
where m and s.g. are the mass and specific gravity of the alloy, s.g.1 and s.g.2 refer to the measured
specific gravities of lead and tin respectively, and m 1 and m2 are the masses of lead and tin in the alloy
sample (not the masses of the pure lead sample and tin sample).
PROCEDURE:
1.
Measure and record the masses, m, (using the scale next to the sink) in air of each of the three
samples, to the nearest 0.01 gram.
2.
Next, place the beaker of water on the platform and suspend one of the samples with the string
from the hook that folds the weight pan suspension, and adjust the height of the platform (and/or
the length of the string) so that the sample is completely submerged without touching the container
and the weight pan does not touch the platform.
3.
Weigh each of the three samples in water, and record the apparent masses, m', to the nearest .01
gram.
4.
Measure the mass of the suspending string and subtract it from each of your weighings.
ARCHIMEDES’ PRINCIPLE LAB SHEET 1
DATA TABLE:
Mass (m)
Mass (m')
Lead
Tin
Alloy
String
CALCULATIONS:SHOW ALL WORK
1. Using equation 3 calculate the specific gravity of each of the three samples.
2. Compare for each metal the experimental values to the theoretical value of specific gravity using
the percent error formula.
3. Using equations 4 and 5 calculate the percentages of lead and tin in the alloy sample
RESULTS TABLE:
Experimental Specific
Theoretical Specific
Gravity
Gravity
Tin
Lead
Alloy
CONCLUSION: TURN IN LAB SHEET 1
Percent of metal in the
alloy
XXXXXXX
Percent Error