Buoyancy
Terian Sherman
Tucker Manton
Week 7
OBJECTIVE(S):
The objective of this lab is to understand buoyancy in different situations. Understanding buoyancy in
different situations will then enable us to understand how to calculate the force and density as well as
how to utilize Archimedes’ principle.
Experimental Data:
500 mL graduated cylinder weight = 0.98 N
(Data collected in Part 1 can be used in Part 2)
Object
Weight on
Weight T1 Weight T2
Displaced water Displaced water
digital scale (N) (air) (N)
(submerged) (N) weight (N)
volume (cm3)
Cork
0.71 N
0.7 N
0N
1.69 N
71 cm3
Aluminum
3.70 N
3.70 N
2.30 N
2.35 N
140 cm3
Cork + Al
4.41 N
4.50 N
0.10 N
5.29 N
440 cm3
Cork + ???
3.86 N
3.9 N
0N
4.86 N
400 cm3
Weight of unknown material: 3.15 N
Data Analysis:
Part 1
For all calculations, the following is true:
Density of water: 1000/kg/m3
Gravity: 9.8 m/s2
Based on the volume of displaced water measured, calculate the buoyancy force Fb1 using equation (1)
from the lab manual:
Buoyancy Force Fb1 for Cork:
(1000 kg/m3) * (0.000071 m3) * (9.8 m/s2) = 0.6963N
Buoyancy Force Fb1 for Aluminum:
(1000 kg/m3) * (0.00014 m3) * (9.8 m/s2) = 1.37 N
Buoyancy Force Fb1 for Cork + Aluminum:
(1000 kg/m3) * (0.00044 m3) * (9.8 m/s2) = 4.312N
Buoyancy Force Fb1 for Cork + unknown:
(1000 kg/m3) * (0.0004 m3) * (9.8 m/s2) = 3.92N
Calculate the buoyancy force Fb2 by using the digital force scale and computing the weight of pure
displaced water by subtracting the weight of the empty graduated cylinder from the weight of the
graduated cylinder with the displaced water:
Buoyancy Force Fb2 for Cork:
1.69N-0.98N=0.71N
Buoyancy Force Fb2 for Aluminum:
2.35N -0.98N= 1.37N
Buoyancy Force Fb2 for Cork + Aluminum:
5.29N-0.98N=4.31N
Buoyancy Force Fb2 for Cork + unknown:
4.86N-0.98N=3.88N
Compare these two values by calculating the percent difference:
Cork:
(0.71-0.6963)/ ((0.71+0.69631)/2) *100 = 1.95%
Aluminum:
(1.37-1.37)/ ((1.37+1.37)/2) *100 = 0 %
Cork + Aluminum:
(4.31-4.31)/ ((4.31+4.31)/2) *100 = 0%
Cork + Unknown:
(3.92-3.88)/ ((3.92+3.88)/2) *100 = 1.03%
Calculate the buoyancy force Fb3 using equation (2) in the lab manual by taking the difference in the
force sensor readings for the object in air and submerged in water:
Buoyancy Force Fb3 for Cork:
0.7N-0N= 0.7N
Buoyancy Force Fb3 for Aluminum:
3.7N-2.3N=1.4N
Buoyancy Force Fb3 for Cork + Aluminum:
4.5N-0.10N=4.4N
Buoyancy Force Fb3 for Cork + Unknown:
3.9N-0N=3.9N
Compare the buoyancy force found using equation (1) and equation (2) by calculating percent
difference:
Cork:
(0.71-0.6963)/ ((0.71+0.6963)/2) *100 = 1.95%
Aluminum:
(1.37-1.4)/ ((1.37+1.4)/2) *100= 2.17%
Cork + Aluminum
(4.31-4.4)/ ((4.31+4.4)/2) *100 = 2.07%
Cork +Unknown
(3.92-3.9)/ ((3.92+3.9)/2) *100 = 0.512 %
Part 2a
Calculate the density ρ1 of the aluminum block using equation (3) in the lab manual:
3.70N (0.001 kg/cm3) / 1.34 N = 0.00276 kg/cm3 = 2.76 g/cm3
Calculate the density ρ2 of the aluminum block directly using ρ = m/V, where m is the mass of the
object and V is the volume of the displaced water:
P = m/V
m = 3.70 N / 9.8 m/s2 = 0.3776 kg
P = 0.3776 kg / 137 cm3 = 0.00276 kg/cm3 = 2.76 g/cm3
Compare the average of these two calculated values of aluminum density with the known one.
ρAl = 2.7 g/cm3:
2.7−2.76/ [(2.7+2.76)/2] ×100 =
|−0.06|/ [(5.46)/2] ×100
= 0.06/2.73×100
= 0.021978×100
= 2.1978% difference
Part 2b
Calculate the density ρ1 of the unknown material directly using ρun = Wun/Vung, where Wun = W
(unknown with cork) – Wcork and Vun = Val:
ρun = Wun/Vung,
Wun = 3.86 N – 0.71 N = 3.15 N
Vun = Val = 137 cm3
ρun = [3.15 kg*m/s2] /137 cm3 (9.8m/s2) = 3.15 N / 1342.6 = 0.00235 kg/cm3 = 2.35 g/cm3
Calculate the density ρ2 of the unknown material using equation (6) in the lab manual:
F I b = Wtot – T I = WC + WAl – T I
0.71 N + 3.70 N – 3.86 N = 0.55 N
F II b = Wtot – T II = WC + Wun
0.71 N + 3.15 N = 3.86 N
(3.70 N – 0.55 N + 3.86 N – 3.86 N) / [137cm3 (9.8m/s2)] = 0.00235 kg/cm3 = 2.35 g/cm3
Compare these two densities by calculating the percent difference:
2.35−2.35/ [(2.35+2.35)/2] ×100
=0/ [4.7/2] ×100
=0/2.35×100
=0×100
= 0% difference
Results (3 points):
Object
Fb1 (N)
Fb2 (N)
Fb3 (N)
Cork
0.5
0.71
0.7
Aluminum
1.37
1.37
1.4
Cork + Al
4.31
4.31
4.4
Material
Density ρ1 (kg/cm3)
Density ρ2 (kg/cm3)
Aluminum
2.76
2.76
Unknown
2.35
2.35
% difference between Fb1 and Fb2: 1.95%
% difference between Fb1 and Fb3: 1.95%
% discrepancy between average density of aluminum experimental and theoretical values: 2.20%
% discrepancy between two experimental values of the unknown density: 0%
DISCUSSION AND CONCLUSION:
In this lab we explored buoyancy using the virtual KET experiment and tested Archimedes’
principle. In the first part of the lab, we collected data by weighing the graduated cylinder and
each object we were going to be testing the buoyancy of. After weighing them by themselves
we then hung them on the scale to see what each object weighed in the air and finally
submerged them in water to see buoyancy in affect and to weigh them while submerged as
well. When objects were submerged, we also took the volume of displaced liquid or in this
case, water down as well as weighing the displaced water in the graduated cylinder. This
allowed us to make the necessary calculations of buoyant force in a multitude of ways and then
calculate the percent discrepancy. After figuring all this we were able to calculate the density of
the unknown material that was measured with the cork. This experiment was a success as all
my values were very close to each other where they agreed. The two different ways to calculate
the differences gave me a very low percent discrepancy at 2.20% or aluminum and 0% for the
unknown. This experiment was successful in showing that calculating density and buoyant
force in different ways should yield very similar results if not exactly. My percent discrepancies
for the buoyant force with the different ways to calculate were each less than 2%. Archimedes’
principle touches on that the weight of an object is not the only factor that goes into whether an
object floats or sinks or is partially submerged but also considers the density of the liquid it is
placed in and the amount of liquid the object displaces. Overall, I think this was a very
successful experiment to show how Archimedes’ principle comes into place and to explain
buoyancy and the different ways to be able to find it.