Experiment 9
Archimedes' Principle
Objective:
To verify Archimedes' principle by designing a barge
Equipment:
A computer with internet connection, a calculator (The built-in calculator of the computer may be used.), a ruler, a few sheets of paper, and a pencil
Theory:
Archimedes' principle states that when a non-dissolving object is submerged (or partially inserted) into a fluid, the fluid exerts an upward force onto the object called the buoyancy force, B, that is equal to the weight of displaced fluid. We may write:
B = V_{obj} * D_{fluid}
where D = ρg is the weight density of the fluid. B is the weight of displaced fluid. That's what Archimedes figured out.
The Mass Density (ρ) of Water :
Historically, 1gram, was defined to be the mass of 1cm^{3} of pure water at 4.0^{o}C. This means that ρ_{water} can be written as follows:
The Weight Density (D) of Water:
If we name the weight of 1gram to be 1gram force ( gf ); therefore,
Procedure:
If you have not done so, you may need to add the following Website to your Java exception list: http://www.mhhe.com/
To do this, follow the path (Windows operating system),
Start → All Programs → Java → Configure Java → Security (use High) → Edit Site List … → Add → Type in the site URL (http://www.mhhe.com/).
To verify the "Archimedes' principle," we will use an applet the can measure the buoyancy on a barge. For the barge safety (avoiding it from sinking), we load it such that only 3/4 of its volume goes in water. In other words, we find the measured value of the load that causes 3/4 submersion of the barge. To find the accepted value of the load that can cause 3/4 submersion of the barge, we will use the buoyancy formula.
Click on the following applet: http://www.mhhe.com/physsci/physical/giambattista/fluids/fluids.html . A barge will appear. You can change the volume of the barge by clicking on the top slider in the applet. The height of the barge remains constant at 4cm. The base area of the barge can be changed from 3cm^{2} to 7 cm^{2}. This makes the volume of the barge to change from 12cm^{3} to 28cm^{3}. We will use water as the first choice for fluid.
Before starting this experiment, make sure that you have understood the mass density and weight density of water as explained under "Theory", above.
Case I: Water
Case II: Alcohol
Case III: Mercury
The weight density of mercury is 13.55 gf/cm^{3}. If you choose V = 12 cm^{3}, the max. downward force that puts the barge on the verge of sinking is 12cm^{3}(13.55gf/cm^{3}) = 162.6gf rounded to 160gf. For ¾ submersion, the maximum downward force on the barge is (3/4)(160gf) = 120gf. Since the barge itself weighs 5.0gf; therefore, the safe load is only 115gf. Again, this is the calculated, or expected, or accepted value. Find the downward force for 3/4 submersion as well as the allowable load considering the barge's weight itself. Repeat all possible cases as you did for water and alcohol above with finding the corresponding % errors.
Table 1
Trial | Barge Volume (cm^{3}) |
On-The-Verge-of-Submersion Weight (gf) |
3/4 Submersion Downward Force (gf) |
Accepted (Adjusted)
Allowable Load (gf) |
Measured Allowable Load (gf) |
% Error |
Water D = 1 gf/cm^{3} |
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Alcohol D = 0.8 gf/cm^{3} |
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Mercury D = 13.55 gf/cm^{3} |
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5 |
Comparison of the results:
Provide the percent error formula used as well as the calculation of percent errors.
Conclusion:
State your conclusions of the experiment.
Discussion:
Provide a discussion if necessary.