Archimede’s Principle

Archimede’s Principle -- Buoyancy

The purpose of this exercise is to study Archimede’s Principle, which states:

When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

In other words, suppose an object weighing W₀ Newtons is immersed (completely or partially) in a fluid and displaces a volume of fluid equal to V cubic meters. If the weight of the displaced fluid is W_d then the apparent weight of the object will be W_app = W₀ - W_d. If the density, r , of the fluid is known then W_d = r Vg, where g is the acceleration due to gravity.

The following equipment and materials will be available for this exercise.

Test tube 15cm x 28 mm (freighter)	Displacement Cup
Graduated cylinder (100ml)	Mass set 10g -- 1kg
Spring scale (0-2.5 N)	Small gauge wire
Masking tape	H₂O -- all you want
Test tube guide	Unknown fluid
Beakers	Balance

Tasks:

1. Use Archimede’s principle, to design a way of determining the weight of an empty test tube (freighter). After the weight has been determined, use an equal arm balance to mass the test tube and determine it weight, compare the results and explain any differences.

2. The weight of the cargo on a freighter is determined by observing the amount the freighter is immersed in the water. A scale is painted on the bow of the ship that is calibrated according to the amount of cargo on board. Clearly the more cargo on board, the lower the ship will sit in the water. Using the test tube from the first exercise to represent a freighter, construct a scale to be attached to the test tube that can be used to determine the weight of the cargo. Construct a conversion table that will account for the fact that the ship may be in fresh water, or salt water. Attach the scale to the freighter (test tube) and test the scale by at least two methods. Make sure the weight of the tape is accounted for in the analysis. Explain in detail the test methods employed and the results of the tests.

3. Using the freighter, determine the specific gravity (relative density) of the unknown fluid.