Part A: Bouyancy and Density

Purpose: The purpose of this experiment is to investigate Archimedes' Principle which states that the buoyant force of a fluid is equal to the weight of the displaced fluid. Density and specific gravity are also defined and investigated.

Density is defined as mass per unit volume:
 

In SI units, mass will be given in kilograms and the volume will be obtained in meters³. Other units may be used such as grams for the mass and cm³ (sometimes refered to as cc) or, equivalently, as milliliters (ml) for the volume.

Specific gravity is the ratio of the density of a material to the density of water. For our purposes we will take the density of water to be 1000 kg/m³ or 1 g/cm³. Specific gravity is a useful concept when one is comparing materials. For example, given that the specific gravity of surface material on the Earth is about 3.5, one immediately has a "feel" for the density of the material as one can mentally compare the material to the familiar density of water.

Mass can be determined by weighing the sample on a balance. The volume can be determined by a variety of methods:

1. The volume can be computed from its dimensions.

2. The volume can be measured by determining the volume of the liquid
displaced when the sample is immersed.

3. The volume can be determined by the application of Archimedes'
Principle.

Archimedes' Principle rests on the assumption that the fluid is in static equilibrium. That is, the fluid is everywhere motionless. Consider an imaginary surface enclosing a sample of the fluid. That fluid's weight is supported by the buoyant force of the surrounding fluid. If we were to remove the fluid inside the imaginary surface and were to replace it with a sample of material of the same shape, the buoyant force would remain unchanged. Thus, the buoyant force is equal to the weight of the displaced fluid.

It follows that if a sample is weighed in air and weighed in water, the apparant loss of weight is a measure of the buoyant force and, therefore, of the weight of the displaced fluid. Given that the density of water is known, if water is used as the fluid, the volume can be immediately determined from the equation given above.

Apparatus: calipers, beam balance, spring balance, water, graduated beaker

Procedure:

1. Determine the mass of a block of wood by weighing it on the beam balance.

2. Measure the dimensions of the block of wood with the calipers and determine the volume of the wood.

3. Calculate the density of the wood block.

4. Determine the volume of the block of wood by determining the volume of water displaced when the wood is immersed. Do this by attaching a sinker to the piece of wood. Of course, the sinker should be dense enough and massive enough to pull the wood completely under the water. Determine the level of the water when the sinker is immersed and again when both sinker and wood are immersed.

5. Again calculate the density of the wood.

6. Measure the volume of the block of wood using Archimedes' Principle. Weigh the wood and sinker combination with the sinker totally immersed in the water. Again determine the weight with both sinker and wood immersed. Use the difference in weight to determine the weight and hence the volume of the displaced water. This, of course, is also a measure of the volume of the wood.

7. Again calculate the density of the wood.

8. Compare the three determinations of the density of the wood. Be sure to use significant figures.

9. What is the specific gravity of the wood?

10. Determine the density and the specific gravity of a sample of concrete using the last two methods.

11. Determine the density of lead using Archimedes' Principle.

12. Determine the density of an unknown oil (provided).

13. A gold ring weighs 30 g in air and 28.2 g under water. What is the density and specific gravity of this ring?

14. A crystal weighs 7 g in air and 1.84 g in carbon tetrachloride, which has a specific gravity of 1.6. Calculate the density of the crystal.