Experiment 9

Archimedes' Principle

Objective:

The objective is to verify the Archimedes' principle by measuring the buoyancy for a submerged non-dissolving solid object.

Equipment:

A small solid and regular shape object, a meter of thin string, a mass balance, a force gauge, a caliper or a micrometer, a beaker or a container, a C-clamp and rod, a skew clamp, and a calculator

Theory:

Archimedes' principle states that when a non-dissolving object is submerged in 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 = Vobj* Dfluid

where D = ρg is the weight density of the fluid.  B in fact is the weight of displaced fluid.  That's what Archimedes figured out.

Procedure:

1) Use a regular shape aluminum piece available in your Physics Lab for submersion in water.  The reason for choosing a known geometric shape object is its ease of volume calculation and dimensions measurement.  Available objects are 2"-diameter cylinders and triangular-base prisms both made of aluminum.

2) Use a caliper to measure the dimensions of the selected aluminum piece and calculate its volume by using the appropriate formula for volume calculation.

3) Calculate the accepted value for buoyancy by using the buoyancy formula.

4) Assemble an apparatus as shown in the following figure for the experiment.  One way is to use a rod attached to a C-clamp that is secured to the edge of a table.  A skew-clamp that can be secured at different elevations on the rod may be connected to the rod.   The force gauge then may be hung from the skew clamp.  The force gauge must read zero to begin with.

5) Measure the weight of the aluminum piece in air.  You may simply use a mass scale for this purpose.   Note that air (also a fluid) applies buoyancy onto all objects submerged in it, but since its weight density is very small compared to that of water, the buoyancy imposed by air is negligible.

6) Attach the aluminum piece to the string.  Make a small loop at the free end of the string and hang it on the force gauge.  The force gauge should read exactly the same weight you measured with the mass balance.  You may have to convert grams to kilograms and then find the weight in N if the force gauge reads in N.  It is easier to have all forces expressed in gram-force.  Your instructor will clarify what units to use.

7) Fill the beaker or a larger container with enough water and place it under the aluminum piece that is hanging from the force gauge.  Adjust the position of the skew clamp or change the length of the string attached to the force gauge until the aluminum piece is fully under water but still supported by the force gauge.

8) Read the weight of the aluminum piece in water (the apparent weight) and record its value.  Make sure your eye sight is perpendicular to the force gauge when reading the weight.

9) Use the values of weight in air and weight in water to calculate buoyancy.  This is your measured value for buoyancy.

10) Calculate a % error on B.

11) Repeat the experiment (all of the above steps) for one more object of a different shape.  Your instructor will help you with the selection of suitable non-dissolving objects.

12) Arrange a chart for your measurements and results.

 Data: Given: 1) The densities of the materials used.  Refer to Experiment 1 for mass densities. 2) The formulas for volume calculation of regular-shaped objects Measured: 1) The dimensions of the submerged objects 2) Weights of the submerged objects in air and water

### Provide the necessary calculations.

Comparison of the results:

Provide the percent error formula used as well as the calculated percent error.

Conclusion:

State your conclusions of the experiment.

Discussion:

Provide a discussion if necessary.