Experiment 9
Archimedes’ Principle
Objective:
The objective is to verify the Archimedes’ principle by
measuring the buoyancy for a submerged nondissolving solid object.
Equipment:
A small solid and regular shape object,
a few
meters of thin string, a mass balance, a force gauge, a caliper or a micrometer,
a beaker or a container, a Cclamp and rod, a skew clamp, and a calculator
Theory:
Archimedes’ principle states that when a
nondissolving 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 = (V_{object}
)( D_{fluid})
Where D =
ρg is the weight
density of the fluid. B in fact is the weight of displaced fluid.
Procedure:
 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 triangularbase prisms both made of aluminum.
 Use a caliper to measure the dimensions of
the selected aluminum piece and calculate its volume by using the appropriate
formula for volume calculation.
 Calculate the accepted value
for
buoyancy by using the buoyancy formula.
 Assemble an apparatus as shown in the
following figure for the experiment. One way is to use a rod attached to
a Cclamp that is secured to the edge of a table. A skewclamp 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 in the hanging position with only the string hangs from it.
 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, its buoyancy
force is negligible.
 Attach the aluminum piece to the string. Make a small loop at
the free end of the string and hang it from 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 Newtons
if the force gauge reads in Newtons. It is easier to have all
forces expressed in gramforce. Your instructor will clarify
what units to use.
 Fill the beaker 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.
 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.
 Use the knowledge of the weight in air and the weight in water to
calculate buoyancy. This is your measured value for buoyancy.
 Calculate a % error on B.
 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 nondissolving objects.
 Arrange a table for your
measurements and results.
Data:
Given:
1) The densities of the materials used (refer
to your text or a physics handbook. These values will be useful if the
weight in air is to be calculated and not measured.
2) The formulas for volume calculation of
regularshaped objects
Measured:
1) The dimensions of the submerged objects
2) Weights of the submerged objects in air and
water


Calculation(s):
Provide the necessary calculations.
Comparison of the results:
Provide the percent error
formula used as well as the calculated percent error(s).
Conclusion:
State your conclusions of the
experiment.
Discussion:
Provide a discussion if
necessary.