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Archimedes’ Principle
PURPOSE & OBJECTIVES
The buoyancy force FB on an object submerged in a fluid is caused by differences in pressure
at different heights in the fluid. This difference in pressure can be shown to result in a net upward
force at the center of buoyancy and is equal to the weight of the displaced fluid.
FB = weight of the displaced fluid
(Eq 1)
If a solid is lowered into a fluid using a string, one finds that it “weighs” less as measured by the
tension force in the string.
T
Fig. 1
The free-body diagram for the mass in the fluid is shown in Fig 2.
T
Fg = Weight;
FB
FB = The Buoyancy Force;
Fig. 2
T = Tension in the supporting
string.
Fg
1
06A- Archimedes’ Principle
Since the acceleration of the mass is zero, we expect the vector sum of the three forces to be zero.
 

T  FB  Fg  0
and obviously
T = Fg - FB
(Eq 2)
Fg is the weight of the block. FB is the buoyancy force which based on Eq 1 will equal the weight of
the displaced fluid.
In this lab you will use a cubical block of base area A, and submerge it to various heights (h).
Equation 2 then becomes.
T = mg – 0(Ah)g= mg – 0(V)g
(Eq 3)
where 0 is the density of the fluid. A graph of T vs (Vg) can then be used for finding the density of
the fluid. Plot the apparent weight as measured by the tension T against (Vg). The slope of the
resulting straight line will yield 0. Compare your results with known values for the density of water
at the temperature of the water.
From (3) we can also derive the following relationship for the density () of a solid.
 mg 
  0
 mg  T 
  
(Eq 4)
In this experiment, we will :



Determine the density of a fluid
Determine the buoyant force acting on a solid
Determine the density of solids using buoyant force and fluid density.
MATERIALS
Laboratory balance
Force Sensor
Solid samples
Beakers
Support Stand
Temperature Probe
fluid samples
PROCEDURE
1.
Be sure to use units that are consistent. For instance m, m2, m3, cm, cm2, cm3, etc.
2
06A- Archimedes’ Principle
2.
Measure the bottom sides and calculate the area A of the solid’s base. Take the temperature of
the water.
3.
Make a mark on the solid block every 0.5 cm vertically starting from the bottom.
4.
Make a loop of string so that the block can be hung without touching the beaker located below
the stand holding the Force Sensor.
5.
Make sure the balance is zeroed properly. Determine the mass of the block. Set the empty
beaker in position. Hang the block inside the beaker using the string. Now pour water from
another beaker slowly from the side. Fill the beaker to a level matching the first of your marks.
6.
Record the new force. Repeat for the next mark.
7.
Repeat for the next block sample. Do three sample blocks in total.
8.
Plot the graph of tension T against (Vg), then determine the 0 of the fluid. You will have
three lines on your graph. Determine the average slope. Compare with the accepted value of
water at the temperature.
9.
Using the density determined from the slope of the line and Equation 4, determine the density
of two other solid blocks.
10. Repeat the procedures to determine the density of another unknown fluid.
DATA
Mass of Block
Block 1
Block 2
Block 3
(
)
Height (
)
Block 1
Area ( 2)
Tension (N)
Height (
)
Block 2
Area ( 2)
Tension (N)
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06A- Archimedes’ Principle
Water Temperature (OC)
Height (
)
Block 3
Area ( 2)
Tension (N)
ANALYSIS
1. What was the known value for the density of water at the temperature that your sample was?
2. How did you compare the two values? Show your calculation.
3. If you were to have used water at a higher temperature, how would the tension values been
affected?
4. If you were to have used water at a lower temperature, how would the buoyant force have been
affected?
4
06A- Archimedes’ Principle