PHYS 1401 –General Physics I
Archimedes
Principle
Leader:
___________________ Recorder:
__________________________
Skeptic:
___________________ Encourager:
________________________
Materials
600 ml beaker
Masking Tape
Triple beam balance
Density cylinders set
100 ml graduated cylinder
Modeling clay
Ring stand to support balance
Introduction
The story
is told that the Greek mathematician Archimedes liked to lounge around in his
bath all day. He would work out his
geometric proofs on his stomach (he was quite fat) writing with bath oil. One day when he was contemplating why things
floated, the idea, which has become known as Archimedes' Principle, occurred to
him. He became so excited by his
discovery that he jumped out of his bath and ran through the streets of his
town shouting "
Part 1
Discovery Activity
Procedure
1. Fill a
beaker to a known point about half full of water. Mark the level of the water in the beaker
with the masking tape. Take
a small piece of modeling clay and roll it into a ball which will easily fit
into the beaker and drop it into the water.
Mark the new level of water with a piece of masking tape.
Q1. Describe
what happens to the clay and the level of the water in the beaker.
Q2. From the
markings on the side of the beaker, estimate the change in the volume of the
water in the beaker when the clay was added.
Q3. Estimate
the volume of the clay by treating it as a sphere. (V = 
pR3)
Q4. Compare
your estimate of the volume of the clay ball with the change of the volume of
the water? Do they seem comparable? Why should they be the same?
A liquid
will tend to be as dense as it can at a given temperature, and if you apply a
force to it, you cannot make it any denser.
This property of liquids is known as incompressibility. Thus when you drop a solid object into a
liquid, it will merely add its volume to the volume of the liquid. We describe this by saying the solid displaces
its volume.
Q5. Is your
estimate of the change of volume consistent with the clay displacing its volume
in the liquid? Explain.
2. Now shape
the clay into a very thin tall boat.
Make sure that there are no holes and that the sides don't flop
over.
P6. Before
dropping the boat into the water, predict whether the water level will be
higher for the boat or for the clay ball.
Explain your reasoning.
Drop the clay boat into the beaker so that the boat
floats. (If the boat doesn't float, work
on it a little more.) With a piece of
masking tape, mark the level of the water in the beaker.
Q7. From the
markings on the beaker, estimate the displaced volume of the water when the
boat is in the beaker.
Q8. When the
boat is floating in the beaker, is the volume of the displaced water greater or
less than when you dropped the ball of clay into the beaker?
Q9. If the
volume is larger, then is the mass of water that you lifted greater or less
than before? Explain.
Q10. What force
is required to lift the mass of water?
What exerts that force on the water?
Q11. If the
mass is greater when the boat is in the water compared to the ball of clay,
then is the force required to lift the water greater or less? Explain.
Q12. If the
clay exerts a force on the water, then by
Q13. The
reaction force of the water on the clay is called the buoyant force. Using
Q14. The
buoyant force is equal to the ________ of the displaced liquid. This is a statement of Archimedes' Principle
which we will explore more quantitatively below.
Part 2
Procedure for Determining Archimedes’ Principle
No
eating or drinking in the lab while performing this procedure.
Fill a graduated
cylinder half full and record the reading.
Hang one piece of the provided metal set from underneath the pan of the
triple beam balance and measure the mass.
Record the mass in the column labeled Scale reading (Air) in the table
below. Lower the mass so that it submerges completely in the graduated
cylinder. Use the triple beam balance to
determine the reading when the mass is submerged and record the value in the
data table below in the column labeled Scale Reading (Water). Record the change in volume of the water in the cylinder in the
column headed Displaced Volume. Determine the mass of the displaced water by
multiplying the displaced volume in ml by the density of water in units of .001
kg/ml. Repeat the entire procedure for
each of the different metals in the provided set so that you have a total of 5
sets of data.
Wash
your hands thoroughly after completing the procedure to remove any lead dust
that may have gotten on you.
Data
Initial
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Scale Reading (Air) (kg) |
Scale Reading (Water) (kg) |
Displaced Volume (ml) |
Mass displaced water (kg) |
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Data Analysis
and Questions
1) How do you calculate the weight of an object
if you know it’s mass?
2) The mass is supported by a force provided by
the string called a tension. Draw
a free body diagram for the mass when it is suspended in the air and solve for
the tension in terms of the weight.
Label the tension T and the weight W.
3) When the mass is submerged in the liquid an
extra upwards force called the buoyant force acts on it. Draw a free body diagram for the mass when it
is suspended in the liquid. Solve for
the tension in terms of the weight and buoyant force. Label the tension T, the buoyant force B, and
the weight W.
4) Is the tension greater when the piece of
metal is suspended in air or when in water?
Explain your answer.
5) What is actually pulling the pan of the
triple beam balance?
6) So which of the forces is the triple beam
balance actually measuring?
7) Copy your readings from the table above and convert
each of the readings of the scale to a tension and record in the table
below. Also convert the mass of the
displaced water to a weight for each case.
Leave the last column blank for now.
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Scale Reading (Air) (kg) |
Tension (Air) (N) |
Scale Reading (Water) (kg) |
Tension (Water) (N) |
Mass of Displaced Water (kg) |
Weight of Displaced Water (N) |
Buoyant Force (N) |
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8) Compare your answer to 2) and 3) above and explain
how you can determine the buoyant force from the two readings of the tension.
(Tension in air and Tension in liquid)
9) Use your answer to 8) to record the buoyant
force on each piece of metal in the last column of the table above.
10) How does the buoyant force compare to the
weight of the displaced water? This idea
is Archimedes Principle.
11) Complete the following:
The ____________
force on an object immersed in a liquid is equal to the ___________of the
displaced liquid.