Density, Buoyancy and
Archimedes’ Principle
UM Physics Demo Lab 07/2013
Pre-Lab Question
What two vertical forces act on an object floating in equilibrium, partially submerged
in a liquid?
EXPLORATION
Materials
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1
1
1
1
1
1
1
1
1
1
1
bent fork
paper clip
Petri dish
brass block
aluminum block
wood block
Teflon rod
wood rod
aluminum rod
film canister
portion of fine sand
plastic spoon
1 graduated cylinder
1 digital gram scale
1 cut-off 2 liter soda container (vessel for
floating film canister)
1 clear plastic ruler
1 calculator
2 paper coffee filters (sand containment)
Shared Components:
soapy water
paper towels
vacuum cleaner for sand cleanup
Density
Density is the ratio of mass to volume of a uniform material. You are going to
measure and compare the densities of some common materials.
1. Objects float or sink in water depending on their density. Fresh water has
density of about 1g/cm3. Predict which blocks and cylinders will float or sink in
Dennison water using the cut-off 2 liter soda bottle container, then test your
predictions.
Object
Float or Sink
(Prediction)
Float or Sink
(Observation)
Brass Cube
Aluminum Cube
Wood Cube
Wood Cylinder
Teflon Cylinder
Aluminum Cylinder
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2. Measure the dimensions of the blocks using your ruler (use cm):
Brass
Aluminum
Wood
Length (l)
Width (w)
Height (h)
3. Measure the dimensions of the cylinders (use cm):
Dimension
Wood
Teflon
Aluminum
Height (h)
Diameter (d)



Measure the mass of the blocks and cylinders in grams with the scale and
record in the table below.
Calculate the volume of the blocks and the cylinders.
The volume of a block is: V  l  w h
The volume of a cylinder is the area of the base times the height:
2


d 
V    h
2
Density (ρ, the Greek letter “rho”) is defined as the ratio of mass (m) to
m
volume (V):  
V
Calculate the density of each block and cylinder from your mass and volume
measurements and record your results in the table below:
Object
Mass
(grams)
Volume
(cm3)
Density
(g/ cm3)
Brass Cube
Aluminum Cube
Wood Cube
Wood Cylinder
Teflon Cylinder
Aluminum Cylinder
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4. Which has a larger density: a 10 lb. bag of marshmallows or a 10 lb. bag of
lead?
5. Which has the larger volume the marshmallows or the lead?
6. Based on your observations for questions 1 and 3, what relationship between
the density of an object and the density of water determines whether the
object floats or sinks in water?
7. Measure the density of water in Dennison. Use the graduated cylinder. First,
measure the mass of the cylinder alone, and then measure the mass of the
cylinder with some water in it (preferably an even volume such as 20ml).
Subtract the mass of the cylinder from the mass of the cylinder with water in it
to find the mass of the water. Milliliters are a unit of volume, 1 ml = 1 cubic
centimeter. Calculate the density of Dennison water in g/cm 3. Show your
calculations!
Mass of Graduated
Cylinder
(grams)
Mass of Graduated
Cylinder and Water
(grams)
Mass of Water Only
(grams)
Density of Dennison Water: ___________________
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Archimedes’ Principle
Archimedes’ Principle states that the upward buoyant force on an object fully or
partially immersed in a fluid is equal to the weight of the fluid it has displaced,
which is in turn equal to the product of the submerged volume of the object, the
density of the fluid and the acceleration of gravity. For the object to float in
equilibrium the upward buoyant force must equal the downward weight of the
object, which is in turn the product of the object’s mass and the acceleration of
gravity g.
Testing Archimedes’ Principle
Carefully measure the diameter of the bottom of the film can with your ruler and
record in the table below. Next, place the film can inside the coffee filters and fill the
can with 2-3 plastic spoonfuls of sand and tightly seal the lid. Now float the can
bottom down in the 2-liter soda bottle, next to the wall of the bottle. If necessary,
add or remove some sand until the can floats vertically with the lid clear of the water.
Carefully measure the distance from the surface of the water to the bottom of the
submerged can. Calculate the volume of the portion of the can which is submerged
(see question 3) and calculate the corresponding mass of water the can has
displaced (submerged volume x density of water). Finally, dry the can, weigh it with
the scale and record the can’s mass below.
Diameter
(cm)
Submerged
Height
(cm)
Submerged
Volume
(cm3)
Mass of
Can
(g)
Mass of
Displaced
Water
(g)
8. Draw a Free Body Diagram for the film can floating in water. Indicate the
surface of the water and include the buoyant force and the object’s weight.
Express the magnitude of the buoyant force in terms of the mass of the
displaced water and the weight of the can in terms of the can’s mass. How do
the magnitudes of these two forces compare?
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9. In light of the answer to question 8, what relationship must hold between the
mass of the displaced water and the mass of the film can? Justify your
result by writing a simple expression relating the magnitude of the buoyant
force and the weight of the can consistent with both Archimedes’ Principle and
the fact that the can is floating in equilibrium. (Hint: consider your answer to
question 8).
10. Compare the mass of displaced water you have estimated for the floating
film can and the mass of the can. In light of your answers to questions 8 and
9, do your results support the validity of Archimedes’ principle? Explain.
Surface Tension
11. Pour water into a Petri dish as full as possible. How far over the rim can you
go before it overflows? Draw a picture of the shape.
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12. How is it possible for the water to extend above the rim of the dish without
spilling?
13. Prediction: Paper-clips are made out of steel with a density of 7 g/cm3. Can
a paper-clip float on water? Explain your reasoning.
14. Place a paper-clip in the water by carefully lowering it onto the water’s
surface with the bent fork. Does the result agree with your prediction? Explain
your observations. Are these observations consistent with Archimedes’
Principle? Explain. (Hint: Sometimes the paper clip will perform better if it is
somewhat greasy; consider rubbing it with your fingers or on your forehead or
nose).
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APPLICATION
1. While floating a paper clip, add a drop of soapy water with your finger onto the
surface of the pure water. Place the drop on the far side of the Petri dish from
the clip. Observe what happens. Discuss with your group what you’ve
observed and record your conclusions about what happened.
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Everyday Applications
1. Some redwood trees on the coast of Northern California grow to a height
of 122 m (367 ft) and a diameter of 7 m (22 ft). The mass of one of
these trees is 2.2 x 106 kg (4.6 million pounds!). If one of these
massive trees fell into the water, would it float or sink? Explain your
reasoning and show your calculations. (Data: In SI units the
density of water is 1,000 kg/m3.)
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Summary
 Density is the ratio of an object’s mass and volume
 Archimedes’ Principle states that the buoyant force on an object is equal to
the weight of the fluid it has displaced.
 As a consequence of Archimedes’ Principle, an object will float if its density is
less than that of the fluid, sink if its density is greater than that of the fluid
and be neutrally buoyant if its density exactly equals the density of the fluid
 Water exhibits a surface tension which causes the surface of water to behave
like a membrane. Small objects with a density greater than that of water can
be supported on the water’s surface in violation of Archimedes’ Principle.
 Soaps and detergents dispel the surface tension of water and eliminate water’s
ability to support objects on its surface.
 The most famous use of a density measurement was done by Archimedes (290210 B.C.). He was hired by the king to verify that a gold crown he’d
commissioned had not been substituted in part by less valuable (and less
dense) silver. However, the crown was very expensive and Archimedes could
not melt the crown to ascertain its volume. While stepping into a bath he
observed the change in water level, and realized he could do a volume
displacement measurement. In his excitement, he ran naked through the
streets yelling “Eureka! Eureka!” (Greek for “I have found it!”).
 Product manufacturers (in industries such a food, beauty, and health) use
density measurements to verify consistency among products. They measure the
density of product from different batches to make sure that there is
consistency. Distillers of illegal “moonshine” liquor will often adulterate their
product with ash or other substances to alter the density to mimic a higher
alcohol content than the liquor actually contains.
Final Clean-up
Please clean all table surfaces you used and return equipment to the carts. Please dry
individual pieces that may be wet and dispose of water in the sink. Please sweep any
spilled sand into the trash.
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