Download Density, the Buoyant Force, and Archimedes` Principle

4CArchimedes
05/31/2007 03:27 PM
Density, the Buoyant Force, and Archimedes' Principle
Goal: To verify Archimedes' principle by comparing the density of a metal cylinder obtained by two
methods.
Equipment List:
graduated cylinder
beaker
vernier calipers
metal cylinder
string
pan balance with rods for raising
paper towels for cleaning up
Pre-lab Exercise: none
Background:
Archimedes' principle states that an object wholly or partially submerged is buoyed up by a force equal
to the weight of the displaced fluid.
The pressure at any point in a volume of fluid is due to the weight of the column of fluid above it. In an
incompressible liquid, the pressure is a linear function of depth: P = Dgh where D is the density and h is
the depth. This pressure is independent of the horizontal cross-sectional area of the liquid or of the object
submerged in it. Since the pressure, P, increases with depth, there is a higher pressure on the bottom of the
object than the top. Thus there is a greater force up on the object than down. The net force, called the
buoyant force, is equal to the weight of the fluid displaced by the object. If the object is less dense than the
fluid, it sinks until the buoyant force is equal to its own weight and it then floats at equilibrium. If the
object is more dense than the fluid, the buoyant force is less than the weight of the object, but the apparent
weight of the object is less by the amount of the buoyant force which is still equal to the weight of the fluid
displaced.
Note the following relationships:
spec. gravity = weight of object in air = Do
weight of an equal vol of water
Dw
=
weight of the object in air
apparant weight loss
Where Do is the density of the object and Dw is the density of water
.
Procedure:
Part 1: Direct calculation of the density of water:
Measure and record the mass of the small beaker (or the graduated cylinder if you have one), with an
uncertainty.
Partially fill the graduated cylinder with tap water. Record the volume and estimate the uncertainty in
the volume.
Pour the water into the small beaker and determine the mass of the water alone, with an uncertainty.
http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html
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4CArchimedes
05/31/2007 03:27 PM
Determine the density of water with an uncertainty. Is your value within the uncertainty of the
accepted value? (Note: the density of water is 1.0 g/cm3 .) Why or why not?
Part 2: Direct calculation of the density of the metal block:
Measure and record the mass of the metal block, with uncertainty.
Partially fill the graduated cylinder with water. Record the volume of water (with
uncertainty).
Completely immerse the metal block in the water, determine the volume of the block with
uncertainty.
Compare the volume of the block measured by immersion to a measurement of the volume using the
vernier calipers.
Determine the density of the block with uncertainty.
Part 3: Using Archimedes' Principle to determine the density of a metal block:
Using the small metal rod, raise the pan balance off the surface of the table.
Tie a string to the small metal block and measure its mass by attaching the string to the
underside of the balance. This is called a Jolly balance after German physicist Philip Van
Jolly.
Verify that your reading for the mass of the block is the same as it was on the pan itself.
Remember there is additional mass due to the string.
Fill the small beaker with water. Completely submerge the metal block attached to the underside of
the pan balance in the beaker filled with water. Record the new apparent mass.
Using Archimedes' Principle, determine the specific gravity of the metal block and use that to
determine the density of the block with uncertainty. Use your value for the density of water
calculated in part a. Then, try it again using the accepted value for the density of water.
http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html
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4CArchimedes
05/31/2007 03:27 PM
Do your values for the density of the block from part 2 and 3 agree within uncertainty? Why or why not?
Conclusion:
Review your results.
http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html
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