AP PHYSICS Archimedes’s Principle LabNAMES: ______
Introduction:
Buoyancy: Aristotle thought it was due to the shape of a body. If the body had sharp edges, it would sink. If the body was smooth and rounded – like the hull of a ship – it would float. He apparently ignored all of the round river rocks at the bottom of any river. Like most of the teachings of the old dead Greed Aristotle, his idea of buoyancy is pure nonsense.
Enter the old dead Greek guy Archimedes of Syracuse (Sicily). Archimedes was a mathematical genius. He came up with some cool stuff. Some highlights include figuring out how to calculate pi accurately to 10,000 digits and determining the volumes of conic sections like parabolas and ellipses. He also figured out how to calculate the diameter of the Sun, invented the Archimedes screw, the compound pulley, singlehandedly defended his city with home made seige weapons during the punic wars, discovered what we now call Archimede’s Principle, and most importantly, coined the word “Eurika.”
Archimedes’s Principle states that a body immersed in a fluid is buoyed upward by a force equal in magnitude to the weight of the fluid displaced by the body. 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. Also, the volume of fluid displaced by an object is equal to the volume of the object (Vo = Vf).
Pre-lab:
Fb = weight of the displaced fluid
If a solid is lowered into a fluid using a string, one finds that is “weighs” less as measured by the tension force in the string.
1.) In the space below, draw a free-body diagram for the mass hanging in the air, then the mass in the fluid (as shown above): Label Fg, Fb, and Ft
AIRFLUID
2.) From the freebody diagram of the mass in the fluid, write the equation for the total forces acting on the mass. Remember, a = 0 of the mass (it’s not moving).
3.) Solve the equation for Ft
In this lab you will use a mass of a cross sectional area A, and submerge it to various height (h).
Fb = mg. o = m/V The volume of the shape is V = Ah
4.) Substitute V into the o equation, and use the o equation to substitute m in the Fb equation. Where o is the density of the fluid. Then plug this into equation from step #3.
A graph of the apparent weight (Tension) vs (Agh) can then be used for finding the density of the fluid. The slope of the resulting straight line will yield o, the density of the fluid..
Going back to the equation from step 4, we can derive the following relationship for the density () of a solid:
=
Lab Procedure 1 (Determining the density of objects using Archimedes’s principle):
Materials: 4 different materials, beaker, water, spring scale, string
Be sure to use consistent units. Use m’s not cm’s.
Using equation: = , and assuming you know the density of water (1000 kg/m3), calculate the densities of 4 materials.
1.)Weigh your material on the spring scale, and record the weight in the chart.
2.)Submerge your material, and record the apparent weight in the chart.
3.)Subtract the two weights, and record in the chart.
4.)Using the above equation, calculate the materials density.
5.)Use a density chart to determine what your object is composed of.
Object # / Weight / Weight apparent / Delta Weight / Density1
2
3
4
Lab Procedure 2 (Determining the density of 3 fluids using Archimedes Principle)
(Water, Oil, Alcohol)
Materials: 2 materials of different mass, string, spring scale, graduated cylinders – one with water, oil, and then alcohol)
Be sure to use consistent units. Don’t use m2, then cm2, use the same units.
*** The Oil is messy, please be careful when using it.
During this lab, create a data table with the following information
1.)Select one material (long cylinder). Measure the bottom and calculate the area A of the base. Be sure to measure this ACCURATELY.
2.)Mark off the material every 2.0 cm vertically starting from the bottom.
3.)Hang the material on a string connected to a force reader such that it can be submerged in the graduated cylinder without touching the sides.
4.)Calculate the mass of your material using the force scale
5.)Hang the material inside the graduated cylinder with the fluid in it. Submerge the material to the first marked line. Record the tension force on your force reader.
6.)Continue repeating step 5 for the next 0.5 cm marks, until you have readings at all of the marks.
7.)Repeat steps 1 – 6 again, with a different material.
8.)From the equation in pre-lab step 4, plot the graph of tension Ft against (Agh), (Ft is on the Y-axis, Agh is on the X-axis) then determine the o of the fluid. You will have two lines on your graph (you used two materials), determine the average slope. This is average slope is your value for o, the density of the fluid.
9.)Repeat steps 1-8 for the additional two fluids, and fill in the charts below.
Fluid 1 -
Material 1A = / Ft / h / (Agh) / Material 2 A = / Ft / h / (Agh)
- / 0.0 / - / 0.0
- / .02 / - / .02
- / .04 / - / .04
- / .06 / - / .06
- / .08 / - / .08
Average slope of graph = o =
Fluid 2 -
Material 1A = / Ft / h / (Agh) / Material 2 A = / Ft / h / (Agh)
- / 0.0 / - / 0.0
- / .02 / - / .02
- / .04 / - / .04
- / .06 / - / .06
- / .08 / - / .08
Average slope of graph = o =
Fluid 3 -
Material 1A = / Ft / h / (Agh) / Material 2 A = / Ft / h / (Agh)
- / 0.0 / - / 0.0
- / .02 / - / .02
- / .04 / - / .04
- / .06 / - / .06
- / .08 / - / .08
Average slope of graph = o =