Laboratory #4: Archimedes` Principle

```Ph202: General Physics II Laboratory
Instructor: Tony Zable
Experiment #2 - 1
Laboratory #2: Archimedes' Principle
Preliminary questions:
1) A solid object is held above a container (mass = 0.10 kg) of water (volume = 1.0 x 10-4 m3) attached to
a force sensor as shown in the figure below. The mass of the object is 0.20 kg and the volume of the mass
is 2.5 x 10-5 m3. The density of the liquid is 1000 kg/m3.
i) What is the weight measured by the force sensor?
Force Sensor
ii) The object is lowered partially into the liquid.
How does the weight of the mass (as measured by
mass
container
iii) The object is lowered further into the liquid until
it is completely submerged (just barely). How does
the measured weight of the object compare with:
A) the weight of the object in (i)?
liquid
B) the weight of the object in (ii)?
Scale
iv) The mass is lowered until at the bottom of the
liquid container (just not touching the bottom). How
does the measured weight of the mass compare to the weight in (iii)?
v) The mass is now sitting on the bottom of the container (completely submerged) and a scale is placed
below the container. What is the reading on the scale?
Ph202: General Physics II Laboratory
Instructor: Tony Zable
Experiment #2 - 2
Introduction:
Eureka!! In this lab your goal is to perform some experiments to understand the source of Archimedes’
excitement when he discovered that the buoyant force on an object in a liquid is equal to the weight of the
liquid that the object displaces.
Archimedes made his discovery without the benefit of Newton's insights. He was arguably the premier
scientist of antiquity. Since you have Newton's achievements as part of your intellectual heritage (Ph201)
we'll use the concepts of force and equilibrium to measure the buoyant force acting on a (partially or
totally) submerged object.
Here is the idea behind the experiment. Suppose we hang a plumb bob (or small mass) from a force
sensor, arranged in the configuration shown in the figure below. The bob in the liquid may be partially or
totally submerged.
Force Sensor
plumb bob
cylinder
H2 O
According to Archimedes, the upward buoyant force (FB), which the liquid exerts on the object, is equal
to the weight of the fluid displaced or:
FB = mfluidg = (fluidV)g
(1).
It should be noted, the buoyant force produced by the displacement of fluid in the cylinder will result in a
reaction force of equal but opposite magnitude exerted by the bob on the liquid (according to Newton’s 3rd
Law). We will use this action-reaction relation to measure the buoyant “reaction” force with a standard
digital scale. When the plumb bob is inserted into the liquid, the force sensor will measure the net hanging
force, which should be equal to the weight of the bob minus the buoyant force, FB. Thus, when we look at
the forces acting on the force sensor:
Fext = FS = mg - FB = 0
(2).
Rearranging terms,
FB = mg - FS
(3).
Combining equations (1) and (3), the relationship between the buoyant force, the normal force (from the
scale) and weight of the cylinder and liquid is given by:
Ph202: General Physics II Laboratory
Instructor: Tony Zable
Experiment #2 - 3
FB = mg - FS = (fluidV)g
(4)
FS = mg - (fluidV)g
(5).
or
The Experiment:
Part I. The density of water
1. Using the force sensors in the lab, set up the experiment and measure the buoyant force on a plumb bob
as it is lowered into a graduated cylinder. Start LoggerPro then Open the experiment file called “Exp 2
Archimedes” in the \Home\Physics\Phy202 network directory. Note: Use 60 mL as your initial volume
of liquid. Record at least 4 readings.
Initial Volume of Liquid =
Volume (mL)
Volume Displaced (mL)
2. On a graph you should plot your measured force (Fs) vs. the volume of the water displaced. If
Archimedes is right, the slope of that line should be equal to (
). You fill in the blank. Use the
graph to determine the density (H2O) of the water. Be sure to express your answer in SI units.
 =_____________
% Error = _________________
3. Put the graduated cylinder with water on a digital scale. Record the reading. Suppose that, by the means
of a string, you submerge an object into the water (partially). Do you expect the indication of the digital
scale to change? Why? Write your prediction and explanation below.
4. Zero the scale with the liquid and container positioned on it (to eliminate this force from the scale
reading). Now submerge an object partially into the water. Read the indication of the scale and the
Ph202: General Physics II Laboratory
Instructor: Tony Zable
Experiment #2 - 4
volume displaced. Convert the scale value (in grams) to force units and record the value the table below.
Repeat the measurement by lowering the mass further into the liquid.
Initial Volume of Liquid =
Volume (mL)
Volume Displaced (mL)
5. Plot the buoyant force FB versus Vdisplaced graph and determine the density of the water.
=__________________
% Error =__________________
Part II. Determining unknown mass of added salt
6. Measure the mass of two teaspoons of table salt, then stir the salt into the water (in the graduated
cylinder). Wait for the salt to dissolve completely. Using either approach described above, perform an
experiment to determine the density of the salt water solution. Use the slope from your new graph to
determine the density (salt+H2O).
Mass of salt (measured) = _____________
solution=_________________
Initial Volume of Liquid =
Volume (mL)
Volume Displaced (mL)
7. Using the values for H2O and salt+H2O, estimate the mass of salt you added to the water.
Ph202: General Physics II Laboratory
Instructor: Tony Zable
Experiment #2 - 5
Hint: The mass of the salt-water solution (msalt&amp;water) is the same as the mass of the water (mwater) and the
mass of the salt (msalt). Re-write this statement as an equation and substitute density and volume values
(for the salt-water and the water) for the masses then solve this equation for the mass of the salt
msalt = ___________(write the final equation here ).
Using your measured values for volume and density, predict (calculate) the mass of the added salt.
How does this value compare with the measured value for the mass of a level teaspoon of salt?
Mass of salt (calculated) = _____________
% Error =_________________
8. Based on your observations, revisit the predictions you made in the first section of this exercise. How