Archimedes principle and buoyancy

In this lab exercise your goal is to determine the density and specific gravity of solid and liquid
Part I
Demonstration of Archimedes’ Principle
1. The setup consists of a pan balance from which a string can be attached, so that the mass may
be immersed in an “overflow can”. The water that overflows is caught in a beaker and can be
weighed to determine its volume, or the volume can be directly read from the graduations on the
beaker. The weight of the mass can be measured while it hangs in air or immersed in water.
Determine the mass of the metal sample by weighing it on a laboratory balance.
Record the result on the data table. Weigh the empty beaker also.
Fill the overflow can with water until it overflows. Catch any overflow water in a beaker
and dump it down the drain. Now suspend the mass in the water and catch the overflow
in the beaker in order to determine the volume of water displaced. Record this volume.
You should also weigh the beaker with this water in order to determine the mass of water
displaced, in order to compare with your estimate of the volume of the water as measured
by the graduated marks. (Here you need to know that 1 gram of water has a volume of 1
cubic centimeter.) Which estimate do you think is more accurate?
The metal sample should also be weighed while it is under water, in order to determine
the buoyant force. This can be done while you are capturing the overflow water, or as a
later procedure. You just need to make sure that you are measuring the force in the
string, and that this is due to the weight of the mass, minus the buoyant force. In order
for this to be true, you must ensure that the mass is not touching the sides or bottom of
the beaker. (Think of how the free-body diagram for the mass would change if it were
partly supported by the bottom of the beaker; you wouldn’t be able to measure that
contact force and would therefore be unsure of the size of the force in the string.) By
looking at the free-body diagram for the mass suspended in water, you can see that this
buoyant force is the difference between the object’s true weight and submerged weight,
Fb = mog – (mog)’ Archimedes’ principle says that this buoyant force is equal to the
weight of the displaced water (which was the water that overflowed). Fb = ww = mwg
You should compute the (measured) buoyant force and compare it to the weight of the
displaced water and find the percent difference.
Finally, compute the specific gravity of the metal sample and compare to the accepted
value. (Al – 2.7, Brass – 8.4, steel – 7.9. lead – 11.3)
Part II
Density of a light object
Determine the density of a wooden block by using a heavy metal object as a sinker.
There are several ways to do this, and your instructor will show one before lab. First,
though, weigh the wooden block while it is still dry.
One way is to hang the sinker below the wooden block so that 1 or 2 cm of string
separates the two, then immerse the sinker but leave the wooden block above the surface.
Record the apparent mass of the two objects, as measured by the balance. Then raise the
container of water so that both the sinker and block are immersed, and record the
apparent mass of the two. The difference between these two measurements is that the
block is immersed or not, and so the difference in the apparent masses is related to the
buoyant force created when you immerse the wooden block. Therefore, you can just take
the difference in apparent masses, write it in grams, and immediately conclude that this is
the mass of the water displaced (by Archimedes’ principle). Therefore, the volume of
water displaced is equal to this number (of cubic centimeters) and you don’t even need to
measure the actual water displaced. Now that you know the volume of water displaced
by the block, you deduce that it is also the volume of the block. Then, knowing the mass
and volume of the block, you calculate the density of the wooden block by using the
recorded dry mass of the block and its deduced volume, and applying the definition of
density  = m/V.
Part III
Density of a liquid
The density of a liquid will be determined directly by using a container with an accurate
volume of liquid and simply weighing the volumetric flask with and without the liquid to
determine the mass of the liquid. Therefore the calculation of density is immediate. This
will be done with a “mystery” liquid which will be available in the laboratory. This
liquid is harmless unless you drink a moderate amount of it. Start by weighing the empty
flask (with its glass plug). Fill the flask to slightly overflowing with the unknown liquid,
and then put the plug in (gently, don’t push too hard or it might get jammed). Wipe off
excess liquid and weigh the full flask. Please recycle the liquid to the Erlenmeyer flask
(conical flask) after weighing the full volumetric flask. You can read the volume of the
flask off the side and directly calculate the density of the fluid from the mass of liquid
and its exact volume. Compare your calculated density to the known density of some
possible fluids.
Physics 124
Data and results for Lab 8
Name _____________________________
a) Density of heavy solid
Type of metal ______________
Mass of metal mo in air ___________________
Mass of beaker mb ____________
b) Mass of beaker and displaced water (mb + mw) _________________
Mass of displaced water ___________
Volume of displaced water (cm3) ____________ (How does this relate to the mass of water?)
c) Apparent mass of metal mo’ when suspended in water ________________
Difference between true mass and apparent mass under water (mo – mo’) ______________
Buoyant force (in Newtons) Fb = mog – (mog)’ = (mo – mo’)g = ___________________
Weight of displaced water (in Newtons) _______________________
Percent difference of these two forces ____________
d) Density of metal sample _________________ Specific gravity of metal sample ________
Show calculations here:
e) Density of light solid (wood)
Mass of dry wooden block in air _________________
Mass of block and sinker with only sinker submerged __________________
Mass of block and sinker with both submerged __________________
Difference in measured apparent masses ______________________
Deduced volume of displaced water (hence volume of block) _________________
Density of wooden block ______________________
f) Density of liquid
Mass of empty volumetric flask _____________________
Mass of full flask ______________________
Mass of liquid (difference of above masses) ___________________
Density (divide by 50 mL volume of flask) __________________
Question: The accepted value of specific gravity for pure isopropanol is 0.786. For rubbing
alcohol it is 0.79. For methanol it is 0.81. For water it is 1.00. Which liquid do you think it is?
Is your value a little high? If so, what contamination might there be in the liquid?
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