Archimede’s Principle
PRE LAB QUESTIONS
1) State Archimede’s principle.
2) Use Archimedes' principle to prove the following: "When a body is floating on a liquid, it
displaces a weight of liquid equal to its own weight."
3) How would you determine the density of an irregularly shaped rock?
4) Lead has a greater density than iron, and both are denser than water. Is the
buoyant force on each one the same? Explain.
5) A beaker resting on a scale contains a fluid. If an object is submerged in the fluid,
how would you find the increase in the reading of the scale?
OBJECTIVE
The purpose of this experiment is to calculate the density of two solids by applying Archimede’s
principle and compare the result to the correct values. One of the solids is denser than water
while the other one is lighter.
MATERIALS
Triple beam balance
Graduated cylinder
Metal object
Wooden cylinder
INTRODUCTION
Any object of mass M and volume V has a density
=M/V
T
(1)
Archimede’s principle states that any object totally submerged in a fluid of
density f is buoyed up by a net upward force B equal to the weight of the fluid
displaced by the object. The displaced fluid is that volume of fluid equal to the
volume of the object below the fluid surface such that B = f gV. Hence, when an
object that is denser than water is in air, a balance measures its true weight Mg.
However, if it is submerged in water then the balance reads its apparent weight T
(or apparent mass Ma) such that
T = Mg – B = Ma g
M
B
Mg
(2)
Proceeding from the previous equations, the density  of the object is given by:
 = f [ M / ( M - Ma )]
(3)
However, if the object is lighter than water ( i.e wood) one must use a sinker
attached to the bottom of the object to make it submerge into the water. By
following the same above procedure, we can calculate the density of wood to be:
w = f [ M / ( Ms – Mw )]
(4)
where Ms is the apparent mass when only the sinker is submerged and sinker Mw
is the apparent mass when both sinker and wood are submerged.
M
EXPERIMENTAL PROCEDURES
1) Tie a string to the metal object and submerge it in a graduated cylinder filled with
water. Measure its volume from the amount of water it displaces.
2) Remove the object from water and tie the other end of the string to the hook
underneath the pan of the triple beam balance. Read the mass M of the metal
object.
3) While the situation is still the same, submerge the metal object in the graduated
cylinder and read now its apparent weight Ma. Be sure that the object is not
touching the side of the cylinder and that no bubbles are adhering to the object.
4) Put aside the metal object and replace it with of the wooden object. With a vernier
caliper, measure its radius and length.
5) As in procedure 2, read its mass M.
6) Attach a sinker to the bottom of the wooden object and submerge only the sinker
in the water. Read the apparent mass Ms.
7) Read the apparent mass Mw while both the sinker and the wooden object are
submerged in the water.
REPORT FORM
Part I Density of metal object
Mass M of metal object _______
Volume of metal object _______
Density of metal object from (1) ________
Apparent mass Ma of metal object _______
Density of metal object from (3)
_____________
Percent difference ___________
Part II Density of wooden object
Mass M of wooden object
___________
Radius of wooden object
_________
Length of wooden object
_________
Volume of wooden object
_________
Density of wooden object from (1)
_________
Apparent mass Ms
_________
Apparent mass Mw _________
Density of wooden object from (4) _________
Percent difference ___________
CALCULATION
1) Compute the density of the metal cylinder from equation (1).
2) Compute the density of the metal cylinder from equation (3).
3) Compute the percent error between the two values for the density of the metal
cylinder.
4) Compute the volume of wooden object using V = πr2h
5) Compute the density of the wooden object from equation (1).
6) Compute the density of the wooden object from equation (4).
7) Compute the percent error between the two values for the density of the metal
cylinder.
POST LAB QUESTIONS
1) How would an air bubble clinging to the metal object affect the value for its
density?
2) Derive Equation (3).
3) A lead sinker of mass 225 grams and density of 11.3 g/cm3 is attached to the bottom of a
wooden block of mass 25 grams and density 0.5 g/cm3. Calculate the apparent weight
when both are submerged in water.
4) A block of wood has a density of 0.53 g/cm3. What fraction of its volume is submerged in
oil of density 0.8 g/cm3?
5)
What is your conclusion from this experiment?