PHYSICS-1
ARCHIMEDES PRINCIPLE
EXPERIMENT-13: Archimede’s Principle
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
T
INTRODUCTION
Any object of mass M and volume V has a density
=M/V
(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 the
volume of fluid equal to the volume of the object below the fluid
surface, V (effectively, the volume of solid inside the liquid). We have:
B = f gV.
T
When an object is in air, a balance measures its true weight Mg.
Object denser than water:
When such an object is submerged in water then the balance reads its
apparent weight T ( or apparent mass Ma ) such that
T = Mg – B = Ma g
In air
M
MMm
Mg
(2)
B
M
MMm
Mg
Using previous equations, the density  of the object is given by:
 = f [ M / ( M - Ma )]
(3)
Object lighter than water:
For such objects (e.g. 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
Mw is the apparent mass when both sinker and wood are submerged.
T
M
MMm
Sinker
B
PHYSICS-1
ARCHIMEDES PRINCIPLE
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. Alternatively, fill the
overflow can to the rim (let some water flow out), then dip the object in the can and
collect the overflow water in a graduated cylinder.
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 M a. 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.
CALCULATIONS
1) Compute the density of the metal object from equation ( 1 ) .
2) Compute the density of the metal object from equation ( 3 ) .
3) Compute the percent error between the two values for the density of the metal object.
4) Compute the volume of wooden cylinder using V = πr2h
5) Compute the density of the wooden cylinder from equation ( 1 ) .
6) Compute the density of the wooden cylinder from equation ( 4 ) .
7) Compute the percent error between the two values for the density of the wooden cylinder.
PHYSICS-1
ARCHIMEDES PRINCIPLE
EXPERIMENT-13: Archimede’s Principle
REPORT FORM
Part I
Name: _______________________________
Density of metal object
Mass M of metal object:
________
________
________
________ (ave)
Volume of metal object
________
________
________
________ (ave)
Density of metal object from ( 1 )
________
________
________
________ (ave)
Apparent mass Ma of metal object ________
Density of metal object from ( 3 )
________
Percent difference
________
Part II
Density of wooden cylinder
Mass M of wooden object
________
________
________
________ (ave)
Radius of wooden object
________
________
________
________ (ave)
Length of wooden object
________
________
________
________ (ave)
Volume of wooden object
________
________
________
________ (ave)
Density of wooden object from ( 1 ) ________
Apparent mass Ms
________
________
________
________ (ave)
Apparent mass Mw
________
________
________
________ (ave)
Density of wooden object from ( 4 ) ________
Percent difference
________
PHYSICS-1
ARCHIMEDES PRINCIPLE
EXPERIMENT-13: Archimede’s Principle
Post- Laboratory Questions
Name: _________________________________________
1) How would an air bubble clinging to the metal object affect the value for its density?
2) A block of wood has a density of 0.50 g/cm3. What fraction of its volume is submerged in
water , and in oil of density 0.8 g/cm3.
3) A beaker containing water is placed on a weighing scale. A steel cylinder is then placed at
different locations. Masses of: beaker = 100 g; water in beaker = 800 g; cylinder in air=200 g.
What is the masses shown by the scale in cases A to D.
A
B
C
D
4) 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.