Physics 2015: Archimedes’ Principle
Purpose
The purpose of today’s lab is to investigate Archimedes’
Principle and buoyant forces.
First, we will determine the density of metal balls of the
same substance, but different radii.
Then, once this density is known, we will use a metal
slug (made of the same metal) to find the buoyant force
of 4 different liquids and determine the density of these
liquids.
Physics 2015: Archimedes’ Principle
Activity 1: Finding the density of the metal spheres
• Force sensor
• Metal tray (place the metal
spheres into the tray)
• Glass cylinder filled with
water.
Please remember to only fill water
into the glass cylinders and not any
other type of liquid.
Physics 2015: Archimedes’ Principle
Activity 2: Finding Fluid Densities
•
You will find 4 different plastic containers filled with the
following liquids:
•
•
•
•
•
Tap Water (get yourself)
Salt Water
Corn Syrup
Vegetable oil
Attach the cylindrical metal mass to the end of the force
sensor, and place it into the substances to measure
force.
Cylindrical metal mass
Physics 2015: Archimedes’ Principle
Notes:
1) In your lab manual we mention using
isopropyl alcohol as one of the fluids. We have
substituted vegetable oil for the isopropyl
alcohol.
2) On page 104 a few equations were not
printed correctly. There is a corrected version of
that page on the website under Hints/Links in a
pdf file. Please print out that pdf file and replace
page 104.
Physics 2015: Archimedes’ Principle
Archimedes’ Principle
An object that is submerged in a liquid will experience an
additional upward force (due to the submersion) that is
equal to the weight of the amount of liquid that was
displaced by the object. This force is called the “buoyant
force”.
Translated into simpler language, this means:
An extra force acts on an object when it is placed, for
example, in water. This makes the object appear lighter
than it really is.
Physics 2015: Archimedes’ Principle
Example of a buoyant force
A metal ball of volume 50cm3 fully submerged in water
will experience a buoyant force of the following
magnitude:
mass of displaced water
density of water
Fb  mw g  w V g
(  0.001
volume of ball
kg
m
3

50
cm

9
.
8
 0.49 N )
3
2
cm
s
Physics 2015: Archimedes’ Principle
Free Body Diagram (3 forces)
string
density of water
T
Fb  mw g  w V g
W  mg  m V g
volume of ball
density of metal
Physics 2015: Archimedes’ Principle
Using Newton’s Second Law…

In this static situation there is no acceleration, therefore  F  0

T   w V g  m V g  0

T  V g ( m   w )
 By measuring T and V, and knowing the density of water and the
acceleration of gravity, the density of the metal can be calculated.
Physics 2015: Archimedes’ Principle
In Activity 1, we will use metal spheres in water:
Vsphere
4 3
4 3
  r  T   r g  m   w 
3
3
In Activity 2, we will use a cylindrical metal object in a fluid:
Vsphere   r h  T   r h g m   fluid 
2
2
Physics 2015: Archimedes’ Principle
There is one more idea you will want to consider
before starting Activity 1
• Remember to “Tare” your force sensor in a
clever way before any procedure. In this case,
first hang the empty basket on the force sensor
and into the water. THEN tare the force sensor.
This will negate both the weight of the basket
and the buoyant force on the basket in your
force measurement!
• Tared this way, when you graph the tension
versus r3 in Excel, you should expect the line to
go through the origin. Why do you think this is?
Physics 2015: Archimedes’ Principle
In Activity 1 (spheres)
4 3
V r
3

4 3
T   r g ( w  m )
3
Measure T for different size spheres (different radii) and determine
the density of the spheres.
measured
r
r
calculated
3
measured
T
T
plot
What is the slope?
Get m from slope.
r
3
Physics 2015: Archimedes’ Principle
Careful when doing the Excel Plot of T versus r3
Plotting T versus r3 and using m3 as your unit results in a
large number for the trendline slope.
When you display the trendline equation in the trendline
label, not all digits of the slope may be displayed. So, your
slope k result may be off by a factor of 10 or 100 etc.
Here is how to fix it:
Right click on the trendline label (not on the trendline).
Choose “Format Trendline Label”
Choose “Number” or
Choose “Scientific” with 3 or 4 digits.
Physics 2015: Archimedes’ Principle
For Activity 2
Step 1: Hang slug
on force sensor
Step 2: Tare the
force sensor
Tare
Step 3: Hang slug into
Liquid. This way you
measure only Fbuoyant
Physics 2015: Archimedes’ Principle
Then get the density of the liquid from the
measured buoyant force using the equation:
Fb  liquid Vslug g
Note: You will need to figure out the volume of the slug
somehow!.
Physics 2015: Archimedes’ Principle
Activity 3
Determine the density of the fluids again by measuring
mass and volume of the fluid:
mass
density 
volume
m
 
V
This method of determining the density will give you a
direct comparison to the density results obtained from the
buoyancy measurement.
Note: It will be easiest to measure an empty plastic
container first.
Physics 2015: Archimedes’ Principle
Final Reminder
•
•
•
•
DO NOT POUR ANYTHING BUT WATER down the
drain (not even the salt water which we reuse)!
DO NOT POUR ANYTHING BUT WATER into the
tall glass cylinders!
Clean up anything that spills IMMEDIATELY!
These can damage equipment in the lab! Use a
paper towel or a sponge
Put the cardboard covers back on the plastic
beakers containing the syrup before you leave.