GateWay CC
BUOYANCY FORCE –
ARCHIMEDE’ PRINCIPLE
PHY101 Physics Lab:
Purpose


To investigate the Buoyancy Force for various types of liquids
To determine the density various liquids
Theory
The buoyant force upward on a submerged object Fb due to the fluid in which the object
is submerged is equal to the weight of the fluid displaced by the submerged object.
Fb  m fluid  g
m fluid  D fluid  Vobject
Substitute mass of fluid with:
Fb  D fluid  Vobject  g
(1)
Dfluid – is the density of the fluid in (kg/m3)
Vobject - is the volume of the object – assuming that object is completely submerged in
(m3)
g – is the acceleration due to gravity in (m/s2)
Mathematical model for buoyant force shown above in equation 1 is called Archimedes
Principle. This principle can be used to design a simple method of measurement of
density of a liquid. The idea here is to find the buoyant force on an object when it is
totally submerged in a fluid. Then we measure the volume of the same object using
length metering tools. With these two data sets we can determine the density of a fluid:
D fluid 
Fb
Vobject  g
(2)
What is the procedure for buoyancy force measurement? If we measure the weight of an
object when submerged, we will find that the object weighs less than in air. The
difference in weighs is due to the fact then when we measure the weight of the object
under the water we measure the weight of minus the buoyant force. If we use the spring
scale then the mass under water mfluid, will be less than the mass on air mair. The
difference between the two masses is due to the buoyant force on the object. Using these
two measurement data we can now calculate buoyant force:
Fb  mair  g  m fluid  g  g (mair  m fluidr )
If we substitute this force into the equation 2, for density:
GWC – Buoyancy.doc
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GateWay CC
D fluid 
g (mair  m fluid )
Vobject  g

(mair  m fluidr )
Vobject
If the submerged object is a cube then:
Vobject  l  h  w
Where: l, h, and w are the length, height and the width of the cube.
If the submerged object is a cylinder then:
Vobject    R 2  H
Where: R is the radius of the cylinder, and H is the height of cylinder.
We are going to use various types of liquids in order to determine how the buoyant force
varies with the kind of liquid used.
Procedure
For Part I – Determine the mass of an object on air (mair), and its volume.
For four different size objects (cubes and cylinders), measure their mass on air using the
balance – spring scale. For objects with mass less than 250 mg, use spring scale with 0 –
250 mg range. For objects with mass more than 250 mg, use spring scale with 0 – 500
mg range. Using the meter stick or other length measuring tools, determine their
volumes. Record the data on table 1 and convert each mass in kg, and volume in m3.
Table 1
Object
Mass on air
( kg )
Volume
( m3 )
Object 1
Object 2
Object 3
Object 4
GWC – Buoyancy.doc
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Last Updated: 2/6/2016
GateWay CC
For Part II – Determine the mass of an object when immersed (mfluid) in various fluids.
For all the fluids provided, measure the mass of each object under the fluid. See figure
above. Use spring scale balance for this measurement. Before we change the fluid on the
beaker, we should dry the beaker and the object each time. Record the data on table 2.
Table 2
Mass
( kg )
Mass
( kg )
Mass
( kg )
Mass
( kg )
Mass
( kg )
Fresh water
Salt water
Oil
Milk
Sprite
Object
Object 1
Object 2
Object 3
Object 4
For Part III - Determine the density of each fluid.
Using the data collected in parts 1 and 2, and equation:
D fluid 
mair  m fluidr
Vobject
determine the density of each fluid tested, and complete table 3.
Table 3
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Fresh water
Salt water
Oil
Milk
Sprite
Object
Object 1
Object 2
Object 3
Object 4
Average
For Part IV – Accepted Values for Density.
Search on the web or your textbook and find the densities – accepted values, of each
fluid tested and complete table 4.
Table 4
Source of the data
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Density
( kg/m3 )
Website or textbook
Fresh water
Salt water
Oil
Milk
Sprite
GWC – Buoyancy.doc
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GateWay CC
For Part V – Difference Between Calculated and Accepted Values for Density.
Using average data from part III and accepted values from part IV, calculate the absolute
and relative difference between them.
Absolute Difference  Calculated Value  Accepted Value
Relative Difference 
Absolute Difference
 100%
Accepted Value
Complete table 5.
Table 5
Liquid
Calculated
Density
( kg/m3 )
Accepted
Density
( kg/m3 )
Absolute
Difference
( kg/m3 )
Relative
Difference
( kg/m3 )
Fresh water
Salt water
Oil
Milk
Fresh water
Salt water
Oil
Milk
Sprite
Questions
1. Does the buoyant force on an object change as the depth that the object is submerged
increases? Explain.
2. If an object floats in water, what is the relationship between the object's density and the
water's density?
4. In which direction does the buoyant force act on the objects when they are immersed in the
fluids during this lab?
a) Vertically upwards
b) Vertically downwards
c) Horizontally to the right
d) Horizontally to the left
5. Lead has greater density than iron, and both are denser than water. Is the buoyant force on a
lead object greater than, equal to or less than the buoyant force on an iron object of the same
volume? Explain.
GWC – Buoyancy.doc
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Last Updated: 2/6/2016