Archimedes Principle
October 4, 2008
Sloane Schneider
Lab Partners:
Taylor Whipple,
Cory Wilkinson,
Amy Kalal
Objectives:
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In this experiment Newton’s 2
nd
Law can be applied to yield
B = T – T’
and Archimedes Principle can be
used as
B =
ρw
gV
.
Both Newton’s 2
nd
Law equation and Archimedes Principle can be used to solve for
the density of unknown objects or fluids.
Theory:
To accurately measure the weight of an object one must take into account not only the objects mass, but
also the force that gravity exerts upon the object.
To begin this experiment an object is hung from a scale
in the air that allows the true weight of the object to be calculated.
This can be seen by applying
Newton’s 2
nd
Law when
T – mg = 0
, where
T
is the scale reading,
m
is the mass of the object, and
g
is the
acceleration due to gravity.
Since the object is motionless, the acceleration is zero and the tension must
equal the weight.
In order to accurately measure the density of the same object it must be entirely submersed in fluid.
The
fluid exerts an upward force on the object, this upward force is labeled
B
because it is a buoyant force.
In
applying Newton’s 2
nd
Law again the equation
T’ + B – mg =0
is given where
T’
is the new scale reading.
To solve for the buoyant force exerted on the object the two Newton’s Law equations can be equated,
giving:
= 
B
T T'
There are other ways to determine the buoyant force exerted on an object, one such method is known as
Archimedes Principle.
This principle states that the buoyant force is equal to the weight of the fluid
displaced.
When weight is calculated in terms of density (
ρw
) the following equation can be used
=
B
ρwgV
where
g
is the force due to gravity and V is the volume of the submerged object.
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 Spring '08
 SOWELL
 Physics, Buoyancy, Force, Archimedes, force sensor

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