Transcript The Cavendish Experiment

The Cavendish Experiment
Determining the Value of the Universal Gravitational Constant
By Gabriel Shields-Estrada and Tiffany Meshkat
COSMOS 2004
July 23, 2004
History
• Originally performed by Henry Cavendish
in the mid 1800’s
• Performed experiment in basement of his
castle
• Used much less precise techniques
• Obtained amazingly and accurately
precise results
Research Question
• What is the value of the universal gravitational
constant (G) ?
• Preliminary Questions
– How can this constant be determined?
– What are the expected results of the experiment?
• Secondary Questions (once the results are calculated)
– What are the effects of these results on the real
world?
– Why should we care?
Experimental Procedure
• A balance with 15 gm lead
weights is suspended by a
gold-plated Tungsten wire of
diameter 25 microns.
• The balance is left for 24
hours to obtain equilibrium.
• A second balance holding
two 1 kg lead weights is
then rotated and left for a 24
hour period.
• A mirror attached to the
center of the balance
reflects a laser light onto a
wall, 1.75 meters away.
Experimental Procedure
• One can determine the gravitational constant by:
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–
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–
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Using the distance the laser light has traveled
The angle the balance has rotated
The mass of the lead balls
The torsion constant of the gold-plated Tungsten wire
The distance by which the masses are separated
Experimental Procedure
• Each of the variables, which will be
determined in the experiment, will then
inserted into the following equation:
2 G M1 M2 x L = α x Ø
B^2
M1= 15 grams
α= torsion constant of
M2= 1 kg
gold-plated Tungsten wire
B= distance between the masses
Ø= the angle the wire twists
L= distance from the axis to the small mass
G= ?????
Results
• After 24 hours…
– The reflected laser light moved 1 mm on the wall in both trials
– The balance rotated 5.71 x 10^-4 radians (Ø)
• these results combined with the measurable quantities of
the set up…
– The distance between the masses is measure at 4.5 cm
– The distance from the axis to the small mass is 7.2 cm
– The torsion constant is 1.41 x 10^-6 Nm/radian
• allow us to complete the equation:
2 G M1 M2 x L = α x Ø
B²
Results
• With the values of each variable imputed,
the equation appears like this:
2(G)(15 gm)(1 kg) x L = (1.41 x 10^-6 Nm/radian)(5.71 x 10^-4 radians)
(4.5 cm)²
• After each number is input the only variable left is G.
• Using simple algebra we can solve for G.
Results
• After solving the equation for the universal
constant of gravity (G)
G = (6.57)(10^-11) Nm²/kg²
• This answer is just a single tenth in difference
from the exact value as calculated by scientists
of (6.67)(10^-11) Nm²/kg²
Problems
• Tying the Tungsten wire
– The wire was extremely thin
(25 microns)
– The gold-plating made it
susceptible to heat
• Waiting an extended period
of time
– Inaccurate results after the
initial hour
• Accurate measurement
• Time constraints
Effects on the Real World
• All matter in the
universe is attracted
to all other matter at a
constant rate
• For us, it means that
life can continue as it
always has
Conclusion
• There are many questions in science that
have yet to be answered, but performing
experiments, like the Cavendish
experiment, help the human race to further
understand the fundamental laws that
govern the universe.