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The Cavendish Experiment Determining the Value of the Universal Gravitational Constant By Gabriel Shields-Estrada and Tiffany Meshkat COSMOS 2004 July 23, 2004

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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

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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?

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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.

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Experimental Procedure One can determine the gravitational constant by: –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

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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 gramsα= torsion constant of M2= 1 kg gold-plated Tungsten wire B= distance between the massesØ= the angle the wire twists L= distance from the axis to the small mass G= ?????

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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

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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.

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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) Nm ²/kg²

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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

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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

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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.

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