Universal Gravitation
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Transcript of Universal Gravitation
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Universal Gravitation
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What causes the planets to orbit the sun?
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What causes an apple to fall from a tree?
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Isaac Newton – 1642 - 1727
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Newton’s Universal Law of Gravitation
A gravitational force exists between all objects with mass.
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3 things can affect the amount of gravitational force between 2 objects:
mass of object 1 (m) - directly proportional Fg α mmass of object 2 (M) - directly proportional Fg α Mthe distance between their centers (r) - inversely proportional
Fg α 1r2
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Put it together!
Fg α m*M r2
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Ex: Sandy and Bob an standing near each other such that the gravitational force between them is 6 x 10-8 N. If Years later Sandy is now 2/3 her original weight and Bob’s weight quadruples. The distance between them is ¼ the original distance. What is the new gravitational force between them?There are many ways to solve this problem. Here are a couple methods:
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1. Multiply each variable by the number given in the problem. From math class: what you do to one side, you do to the other. Multiple the gravitational force by the new proportion.
Fg α m*M r2
2/3*4 Fg α 2/3m*4M(¼)2 (¼r)2
Fgnew = 2/3*4 * 6x10-8 = 2.56 x 10-6 N (¼)2
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2. Create a proportion.
Fg new (2/3)m*4M
(¼r)2 _________ = ______________
Fg old mM r2
Cancel the mM and cross multiply.
r2
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Fgnew (2/3)*4
(¼)2 _________ = ______________
Fgold 1 Fgnew = (2/3)*4 x Fgold
(¼)2
Fgnew = (2/3)*4 x 6x10-8 = 2.56 x 10-6 N (¼)2
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Turn a Proportion into an Equation
A constant must be added to the proportion.Henry Cavendish (1731-1810) and his Torsion Balance Experiment found the value of this constant.
Torsion Balance Experiment
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Universal Gravitation Constant
G = 6.67 x 10-11 N m2/kg2
Fg = G mM r2