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Universal Gravitation

Universal Gravitation. What causes the planets to orbit the sun?. What causes an apple to fall from a tree?. Isaac Newton – 1642 - 1727. Newton’s Universal Law of Gravitation. A gravitational force exists between all objects with mass.

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Universal Gravitation

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  1. Universal Gravitation

  2. What causes the planets to orbit the sun?

  3. What causes an apple to fall from a tree?

  4. Isaac Newton – 1642 - 1727

  5. Newton’s Universal Law of Gravitation A gravitational force exists between all objects with mass.

  6. 3 things can affect the amount of gravitational force between 2 objects: • mass of object 1 (m) - directly proportional Fg α m • mass of object 2 (M) - directly proportional Fg α M • the distance between their centers (r) - inversely proportional Fg α 1 r2

  7. Put it together! Fgα m*M r2

  8. 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:

  9. 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. Fgα m*M r2 2/3*4Fgα 2/3m*4M (¼)2 (¼r)2 Fgnew = 2/3*4 * 6x10-8= 2.56 x 10-6 N (¼)2

  10. 2. Create a proportion. Fg new(2/3)m*4M (¼r)2 _________ = ______________ Fg oldmM r2 Cancel the mM and cross multiply. r2

  11. 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 10-6N (¼)2

  12. 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

  13. Universal Gravitation Constant G = 6.67 x 10-11 N m2/kg2 Fg = G mM r2

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