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Universal Gravitation

Universal Gravitation. “Every object in the universe attracts every other object in the universe”. Universal Gravitation Facts. Gravity is universal: ALL objects attract each other. The force of gravity is directly proportional to the product of the masses.

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Universal Gravitation

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  1. Universal Gravitation “Every object in the universe attracts every other object in the universe”

  2. Universal Gravitation Facts • Gravity is universal: ALL objects attract each other. • The force of gravity is directly proportional to the product of the masses. • The force of gravity is inversely proportional to the square of the distance between the masses.

  3. Universal Gravitation Key Points • These ideas should be able to be combined. • In order for it to be successful, two important things happened: 1. Newton invents a new branch of calculus 2. Henry Cavendish determines a gravitational constant G = 6.67 x 10-11

  4. Universal Gravitation Formulas • Force of Universal Gravitation: Fg = G x m1 x m2 d2 ( m must be in “kg”; d mustbe in “m”) • Gravitational Acceleration: Ag = G x m d2 (m = mass of bigger object)

  5. Fgα m1m2 If you want to know how Fg changes with mass simply multiply the changes in mass. Ex. 1: If the force of gravity is 18N, what would be the new force if one of the masses was tripled? Since Fg α m1m2 then (3m1)(m2)=3Fg The new force of gravity is 3(18)= 54N.

  6. Fgα m1m2 Ex.2: If the force of gravity is 18 N, what would be the new force if one mass is cut in half? Since Fg α m1m2 then (1/2m1)(m2)=1/2Fg The new force of gravity is 1/2(18) = 9 N

  7. Fgα m1m2 Ex.3: If the force of gravity is 18 N, what would be the new force if both masses were doubled? Since Fg α m1m2 then (2m1)(2m2)=4Fg The new force of gravity is 4(18) = 72 N

  8. Fgα 1/d2 If you want to know how Fg changes with distance square the distance and divide by it. Ex.4: If the force of gravity is 60 N, what would be the new force if the distance between masses is doubled? Since Fg α1/d2 then (1/(2d)2)=1/4Fg The new force of gravity is 1/4(60) = 15 N

  9. Fgα 1/d2 Ex.5: If the force of gravity is 60 N, what would be the new force if the distance between masses is cut in half? Since Fg α1/d2 then (1/(1/2d)2)=1/(1/4)Fg =4Fg The new force of gravity is 4(60) = 240 N

  10. Fgα m1m2/d2 If both variables change, simply apply both relationships Ex.6: If the force of gravity is 12 N, what would be the new force if m1 is tripled and d is doubled? Since Fg α m1m2/d2 then (3m1)(m2)/(2d)2=3/4Fg The new force of gravity is 3/4(12) = 9 N

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