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**Newton’s Universal Law of Gravitation**

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Factors Affecting the Gravitational Force mass distance

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**force varies directly with masses**

decrease mass decreased force force varies directly with masses Fg α m1 m2

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Distance r increase r force decreased

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Force varies inversely with distance squared Fg α 1/r2

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Fg α m1m2 Fg α 1/r2 m1 m2 Fg α r2 Fg slope = G m1 m2/r2

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G = 6.67 x 10-11 N m2/kg2

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A 1000 kg car and a 2000 kg truck are 0.50 m apart. Gravitational force: 5.3 x 10-4 N

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**Computing mass of Earth**

radius of Earth: x 106 m 1.00 kg mass has a weight of 9.81 N mass of Earth: 5.97 x 1024 kg

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2F 4F

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¼ F 4F

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F

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“g” gravitational field – weight per mass wtg Fg g = = mass m G M = r2 M = planet mass

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**Effect of changing variables GM g = ----- r2**

if M doubles: if r doubles: if M & r doubles: if r becomes ½: 2g ¼ g ½ g 4g

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**radius: 53% radius of Earth gravitational field for Mars?**

mass: 11% mass of Earth radius: 53% radius of Earth gravitational field for Mars? 0.39 gE = N/kg

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**Net gravitational force on bottom mass?**

√3 GM2/s2

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**G m1 m2 Fg = ---------- = weight r2**

What would happen to your weight if: Earth had twice mass but the same radius: Twice weight Earth had twice radius but same mass: ¼ weight

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**What is “g” at top of Mt. Everest**

(8848 m elevation)? 9.77 N/kg = 9.77 m/s2

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Universal Law of Gravitation. So because of Newton’s 3 rd law every body in the universe exerts a force of attraction on every other body. This is Newton’s.

Universal Law of Gravitation. So because of Newton’s 3 rd law every body in the universe exerts a force of attraction on every other body. This is Newton’s.

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