lecture 21

lecture 21 - Lecture 21 Gravity Weight Gravitational field...

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1 Lecture 21 Gravity Weight Gravitational field strength Work by gravity/gravitational potential energy Escape velocity

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2 2 2 1 r M GM F = Gravity is the force between two masses. Gravity is a long- range or field force. No contact is needed between the bodies. The force of gravity is always attractive! r is the distance between the two masses M 1 and M 2 and G = 6.67 × 10 -11 Nm 2 /kg 2 . M 2 r M 1 F 21 F 12 . 12 21 F F - =
3 Where the unit vector points from the source of the gravitational field (location of M 1 ) to the field point (location of M 2 ). r F ˆ 2 2 1 r M GM - = In vector form

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4 Example: Three masses are arranged as shown. What is the force of mass 1 on mass 3? M 3 M 2 M 1 b a 13 ˆ r y x θ r F ˆ 2 3 1 13 r M GM - = ( 29 ( 29 y x y x r r r y x y x r ˆ cos ˆ sin ˆ ˆ ˆ ˆ ˆ ˆ ˆ 2 2 1 3 1 3 θ θ + = + + = = + = - + - = b a a b a b y y x x
5 Example Continued ( 29 + + + + - = y x F ˆ ˆ 2 2 2 2 2 2 3 1 13 b a a b a b b a M GM

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6 Example: Three masses are arranged as shown. What is the net force on mass 2?
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