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lecture8 - The moon moves in a nearly perfect circle around...

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The moon moves in a nearly perfect circle around the earth. Since it’s moving in a circle, its velocity is changing. v Since its velocity is changing, there must be an acceleration. v Since there is an acceleration, there must be a force. The same force that pulls the apple v toward the earth must also pull the moon. This is the Gravitational Force . v gravity didn’t pull on the moon it would continue to move in a straight line If gravity didn’t pull on the moon, it would continue to move in a straight line. The gravitational force from e earth pulls the moon the earth pulls the moon away from its straight-line motion.
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Newton’s Universal Law of Gravitation: So How do you calculate the gravitational force between two objects? 2 1 m m Let’s consider two objects with masses m 1 and m 2 , and separate them by some distance r : m 1 m 2 -F F x 2 r G F = Notice that the force is directly proportional to the product of the masses of the o objects and in ersel proportional to the sq are of the distance bet een r Then, two objects and inversely proportional to the square of the distance between them. The gravitational force equation is called an inverse square law. Nature ( r is the distance between the centers of each mass.) loves inverse square laws, and we will encounter them again. G is the universal gravitational constant : kg m N 10 67259 . 6 2 11 × = G g Properties of Newton’s Law of Gravitation: 1. It grows weaker with distance. Note: The forces on the two masses are equal but pposite as dictated by 2. It gets stronger for increasing masses. 4. It’s directed along the line containing the two masses. opposite as dictated by Newton’s 3 rd Law! 3. It is always attractive. D
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What is the acceleration of a tennis ball falling near the surface of the earth? It’s – 9.8 m/s 2 , but why??? ass of the ball ass of the earth 2 E B m m G F = We can calculate the force on the ball: Mass of the ball Mass of the earth E r Radius of the earth ut we can also write the force on the ball using Newton’s2 nd aw: But we can also write the force on the ball using Newton s 2 Law: a m F B These two forces have to be equal: 2 E E B B r m m G a m = 2 E E r m G a = This must be the acceleration of the ball. Let’s calculate it: 24 2 1 kg) 10 98 . 5 ( m N 0 7 × 2 6 11 m) 10 (6.38 ) kg 10 67 . 6 ( × × = a g = = 2 m/s 8 . 9 COOL! hus the acceleration due to gravity depends on the mass of the earth and
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This note was uploaded on 08/04/2009 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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lecture8 - The moon moves in a nearly perfect circle around...

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