Solution #3 summer2007

# Solution #3 summer2007 - Physics 2211 A Summer 2007 Quiz#3...

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Physics 2211 A Quiz #3 Solutions Summer 2007 G = 6 . 673 × 10 - 11 N · m 2 / kg 2 g Earth = 9 . 8m / s 2 Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected. I . (16 points) Astronaut Arlene stands at the equator of the (ﬁctional) planet Planteen and measures her apparent weight to be 220N. Arlene knows her own mass to be 82kg, while Planteen has a mass of 3 . 0 × 10 23 kg and a radius of 2 . 5 × 10 6 m. With what angular speed does Planteen rotate on its axis? . . . . . . . . . . . . . . . . . . . . . . . This is a Newton’s Second Law problem with Uniform Circular Motion. Sketch a Free Body Diagram of Arlene. Choose the positive direction to be in the direction of the centripetal acceleration, toward the center of the planet. The only forces acting on her are the force of gravity, and a normal force. The normal force is her apparent weight. The force of gravity on Arlene will be calculated using the Law of Universal Gravitation—it can’t be calculated from w = mg because the acceleration of gravity on Planteen isn’t known. Letting m P be the mass of Planteen, and m A be the mass of Arlene, X F r = F G - n = m A a r G m P m A r 2 - n = m A v 2 r = m A 2 Arlene moves in a circle whose radius is that of Planteen. Solving for the angular speed ω , ω = r Gm P r 3 - n m A r = s (6 . 673 × 10 - 11 N · m 2 / kg 2 )(3 . 0 × 10 23 kg) (2 . 5 × 10 6 m) 3 - 220N (82kg)(2 . 5 × 10 6 m) = 4 . 6 × 10 - 4 rad / s Quiz #3 Solutions Page 1 of 5

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II . (16 points) The upper block in the illustration, with mass m 1 , is pulled horizontally by a rope with a tension of magnitude A . The lower block has mass m 2 , and rests on a horizontal frictionless surface. The coeﬃcient of kinetic friction between the two blocks is μ k . What is the acceleration magnitude of the lower block, in terms of any or all of m 1 , m 2 , A , μ k , and physical or mathematical constants? (On Earth.) . . . . . . . . . . . . . . . . . . . . . . . This is a Newton’s Second Law problem. Sketch a Free Body Diagram of each block. Choose a coordinate
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## This homework help was uploaded on 04/09/2008 for the course PHYSICS 2211 taught by Professor Uzer during the Spring '08 term at Georgia Tech.

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Solution #3 summer2007 - Physics 2211 A Summer 2007 Quiz#3...

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