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Unformatted text preview: Physics 2211 Quiz #5 Solutions Fall 2007 g Earth = 9 . 8m / s 2 R Earth = 6 . 37 Ã— 10 6 m G = 6 . 673 Ã— 10 11 N Â· m 2 / kg 2 M Earth = 5 . 98 Ã— 10 24 kg Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected. I . (16 points) An asteroid heads toward the Earth. As it passes through the Moonâ€™s orbit (radius 3 . 84 Ã— 10 8 m) it has a speed of 8.33km/s. What is the asteroidâ€™s speed as it passes through a point 5 . Ã— 10 6 m from the Earthâ€™s surface? . . . . . . . . . . . . . . . . . . . . . . . Use the WorkEnergy Theorem. There are no external or nonconservative forces on the Earthasteroid system. W ext + W nc = Î” K + Î” U â‡’ 0 = ( K f K i ) + ( U f U i ) Let the mass of the Earth be M , and the mass of the asteroid be m . The only potential energy change in the Earthasteroid system is that due to gravity. Because of the distances involved, the universal gravitation potential energy expression must be used. 0 = ( 1 2 mv 2 f 1 2 mv 2 i ) + GMm r f GMm r i Â¶ Solve for the final speed. The final distance of the asteroid from the center of the Earth is its altitude plus the Earthâ€™s radius, 5 . Ã— 10 6 m + 6 . 37 Ã— 10 6 m = 11 . 4 Ã— 10 6 m. Note that the mass of the asteroid can be divided from each term. v f = s 2 GM 1 r f 1 r i Â¶ + v 2 i = s 2(6 . 673 Ã— 10 11 N Â· m 2 / kg 2 )(5 . 98 Ã— 10 24 kg) 1 11 . 4 Ã— 10 6 m 1 3 . 84 Ã— 10 8 m Â¶ + (8 . 33 Ã— 10 3 m / s) 2 = 12km / s Quiz #5 Solutions Page 1 of 5 II . (16 points) A block of mass m slides down a plane that makes an angle Î¸ with the horizontal. The block was initially at rest, and there is friction between the block and the plane. It slides a distance L where it contacts a spring with spring constant k . It continues sliding, compressing the spring to a distance S where it momentarily comes to rest. What is the coefficient of kinetic friction between the block and the plane, in terms of any or all of m , Î¸ , L , k , S , and physical or mathematical constants? ( On Earth. ) . . . . . . . . . . . . . . . . . . . . . . . Use the WorkEnergy Theorem. W ext + W nc = Î” K + Î” U Choosing the system to be the Earth, block, and spring, no external forces do work on the system. Friction is a nonconservative force within the system. There are both gravitational and elastic poten tial energy changes in that system. The block begins and ends at rest, so there is no kinetic energy change between the initial and final states....
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 Spring '08
 UZER
 Physics, Force, Mass, Potential Energy, gm

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