Solution #5 fall 2007 - Physics 2211 Quiz #5 Solutions Fall...

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Unformatted text preview: Physics 2211 Quiz #5 Solutions Fall 2007 g Earth = 9 . 8m / s 2 R Earth = 6 . 37 10 6 m G = 6 . 673 10- 11 N m 2 / kg 2 M Earth = 5 . 98 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 Moons orbit (radius 3 . 84 10 8 m) it has a speed of 8.33km/s. What is the asteroids speed as it passes through a point 5 . 10 6 m from the Earths surface? . . . . . . . . . . . . . . . . . . . . . . . Use the Work-Energy Theorem. There are no external or non-conservative forces on the Earth-asteroid system. W ext + W nc = K + U 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 Earth-asteroid 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 Solve for the final speed. The final distance of the asteroid from the center of the Earth is its altitude plus the Earths radius, 5 . 10 6 m + 6 . 37 10 6 m = 11 . 4 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 + v 2 i = s 2(6 . 673 10- 11 N m 2 / kg 2 )(5 . 98 10 24 kg) 1 11 . 4 10 6 m- 1 3 . 84 10 8 m + (8 . 33 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 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 , , L , k , S , and physical or mathematical constants? ( On Earth. ) . . . . . . . . . . . . . . . . . . . . . . . Use the Work-Energy Theorem. W ext + W nc = K + U Choosing the system to be the Earth, block, and spring, no external forces do work on the system. Friction is a non-conservative 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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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 Institute of Technology.

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Solution #5 fall 2007 - Physics 2211 Quiz #5 Solutions Fall...

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