ch13-p037 - 37. (a) We use the principle of conservation of...

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37. (a) We use the principle of conservation of energy. Initially the particle is at the surface of the asteroid and has potential energy U i = GMm/R , where M is the mass of the asteroid, R is its radius, and m is the mass of the particle being fired upward. The initial kinetic energy is 2 1 2 mv . The particle just escapes if its kinetic energy is zero when it is infinitely far from the asteroid. The final potential and kinetic energies are both zero. Conservation of energy yields GMm/R + ½ mv 2 = 0. We replace GM/R with a g R , where a g is the acceleration due to gravity at the surface. Then, the energy equation becomes a g R + ½ v 2 = 0. We solve for v : 23 3 2 2(3.0 m/s )(500 10 m) 1.7 10 m/s. g va R == ×= × (b) Initially the particle is at the surface; the potential energy is U i = GMm/R and the kinetic energy is K i = ½ mv 2 . Suppose the particle is a distance h above the surface when it momentarily comes to rest. The final potential energy is U f = GMm/ ( R + h ) and the final kinetic energy is K f = 0. Conservation of energy yields
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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ch13-p037 - 37. (a) We use the principle of conservation of...

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