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380_Physics ProblemsTechnical Physics

380_Physics ProblemsTechnical Physics - 382 Q13.7 Universal...

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382 Universal Gravitation Q13.7 Ten terms are needed in the potential energy: U U U U U U U U U U U = + + + + + + + + + 12 13 14 15 23 24 25 34 35 45 . With N particles, you need i N N i N = = 1 2 1 2 a f terms. Q13.8 No, the escape speed does not depend on the mass of the rocket. If a rocket is launched at escape speed, then the total energy of the rocket-Earth system will be zero. When the separation distance becomes infinite U = 0 a f the rocket will stop K = 0 a f . In the expression 1 2 0 2 mv GM m r E = , the mass m of the rocket divides out. Q13.9 It takes 100 times more energy for the 10 5 kg spacecraft to reach the moon than the 10 3 kg spacecraft. Ideally, each spacecraft can reach the moon with zero velocity, so the only term that need be analyzed is the change in gravitational potential energy. U is proportional to the mass of the spacecraft. Q13.10 The escape speed from the Earth is 11.2 km/s and that from the Moon is 2.3 km/s, smaller by a factor of 5. The energy required—and fuel—would be proportional to v 2
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