380_Physics ProblemsTechnical Physics

380_Physics - 382 Q13.7 Universal Gravitation Ten terms are needed in the potential energy U = U 12 U 13 U 14 U 15 U 23 U 24 U 25 U 34 U 35 U 45

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382 Universal Gravitation Q13.7 Ten terms are needed in the potential energy: U UUUUUUUUUU =+++++++++ 12 13 14 15 23 24 25 34 35 45 . With N particles, you need i NN 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 af the rocket will stop K = 0 . 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 , or 25 times more fuel is required to leave the Earth versus leaving the Moon.
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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