# ps10a25 - Ph 111.01 November 3, 2008 PS 10a (25) Problem 1...

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Ph 111.01 November 3, 2008 PS 10a (25) Problem 1 = Walker P. 12-37. (a) Calculate the gravitational potential energy of a 231 kg mass on the surface of the Earth. J (b) Calculate the gravitational potential energy at an altitude of 5 km. J (c) Take the difference between the results for parts (b) and (a), and then compare with mgh , where h = 5 km. (Do not round your intermediate results!) J (difference between parts a and b ) J ( mgh ) h R E Solution. (a) We calculate the gravitational potential energy at a distance from the center of Earth of R = 6,370,000 m. () ( )( ) 24 11 2 2 10 231 kg 5.97 10 kg 6.67 10 N-m / kg 1.44402 10 J 6,370,000 m E E x mM UG x x R =− (b) Now we add on the extra 5000 m to the distance to the center of the Earth and repeat the calculation. ( )( ) 24 11 2 2 10 231 kg 6.67 10 N-m / kg 1.44289 10 J 5000 m 6,375,000 m E E x mM x x R + (c) And now the difference: 10 10 7 (5000 m up) - U surface 1.44289 10 J + 1.44402x10 J = 1.130x10 J Ux For comparison, ( 231 kg 9.8 mgh ) ( ) 7 N/kg 5000 m 1.132 10 J x == m earth v escape v 0 Pretty good agreement! Problem 2 = Walker P. 12-39. Astronomical data needed to answer this problem can be found on the inside back cover and in Appendix C.

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## This note was uploaded on 05/13/2010 for the course PHYSICS 111 taught by Professor Staff during the Fall '08 term at S.F. State.

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ps10a25 - Ph 111.01 November 3, 2008 PS 10a (25) Problem 1...

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