ps9c24 - Ph 111.01 October 31, 2008 PS 9c (24) Problem 1....

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Ph 111.01 October 31, 2008 PS 9c (24) Problem 1. Practice with proportions. Two masses a distance R apart attract each other with a gravitational force F. For each of the cases below, give the factor by which F is changed, if: a.) if R is multiplied by 3 , then F new = · F old b.) if R is multiplied by 3.9 , then F new = · F old c.) if R is divided by 2 , then F new = · F old Solution. The equation that we are analyzing is 12 2 Gm m F R = We can see that it is proportional to 1/r 2 - that is to say, the equation divides by the square of R. So, if R is multiplied by a certain factor, the force is divided by the square of that factor. Or, equivalently, the force is multiplied by (1/(the factor))^2. (a) The factor is 3. So () 2 new old old 1 * 0.111111 3 FF F ⎛⎞ == ⎜⎟ ⎝⎠ (b) The factor is 3.9. So 2 new old old 1 * 0.0657 3.9 F (c) The factor is 0.5. So 2 new old old 1 *4 0.5 F Problem 2 = Walker P. 12-29. A typical GPS (Global Positioning System) satellite orbits at an altitude of 3.1 10 7 m. (Astronomical data needed for this problem can be found on the inside back cover of the text.) h R earth GPS r=R+h (a) Find the orbital period of such a satellite. hours (b) Find the orbital speed of such a satellite.
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ps9c24 - Ph 111.01 October 31, 2008 PS 9c (24) Problem 1....

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