SolutionsSet04

SolutionsSet04 - Homework Solutions Physics 121 Set 04...

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Unformatted text preview: Homework Solutions Physics 121 Set 04 Spring 2008 - 1 - WebWork Problem 1 The gravitational forces due to the two masses on the third mass located between them will point in opposite directions. If these two forces have the same magnitude, the net force will be equal to zero. x d F1 F2 The force due to the mass location at the origin is pointed towards the left and has a magnitude of F 1 = G mM 1 x 2 The force due to the located at x = d is pointed towards the right and has a magnitude of F 2 = G mM 2 d ! x ( ) 2 These forces will cancel if G mM 1 x 2 = G mM 2 d ! x ( ) 2 or d ! x ( ) 2 M 1 = x 2 M 2 This equation can be rewritten as x 2 M 1 ! M 2 ( ) ! 2 dM 1 x + d 2 M 1 = Solving this equation for x we find Homework Solutions Physics 121 Set 04 Spring 2008 - 2 - x = 2 dM 1 2 dM 1 ( ) 2 ! 4 d 2 M 1 M 1 ! M 2 ( ) 2 M 1 ! M 2 ( ) = 2 dM 1 4 d 2 M 1 M 2 2 M 1 ! M 2 ( ) = d M 1 M 1 M 2 M 1 ! M 2 ( ) This equation has two solutions: x = 43.1 m and x = 256 m. In both cases, the magnitudes of both forces are equal. At x = 256 m both forces point towards the left, and they thus do not cancel. At x = 43.1 m the forces point in opposite directions and cancel. This is thus the proper solution to this problem. Homework Solutions Physics 121 Set 04 Spring 2008 - 3 - WebWork Problem 2 The gravitational force between two objects is given by the following equation: F = G M 1 M 2 r 12 2 In part 1 of this problem, M 1 = 4.2 kg, M 2 = 78.5 kg, and r 12 = 0.7 m. In this case, the gravitational force is equal to 4.49E-08 N. In part 2 of this problem, M 1 = 4.2 kg, M 2 = 1.9E+27 kg, and r 12 = 6.0E+11 m. In this case, the gravitational force is equal to 1.48E-06 N or about 33 times stronger than the gravitational force due to the doctor. In part 3 of this problem, M 1 = 4.2 kg, M 2 = 1.9E+27 kg, and r 12 = 9.0E+11 m. In this case, the gravitational force is equal to 6.57E07 N or about 15 times stronger than the gravitational force due to the doctor. Homework Solutions Physics 121 Set 04 Spring 2008 - 4 - WebWork Problem 3 To solve this problem we use the principle of superposition. To solve this problem we use the principle of superposition....
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SolutionsSet04 - Homework Solutions Physics 121 Set 04...

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