s3a11 - Homework Assignment#3 Solutions Physics E-1b Fall...

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Physics E-1b Homework Assignment #3 Solutions Fall 2011 When solving many of the following problems carefully identify the forces that act on the object. Then draw a free body diagram that includes all of these forces. The sum of the forces or the net force can then be set equal to the mass times the net acceleration. In many cases the acceleration equals zero which implies F = 0 ! 1. F = G Mm R 2 ! F M = G m R 2 ! g = G m R 2 .99 ( ) g g = G m R 2 astro G m R 2 earth ! .99 = 1 R 2 astro 1 R 2 earth = R 2 earth R 2 astro ! R astro = R 2 earth .99 R astro = 6.376 " 10 6 m ( ) 2 .99 = 6.41 " 10 6 m Height above earth 6.40 ! 10 6 m " 6.371 ! 10 6 m = 3.2 ! 10 4 m We can also solve this problem quickly using error analysis techniques (see the Lab Companion pages 9 and 10). If we have a one percent possible error in a quantity then we have a half percent error in the quantity squared. With g proportional to the inverse of the radius squared. g ! 1 R 2 A .01 decrease in g implies a .005 increase in R. .005 ( ) 6.376 " 10 6 m = 3.2 " 10 4 m 2. Remember, if the flea pushes on the ground, then the ground must push on the flea with an equal and opposite force. Therefore, the three forces that act on the flea are;
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