ProblemSet5 - Problem Set 5 Physics 1116 Due Friday Please...

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Problem Set 5 Physics 1116 : Due Friday, 10/01/2010 Please write the names of any classmates with whom you discussed the homework problems at the top of your problem set 1. Consider an infinite flat sheet with uniform mass density σ kg / m 2 . A round hole of radius R centered at the origin ( x = 0 , y = 0 , z = 0) has been cut out of the sheet. (a) Find the gravitational force on a mass m which is directly above the center of the hole at a height Z (i.e. at ( x = 0 , y = 0 , z = Z )). Hint : Consider breaking up the sheet into concentric rings. (b) Assume that the mass starts at rest very close to the center of the hole (i.e. Z R ). Find the frequency of oscillation of the mass oscillating about the center of the hole. Hint : Start with the equations of motion and see if you can make it look like the “spring” equation if Z R . 2. K&K, Problem 3.2 3. K&K, Problem 3.4 4. K&K, Problem 3.5 5. K&K, Problem 3.7 6. A sphere of mass m and radius a is placed inside a larger hollow sphere of mass m and radius 2 a which sits on a surface.
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