# ProblemSet8 - 4 K&K Problem 4.12 5 K&K Problem 4.13 6 K&K Problem 4.14 7 K&K Problem 4.29 8 Extra Credit Question Please work on

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Problem Set 8 Physics 1116 : Due Friday, 10/22/2010 Please write the names of any classmates with whom you discussed the homework problems at the top of your problem set 1. Prove that all central forces ( ~ F = f ( r r ) are conservative. Do the same for all constant forces ( ~ F = A ˆ c , where A is a constant and ˆ c is some arbitrary unit vector). You can use whatever methods you like, including geometric arguments or vector calculus. 2. A bead slides along a frictionless wire under the inﬂuence of gravity. The height of the wire is given as y ( x ), and let’s assume that at the origin ( x = 0 ,y = 0), the wire is horizontal and the bead has a speed v 0 . What should the shape of the wire y ( x ) be such that the horizontal velocity remains v 0 at all times (aside from the trivial y = 0 solution, that is)?
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Unformatted text preview: 4. K&K, Problem 4.12 5. K&K, Problem 4.13 6. K&K, Problem 4.14 7. K&K, Problem 4.29 8. Extra Credit Question Please work on this question by yourself! Consider an isolated Borg cube of uniform density ﬂoating somewhere in the Neutral Zone. Find the ratio of the gravitational potential energy of an atom at the center of the cube (arising from the rest of the mass in the cube) vs. the gravitational potential energy of an atom at the corner of the cube (i.e. U corner / U center ). Take the gravitational potential energy at the edge of the universe (i.e. inﬁnitely far away from the cube) to be zero ( U ( ∞ ) = 0). Hint : There is an easy way of doing this problem that involves breaking the cube into smaller cubes!...
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## This note was uploaded on 11/03/2010 for the course PHYS 1116 taught by Professor Elser, v during the Spring '05 term at Cornell University (Engineering School).

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