Physics 325 Spring 2011 Homework 7

Physics 325 Spring 2011 Homework 7 - Physics 325 Spring...

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Physics 325 Spring 2011 Homework 7A Name: ____________________________ Due: Apr 6, 2011 by 9am (lecture or 325 box) 1. (10 points) A soap bubble placed between two centered hoops will take the shape with the minimum area. Use the calculus of variations to find the curve () yx that defines the surface of revolution. Hint: Assume that the surface is circular everywhere in the xz plane. The problem then reduces to a two-dimensional problem with an element of surface area written as 2 xds , where ds is an element of length in the xy plane. 2. (10 points) In relativity theory, velocities can be represented by points in a certain “rapidity space” in which the distance between two neighboring point is 2 2 2 2 2 1 ds dr r d r  where r and are polar coordinates, and we consider just a two-dimensional space. (An expression like this for the distance in non-Euclidean space is often referred to as the metric of the space.) Use the Euler-Lagrange equation to show that the shortest path from the origin to any other point is a straight line.
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Physics 325 Spring 2011 Homework 7 - Physics 325 Spring...

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