Physics 325 Homework 8 - parametric equations. As your...

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Physics 325, Fall 2010 Homework Assignment #8 Due Thursday 28 October at 11:15 am in Course Homework Box In the following problems, use the variational technique discussed in class and covered in the texts Taylor and . 1) (10 points) Show that the shortest distance between two points on a plane is a straight line. 2) (15 points) Reexamine the problem of the brachistochrone that was explored in class. Show that the time required for a particle to move (frictionless) to the mini- mum point of the cycloid is, t = π q ( a/g ), independant of the starting point, where g is the acceleration due to gravity and a is as given below in the
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Unformatted text preview: parametric equations. As your starting point, use the parametric equations of the cycloid x = a ( -sin ) y = a (1-cos ) 3) (10 points) Show that the shape of a wire loop (length l ) that encloses a maximum area is a circle. Note: consider only shapes that lie in a plane. 4) (15 points) Find the shortest mountain path around a volcano. Describe the surface of the volcano as a cone with z = 1- x 2 + y 2 and nd the shortest path between the points ( x, y, z ) = (0 ,-1 , 0) and (0 , 1 , 0). Calculate the length of the path. TOTAL 50 points...
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