Unformatted text preview: parametric equations. As your starting point, use the parametric equations of the cycloid x = a ( ϕsin ϕ ) y = a (1cos ϕ ) 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 ﬁnd 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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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 mechanics, Work

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