4. Maximum Area You are given a string of fixed length l with one end fastened at the origin O, and you are to place the string in the ry plane with its other end on the x axis in such a way as to enclose the maximum area between the string and the x axis. Show that the required shape is a semicircle. Hint: The area enclosed is of course ydx, but show that you can rewrite this in the form fds, where s denotes the distance measured along the string from O, where f = yvI - y2, and y' denotes dy/ds. Since f does not involve the independent variable s explicitly, you can exploit the "second form" of Euler-Lagrange Equation.
4. Maximum Area You are given a string of fixed length l with one end fastened at the origin O, and you are to place the string in the ry plane with its other end on the x axis in such a way as to enclose the maximum area between the string and the x axis. Show that the required shape is a semicircle. Hint: The area enclosed is of course ydx, but show that you can rewrite this in the form fds, where s denotes the distance measured along the string from O, where f = yvI - y2, and y' denotes dy/ds. Since f does not involve the independent variable s explicitly, you can exploit the "second form" of Euler-Lagrange Equation.
College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
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Chapter28: Special Relativity
Section: Chapter Questions
Problem 13CQ: All galaxies farther away than about 50106ly exhibit a red shift in their emitted light that is...
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Transcribed Image Text:4.
Maximum Area You are given a string of fixed length l with one end
fastened at the origin O, and you are to place the string in the ry plane with its other
end on the x axis in such a way as to enclose the maximum area between the string and
the x axis. Show that the required shape is a semicircle.
Hint: The area enclosed is of course ydx, but show that you can rewrite this in the
form fds, where s denotes the distance measured along the string from O, where
f = yvI - y2, and y' denotes dy/ds. Since f does not involve the independent variable
s explicitly, you can exploit the "second form" of Euler-Lagrange Equation.
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