A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance l apart as shown in Figure P5.54. The string forms an angle 0, with the ceiling at each endpoint. The center section of string is horizon- tal. (a) Find the tension in each section of string in terms of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the sections of string between the outside butterflies and the inside butterflies form with the horizontal. (c) Show that the distance D between the endpoints of the string is L D = 2 cos 0, + 2 cos[un "( an 0,] + 1 co[an (} tan 0,] + 1 D 0, m L = 5€ m m m Figure P5.54

A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance l apart as shown in Figure P5.54. The string forms an angle 0, with the ceiling at each endpoint. The center section of string is horizon- tal. (a) Find the tension in each section of string in terms of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the sections of string between the outside butterflies and the inside butterflies form with the horizontal. (c) Show that the distance D between the endpoints of the string is L D = 2 cos 0, + 2 cos[un "( an 0,] + 1 co[an (} tan 0,] + 1 D 0, m L = 5€ m m m Figure P5.54

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A mobile is formed by supporting four metal butterflies
of equal mass m from a string of length L. The points of
support are evenly spaced a distance l apart as shown in
Figure P5.54. The string forms an angle 0, with the ceiling
at each endpoint. The center section of string is horizon-
tal. (a) Find the tension in each section of string in terms
of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the
sections of string between the outside butterflies and the
inside butterflies form with the horizontal. (c) Show that
the distance D between the endpoints of the string is
L
D =
2 cos 0, + 2 cos[un "( an 0,] + 1
co[an (} tan 0,] + 1
D
0,
m
L = 5€
m
m
m
Figure P5.54

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