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 θ 1 with the ceiling at each endpoint. The center section of string is horizontal. (a) Find the tension in each section of string in terms of θ 1 , m, and g . (b) In terms of θ 1 , find the angle θ 2 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 D = L 5 { 2 cos θ 1 + 2 cos [ tan − 1 ( 1 2 tan θ 1 ) ] + 1 } 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 θ 1 with the ceiling at each endpoint. The center section of string is horizontal. (a) Find the tension in each section of string in terms of θ 1 , m, and g . (b) In terms of θ 1 , find the angle θ 2 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 D = L 5 { 2 cos θ 1 + 2 cos [ tan − 1 ( 1 2 tan θ 1 ) ] + 1 } Figure P5.54
Solution Summary: The free body diagram of the toaster is given below.
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 θ1 with the ceiling at each endpoint. The center section of string is horizontal. (a) Find the tension in each section of string in terms of θ1, m, and g. (b) In terms of θ1, find the angle θ2 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
D
=
L
5
{
2
cos
θ
1
+
2
cos
[
tan
−
1
(
1
2
tan
θ
1
)
]
+
1
}
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