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Problem 7.130
A solid of revolution is produced by revolving the area shown 360
ı
about the
x
axis. Use integration to determine the xcoordinate of the centroid.
2.xrCxl/Dy2
2:(6)
The xposition of the centroid is given by
0
y2
22y3dy
Problem 7.131
A solid of revolution is produced by revolving the area shown 360
ı
about the
y
axis. Use integration to determine the ycoordinate of the centroid.
Solution
The yposition of the centroid is given by
0
1
22mCpx2x 2mpxdx
Problem 7.132
For the solid of revolution described below:
(a)
Fully set up the integral, including the limits of integration, that will yield the
centroid of the object.
(b)
Evaluate the integral determined in Part (a) using computer software such as
Mathematica or Maple.
The solid of revolution is produced by revolving the area shown about the xaxis.
Problem 7.133
For the solid of revolution described below:
(a)
Fully set up the integral, including the limits of integration, that will yield the
centroid of the object.
(b)
Evaluate the integral determined in Part (a) using computer software such as
Mathematica or Maple.
The solid of revolution is produced by revolving the area shown about the yaxis.
Problem 7.134
For the line shown:
(a)
Set up the integrals for integration with respect to
x
, including the limits
of integration, that will yield the xand ypositions of the centroid.
(b)
Evaluate the integrals in Part (a) using computer software such as Mathe-
matica or Maple.
Problem 7.135
A truss-supported solar panel for a satellite is shown. The truss members are
hollow tubes with mass per unit length of
20 kg=m
, and the solar panel has
mass per unit area of
12 kg=m2
. Determine the mass of the structure and the
x
position of the center of mass. If the structure is on the surface of Earth, with
acceleration due to gravity acting in the
y
direction, determine the support
reactions at points Aand B.
Problem 7.136
The structure shown is used to support a sign for a restaurant. The structure has
five truss members, and cables
AC
,
DF
, and
EG
. The sign weighs
0:2 lb=in:2
,
the truss members weigh
0:5 lb=in:
, and the cables have negligible weight.
Determine the
x
and
y
positions of the center of gravity, and determine the
support reactions at points Aand B.
2.12 in./.20 in./0:2 lb
in.2D24 lb 64 in. 16:67 in.
NxDPQxiwi
Pwi
(1)
Problem 7.137
The area of Prob. 7.15 on p. 446 is revolved 360
ı
about the line
xD r
to create a solid of revolution.
Determine the volume and surface area of the solid.
Problem 7.138
The area of Prob. 7.15 on p. 446 is revolved 360
ı
about the
x
axis to create a solid of revolution. Determine
the volume and surface area of the solid.
Problem 7.139
A solar panel has the shape of a 90
ı
sector of a truncated right circular cone,
and hence it is a surface of revolution. Use the Pappus-Guldinus theorem to
determine the outside surface area of the panel.
2.12 ft/ .15 ft/)AD283 ft2:(1)
