978-0073380292 Chapter 2 Part 5

subject Type Homework Help
subject Pages 14
subject Words 5075
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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page-pf1
Problem 2.63
Repeat Prob. 2.62 if point Bis 39 mm from point C.
Solution
(5)
page-pf2
114 Solutions Manual
Problem 2.64
Screw
AC
is used to position point
D
of a machine. Point
A
has coordinates
.185; 0/
mm
and is fixed in space by a bearing that supports the screw. The screw nut at point
B
is supported by lever
ED
and at the instant shown has coordinates
.160; 60/ mm
.
If the length of the screw from
A
to
C
is
130 mm
, determine the position vector
ErAC
and the coordinates of point C.
page-pf3
Problem 2.65
In Prob. 2.64 if point
B
is equidistant from points
A
and
C
and if
ErEA D
.185 O{50 O| / mm
and
ErEB D.155 O{C22 O|/ mm
, determine the position vector
ErAC .
page-pf4
Problem 2.66
A computer numerical control (CNC) milling machine is used to cut a slot
in the component shown. The cutting tool starts at point
A
and advances to
point
B
where it pauses while the depth of cut is increased, and then the tool
continues on to point
C
. If the coordinates of points
A
and
C
are
.95; 56/ mm
and
.17; 160/ mm
, respectively, and
B
is located
45 mm
from
A
, determine the
position vectors ErOA,ErOB , and ErOC and the coordinates of B.
page-pf5
Problem 2.67
A vector
Er
has the two direction angles given below. Determine the possible values for the third direction
angle, and describe the differences in the orientation of
Er
. Provide a sketch showing these different vectors.
xD36ıand yD72ı.
page-pf6
Problem 2.68
A vector
Er
has the two direction angles given below. Determine the possible values for the third direction
angle, and describe the differences in the orientation of
Er
. Provide a sketch showing these different vectors.
yD60ıand ´D108ı.
page-pf7
Problem 2.69
A vector
Er
has the two direction angles given below. Determine the possible values for the third direction
angle, and describe the differences in the orientation of
Er
. Provide a sketch showing these different vectors.
xD150ıand ´D100ı.
page-pf8
Problem 2.70
Consider a vector
En
that makes equal angles with the
x
,
y
, and
´
axes (i.e.,
xDyD´
). Determine the
value of these angles and the value of the direction cosines. Note: In the study of stresses in mechanics of
materials, the direction
En
plays an important role and is the normal direction to a special surface called the
octahedral plane.
Solution
page-pf9
Problem 2.71
A person of dubious technical ability tells you that two of the direction angles for a particular vector are
30
ı
and 40
ı
. If these direction angles are feasible, then determine the possible values for the remaining
direction angle. If these direction angles are not feasible, explain why.
page-pfa
Problem 2.72
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
page-pfb
Problem 2.73
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
page-pfc
124 Solutions Manual
page-pfd
Problem 2.74
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
Solution
page-pfe
Problem 2.75
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
E
RDE
FCE
P
(6)
page-pff
Problem 2.76
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
E
RDE
FCE
PCE
Q(9)
D.2:121 1:327 2:667/ O{kN
page-pf10
Problem 2.77
Write an expression for each force using Cartesian representation, and evaluate
the resultant force vector. Sketch the resultant force in the
xy´
coordinate
system.
page-pf11
Problem 2.78
For each vector, find the direction angles and write an expression for the vector
using Cartesian representation. Evaluate the sum of the two vectors, and report
the direction angles for the resultant. Also, sketch the resultant in the
xy´
coordinate system.
page-pf12
Problem 2.79
For each vector, find the direction angles and write an expression for the vector
using Cartesian representation. Evaluate the sum of the two vectors, and report
the direction angles for the resultant. Also, sketch the resultant in the
xy´
coordinate system.
page-pf13
Problem 2.80
The Space Shuttle uses radar to determine the magnitudes and direction cosines
of position vectors to satellites Aand Bas
for ErOAW jErOAj D 2km;cos xD0:768; cos yD 0:384; cos ´D0:512;
for ErOBW jErOB j D 4km;cos xD0:743; cos yD0:557; cos ´D 0:371:
Determine the distance between the satellites.
page-pf14
Problem 2.81
A cube of material with
1mm
edge lengths is examined by a scanning electron
microscope, and a small inclusion (i.e., a cavity) is found at point
P
. It is
determined that the direction cosines for a vector from points
A
to
P
are
cos xD 0:485
, and
cos yD0:485
, and
cos ´D 0:728
; and the direction
cosines for a vector from points
B
to
P
are
cos xD 0:667
,
cos yD 0:667
,
and cos ´D0:333. Determine the coordinates of point P.

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