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Statics 2e 73
Problem 2.29
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.2 on p. 43.
Problem 2.30
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.3 on p. 43.
Solution
y
x
R
18 kN
35 kN
Part (a)
The
18 kN
and
35 kN
force vectors are shown to the right with an
xy
Cartesian coordinate system, and the sum of these vectors is given by
E
RD.18 O{C35 O|/kN:(1)
1.23 ft 1.89 ft
R
60◦
45◦x
y
The
1:23 ft
and
1:89 ft
position vectors are shown at the right with an
xy
Cartesian
coordinate system, and the sum of these vectors is given by
E
RD1:23.cos 45ıO{sin 45ıO|/ ft C1:89.cos 60ıO{Csin 60ıO|/ ft
D.1:81 O{C0:767 O|/ft:
(2)
(3)
Problem 2.31
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.13 on p. 45.
Problem 2.32
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.16 on p. 45.
Problem 2.33
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.17 on p. 45.
Problem 2.34
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.18 on p. 45.
Solution
Problem 2.35
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.21 on p. 46.
Problem 2.36
For the following problems, use an
xy
Cartesian coordinate system where
x
is horizontal, positive to the
right, and
y
is vertical, positive upward. For problems where the answers require vector expressions, report
the vectors using Cartesian representations.
Repeat Prob. 2.22 on p. 46.
Solution
400 N
200 N
F1
60◦
a
x
y
30◦
60◦
The dashed line in the figure to the right represents the direction along which
the resultant force vector
E
R
is required to act. The horizontal and vertical
components of E
Rare given by
RxD400 NF1cos 30ı;and RyD200 NCF1sin 30ı:(1)
It follows that
tan 60ıDRy
Rx
D200 NCF1sin 30ı
400 NF1cos 30ı)F1D246 N:(2)
Note that ˛equals 60ısince F1is perpendicular to line a. Using Cartesian representation, E
F1is given by
E
F1D.246 N/.cos 30ıO{Csin 30ıO|/ D.213 O{C123 O|/ N:(3)
May 11, 2012
This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or possessed only by permission
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Problem 2.37
Let
E
AD.150 O{200 O|/ lb
and
E
BD.200 O{C480 O|/ lb
. Evaluate the following, and for Parts (a) and (b)
state the magnitude of E
R.
(a) E
RDE
ACE
B.
(b) E
RD2E
A.1=2/ E
B.
(c) Find a scalar ssuch that E
RDsE
ACE
Bhas an xcomponent only.
(d) Determine a dimensionless unit vector in the direction E
BE
A.
Solution
Problem 2.38
Let
E
AD.6O{C8O|/ kN
and
E
BD.9O{12 O|/ kN
. Evaluate the following, and for Parts (a) and (b)
state the magnitude of E
R.
(a) E
RDE
ACE
B.
(b) E
RD 2E
ACE
B.
(c) Find a scalar ssuch that E
RD E
ACsE
Bhas a ycomponent only.
(d) Determine a dimensionless unit vector in the direction E
AE
B.
Solution
Part (a)
84 Solutions Manual
Problem 2.39
Let
E
AD.150 O{C200 O|/ mm
,
E
BD.300 O{450 O|/ mm
, and
E
CD.100 O{250 O|/ mm
. Evaluate the
following, and for Parts (a) and (b) state the magnitude of E
R.
(a) E
RDE
ACE
BCE
C.
(b) E
RD3E
A2E
BCE
C.
(c) Find scalars rand s, if possible, such that E
RDrE
ACsE
BCE
Chas zero xand ycomponents.
(d) Determine a dimensionless unit vector in the direction E
ACE
BCE
C.
Solution
Part (a)
86 Solutions Manual
Problem 2.40
A rope connecting points
A
and
B
supports the force
F
shown in the figure.
Write expressions using Cartesian vector representation for the following:
(a) ErAB : the position vector from Ato B.
(b) ErBA: the position vector from Bto A.
(c) OuAB : the unit vector in the direction from Ato B.
(d) OuBA: the unit vector in the direction from Bto A.
(e) E
FAB : the force vector the rope applies to A.
(f) E
FBA: the force vector the rope applies to B.
Solution
Problem 2.41
A rope connecting points
A
and
B
supports the force
F
shown in the figure.
Write expressions using Cartesian vector representation for the following:
(a) ErAB : the position vector from Ato B.
(b) ErBA: the position vector from Bto A.
(c) OuAB : the unit vector in the direction from Ato B.
(d) OuBA: the unit vector in the direction from Bto A.
(e) E
FAB : the force vector the rope applies to A.
(f) E
FBA: the force vector the rope applies to B.
Solution
Problem 2.42
A cleat on a boat is used to support forces from three ropes as shown. Determine
the resultant force vector
E
R
, using Cartesian representation, and determine the
magnitude R. Also express E
Rin polar vector representation.
Solution
Problem 2.43
A control arm in a machine supports the three forces shown. Determine the
resultant force vector
E
R
, using Cartesian representation, and determine the
magnitude R. Also express E
Rin polar vector representation.
Problem 2.44
A cantilevered bracket supports forces from two bars and two cables, as shown.
Determine the resultant force vector
E
R
, using Cartesian representation, and
determine the magnitude R. Also express E
Rin polar vector representation.
Problem 2.45
A model of a person’s arm is used for ergonomics studies. Distances are
rAB D
35 cm, rBC D28 cm, and rCD D19 cm.
(a) Determine the position vector ErAD and its magnitude rAD .
(b)
Express
ErAD
using polar vector representation, measuring orientation posi-
tive counterclockwise from the right-hand horizontal direction.
(c) Determine a unit vector OuAD in the direction from Ato D.
