978-0073380292 Chapter 2 Part 2

subject Type Homework Help
subject Pages 14
subject Words 4839
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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page-pf1
Problem 2.13
Add the three vectors shown to form a resultant vector
E
R
, and report your result
using polar vector representation.
page-pf2
Problem 2.14
Add the three vectors shown to form a resultant vector
E
R
, and report your result
using polar vector representation.
page-pf3
page-pf4
Problem 2.15
Add the three vectors shown to form a resultant vector
E
R
, and report your result
using polar vector representation.
page-pf5
page-pf6
Problem 2.16
A ship is towed through a narrow channel by applying forces to three ropes
attached to its bow. Determine the magnitude and orientation
of the force
E
F
so that the resultant force is in the direction of line
a
and the magnitude of
E
F
is
as small as possible.
page-pf7
Problem 2.17
A surveyor needs to plant a marker directly northeast from where she is standing. Because of obstacles,
she walks a route in the horizontal plane consisting of
200
m east, followed by
400
m north, followed by
300
m northeast. From this position, she would like to take the shortest-distance route back to the line that
is directly northeast of her starting position. What direction should she travel and how far, and what will
be her final distance from her starting point?
page-pf8
Problem 2.18
A utility pole supports a bundle of wires that apply the 400 and
650
N forces
shown, and a guy wire applies the force E
P.
(a)
If
PD0
, determine the resultant force applied by the wires to the pole
and report your result using polar vector representation.
(b) Repeat Part (a) if PD500 N and ˛D60ı.
(c)
With
˛D60ı
, what value of
P
will produce a resultant force that is
vertical?
(d)
If the resultant force is to be vertical and
P
is to be as small as possible,
determine the value ˛should have and the corresponding value of P.
page-pf9
Statics 2e 61
page-pfa
Problem 2.19
The end of a cantilever I beam supports forces from three cables.
(a)
If
PD0
, determine the resultant force applied by the two cables to the
I beam and report your result using polar vector representation.
(b) Repeat Part (a) if PD1:5 kip and ˛D30ı.
(c)
With
˛D30ı
, what value of
P
will produce a resultant force that is
horizontal?
(d)
If the resultant force is to be horizontal and
P
is to be as small as possible,
determine the value ˛should have and the corresponding value of P.
page-pfb
page-pfc
Problem 2.20
Determine the smallest force
F1
such that the resultant of the three forces
F1
,
F2
,
and F3is vertical, and the angle ˛at which F1should be applied.
page-pfd
Problem 2.21
Determine the smallest force
F1
such that the resultant of the three forces
F1
,
F2, and F3is vertical, and the angle ˛at which F1should be applied.
page-pfe
Problem 2.22
Forces
F1
,
F2
, and
F3
are applied to a soil nail to pull it out of a slope. If
F2
and
F3
are vertical and horizontal, respectively, with the magnitudes shown,
determine the magnitude of the smallest force
F1
that can be applied and the
angle
˛
so that the resultant force applied to the nail is directed along the axis
of the nail (direction a).
page-pff
Problem 2.23
Determine the magnitudes of vectors
Era
and
Erb
in the
a
and
b
directions,
respectively, such that their sum is the 2km position vector shown.
page-pf10
Problem 2.24
Determine the magnitudes of vectors
E
Fa
and
E
Fb
in the
a
and
b
directions,
respectively, such that their sum is the 100 lb force vector shown.
page-pf11
Problem 2.25
The child’s play structure from Examples 2.2 and 2.3 on pp. 38 and 39 is shown
again. The woman at
A
applies a force in the
a
direction and the man at
B
applies
a force in the
b
direction, with the goal of producing a resultant force of
250
N in
the
c
direction. Determine the forces the two people must apply, expressing the
results as vectors.
page-pf12
Problem 2.26
The child’s play structure from Examples 2.2 and 2.3 on pp. 38 and 39 is shown
again. The woman at
A
applies a force in the
a
direction and the man at
B
applies a
force in the
b
direction, with the goal of producing a resultant force of
250
N in the
c
direction. Determine the forces the two people must apply, expressing the results
as vectors.
page-pf13
Problem 2.27
While canoes are normally propelled by paddle, if there is a favorable wind
from the stern, adventurous users will sometimes employ a small sail. If a canoe
is sailing north-west and the wind applies a
40 lb
force perpendicular to the sail
in the direction shown, determine the components of the wind force parallel
and perpendicular to the keel of the canoe (direction a).
page-pf14
Problem 2.28
Repeat Part (b) of Example 2.5, using the optimization methods of calculus.
Hint: Redraw the force polygon of Fig. 3 and rewrite Eq. (1) on p. 41 with
the
45ı
angle shown there replaced by
ˇ
, where
ˇ
is defined in Fig. P2.28.
Rearrange this equation to obtain an expression for
FOC 0
as a function of
ˇ
,
and then determine the value of
ˇ
that makes
dFO C 0=dˇ D0
. While the
approach described here is straightforward to carry out “by hand, you might
also consider using symbolic algebra software such as Mathematica or Maple.

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