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Problem 3.17
Guy wire
AB
is used to help support the utility pole
AC
. If the guy wire
AB
can support a maximum tensile force of
500 lb
, and if the pole
AC
can support
a maximum compressive force of
800 lb
before buckling, determine the largest
force Pthat can be supported.
Problem 3.18
A component of a machine has a frictionless roller
A
that rests in a slot. The
roller is supported by bar
AB
where point
B
is a pin. For the values of
P
and
given below, determine the force supported by bar AB.
PD200 N and D15ı.
Problem 3.19
A component of a machine has a frictionless roller
A
that rests in a slot. The
roller is supported by bar
AB
where point
B
is a pin. For the values of
P
and
given below, determine the force supported by bar AB.
PD400 N and D35ı.
Problem 3.20
A bead
A
weighing
2lb
slides on a quarter-circular frictionless bar
BC
with
radius
r
. The bead is supported by a cable
AC
. For the value of
given below,
determine the force supported by cable AC .
D20ı.
Problem 3.21
A bead
A
weighing
2lb
slides on a quarter-circular frictionless bar
BC
with
radius
r
. The bead is supported by a cable
AC
. For the value of
given below,
determine the force supported by cable AC .
General values of where 0ı< < 90ı.
Solution
y
x
A
C
TAC
2 lb
R
r r sin
r sin
r cos
The FBD for bead
A
is shown at the right. The reaction between
the bead and bar is constructed as follows. The bead may not move
perpendicular to the bar, therefore there is a reaction force
R
perpen-
dicular to the bar. The bead is free to move parallel to the frictionless
bar, therefore there is no reaction force in that direction. To determine
the orientation for
TAC
we consider the triangle shown below. The
hypotenuse hof this triangle is
h2D.r cos /2CŒr.1 sin /2(1)
Dr2cos2C12sin Csin2:(2)
A
C
hr(1 sin )
r cos
Since cos2Csin2D1, Eq. (2) becomes
h2Dr22.1 sin /: (3)
Hence,
hDrp2.1 sin /: (4)
Summing forces in the xand ydirections provides
XFxD0W Rcos CTAC
rcos
rp2.1 sin / D0; (5)
XFyD0WRsin CTAC
r.1 sin /
rp2.1 sin / 2lb D0: (6)
Equation (5) provides
TAC DRp2.1 sin /: (7)
Substituting Eq. (7) into Eq. (6) provides
288 Solutions Manual
Problem 3.22
Two schemes are shown for hanging a large number of flowerpots side by side
on an outdoor porch. The flowerpots are to have
60 cm
spacing. Each flowerpot
weighs 175 N.
(a) Determine the force in wire AB.
(b) Determine the forces in wires CD and CE.
(c)
Compared to the scheme using one wire, the scheme using two wires
may be more resistant to adjacent flowerpots hitting one another in high
winds. Do you believe this statement is valid? Explain. Hint: Consider
the application of a horizontal wind force
P
to points
A
and
C
and
speculate on the ability of each system to resist horizontal motion. To
do this, compare the values of
P
needed to produce the same horizontal
displacement of points Aand Cof, say, 10 cm.
Problem 3.23
A hydraulic cylinder
AB
on a backhoe produces a
4500 lb
compressive force. Deter-
mine the forces in members BD and BC .
Problem 3.24
A worker inside a truck at point
A
applies a force to rope
ABC
to slowly
lower a box
C
down a ramp
DE
. The box has
400
N weight and slides without
friction on the ramp, and the pulley at Bis frictionless. For the position of the
box given below, determine the force the worker must apply to the rope and the
reaction between the box and ramp. Neglect the size of the box and pulley.
The box is 1/4 the distance from point Dto point E.
Solution
y
x
TABC
C
1.2
3.53.7
1.2
3.5
3.7
400 N
R
The FBD for box
C
is shown at the right. If the box is
1=4
the distance from
Dto E, then
ErCB D1
4.3:5 m/0:8 mO{C1
4.1:2 m/C2:5 mO|(1)
D.1:675 O{C2:8 O|/ m;(2)
E
TABC DTABC
1:675 O{C2:8 O|
3:263 :(3)
Summing forces in the xand ydirections provides
XFxD0W TABC
1:675
3:263 CR1:2
3:7 D0; (4)
XFyD0WTABC
2:8
3:263 CR3:5
3:7 400 ND0: (5)
Solving these equations provides
TABC D169:8 N and RD268:8 N:(6)
Problem 3.25
A worker inside a truck at point
A
applies a force to rope
ABC
to slowly
lower a box
C
down a ramp
DE
. The box has
400
N weight and slides without
friction on the ramp, and the pulley at Bis frictionless. For the position of the
box given below, determine the force the worker must apply to the rope and the
reaction between the box and ramp. Neglect the size of the box and pulley.
The box is 3/4 the distance from point Dto point E.
Solution
y
x
TABC
C
1.2
3.53.7
1.2
3.5
3.7
400 N
R
The FBD for box
C
is shown at the right. If the box is
3=4
the distance from
Dto E, then
ErCB D3
4.3:5 m/0:8 mO{C3
4.1:2 m/C2:5 mO|(1)
D.3:425 O{C3:4 O|/ m;(2)
E
TABC DTABC
3:425 O{C3:4 O|
4:826 :(3)
Summing forces in the xand ydirections provides
XFxD0W TABC
3:425
4:826 CR1:2
3:7 D0; (4)
XFyD0WTABC
3:4
4:826 CR3:5
3:7 400 ND0: (5)
Solving these equations provides
TABC D144:2 N and RD315:5 N:(6)
Problem 3.26
The pulley shown is frictionless and all weights are negligible.
(a) Show that D˛.
(b)
By drawing an FBD of the pulley and writing and solving equilibrium
equations, determine the force
F
in terms of the force
T
and angle
.
Plot the ratio F=T versus for 090ı.
(c)
Imagine a structure has this pulley and cable arrangement, and you
carefully measure
and
˛
and find they are not equal. Explain possible
circumstances that might cause this to occur.
Solution
Problem 3.27
Due to settlement of soil, a recently planted tree has started to lean. To straighten
it, the cable system shown is used, where a turnbuckle on cable AB is periodi-
cally tightened to keep the cable taut as the tree gradually straightens. If the
force in cable AB is 450 N, determine the force in cable CBD.
Solution
Problem 3.28
The symmetric cable and pulley arrangement shown is used to lift a fragile
architectural stone beam. If the only significant mass in the system is the
800 kg
mass mof the beam, determine the forces in cables ACB and CDE.
Problem 3.29
The symmetric cable and pulley arrangement shown is used to lift a fragile
architectural stone beam. If the only significant mass in the system is the
800 kg
mass mof the beam, determine the forces in cables ACB and CDE.
Problem 3.30
In Fig. P3.29, cables
ACB
and
FEG
each can support a maximum force of
3kN
. Cable
CDE
can support
a maximum force of 9 kN. The spreader bar
CE
can support a maximum compressive force of
5kN
.
Determine the largest mass
m
of the stone beam that may be lifted, assuming this is the only significant
mass in the system.
Problem 3.31
Bars
AB
and
BC
have the tensile and compressive strengths listed below. If
QD0
and P0, determine the largest value of Pthat may be supported.
Member Strength
AB 4000 lb tension & 2500 lb compression
BC 4500 lb tension & 3000 lb compression
Problem 3.32
Bars
AB
and
BC
have the tensile and compressive strengths listed in Prob. 3.31.
If PD0and Q0, determine the largest value of Qthat may be supported.
Problem 3.33
Blocks
A
and
B
each weigh
100 lb
and rest on frictionless surfaces. They are
connected to one another by cable
AB
. Determine the force
P
required to hold
the blocks in the equilibrium position shown and the reactions between the
blocks and surfaces.
Problem 3.34
Two weights are supported by cable
ABCD
. With the geometry shown, if one
of the weights is
2000
N, determine the other weight
W
and the cable tensions.
