Statics 2e 423
Problem 3.116
The structure consists of two bars and a vertical force
W
. When
WD0
,
point
A
has the position shown (i.e., its coordinates are
A .10; 0/ in.
). When
WD50 lb
, point
A
moves to point
A0
, whose coordinates are
A0.9:6; 1:2/ in.
(a) Determine the force each bar supports when WD50 lb.
(b)
If bars
AB
and
AC
are modeled as linear elastic springs, determine the
stiffness of each of these.
Problem 3.117
The structure consists of a bar
AB
and cables
AC
and
AD
. When
WD20
N,
point
A
has the position shown (i.e., its coordinates are
A .100; 0/ mm
). When
the weight at point
D
is increased to
WD40
N, point
A
moves to point
A0
,
whose coordinates are A0.99:8; 8/ mm.
(a) Determine the force in bar AB and cable AC when WD40 N.
(b)
If bar
AB
and cable
AC
are modeled as linear elastic springs, determine
the stiffness of each of these.
Problem 3.118
The frictionless pulley
A
weighs
20
N and supports a box
B
weighing
60
N.
When you solve for the force in cable
CD
, a “problem” arises. Describe this
problem and its physical significance.
Solution
Problem 3.119
To produce a force
PD40
N in the horizontal member
CD
of a machine, a
worker applies a force
F
to the handle
B
. Determine the smallest value of
F
that can be used and the angle ˛it should be applied at.
Solution
Problem 3.120
Two scenarios are shown in Figs. P3.120(a) and (b) for using a tow truck
A
to
free a car
B
that is stuck on the side of a road. In (a), a cable
AB
is attached
directly from the tow truck to the car and in (b), three cables are used where
point
C
is a fixed support, such as a concrete signpost footing or a large tree
stump. Assume all cables lie in the same plane and cable
CD
is parallel to the
road.
If a
4000 lb
force must be applied to the car, for each scenario determine
the force the tow truck must apply to its cable.
Problem 3.121
Two scenarios are shown in Figs. P3.120(a) and (b) for using a tow truck
A
to
free a car
B
that is stuck on the side of a road. In (a), a cable
AB
is attached
directly from the tow truck to the car and in (b), three cables are used where
point
C
is a fixed support, such as a concrete signpost footing or a large tree
stump. Assume all cables lie in the same plane and cable
CD
is parallel to the
road.
If the tow truck can produce a
6000 lb
force in the cable attached to it, for
each scenario determine the force that is applied to the car.
Problem 3.122
The structure shown consists of five cables. Cable ABCD supports a drum having
weight
WD200 lb
. Cable
DF
is horizontal, and cable segments
AB
and
CD
are vertical. If contact between the drum and cable ABCD is frictionless,
determine the force in each cable.
Solution
Problem 3.123
In Prob. 3.122, if cable ABCD has
600 lb
breaking strength and all other cables
have 200 lb breaking strength, determine the largest value Wmay have.
Solution
Problem 3.124
The structure shown consists of two bars and three cables. If
WD1000 lb
,
determine the force supported by each bar and cable.
Problem 3.125
The structure shown consists of two bars and three cables. If each bar has
3000 lb
strength in tension and
2000 lb
strength in compression, and each cable
has 1500 lb strength, determine the largest value of Wthat may be supported.
Problem 3.126
Two frictionless pulleys connected by a weightless bar
AB
support the 200
and
300
N forces shown. The pulleys rest on a wedge that is fixed in space.
Determine the angle
when the system is in equilibrium and the force in bar
AB.
Problem 3.127
The hoist shown is used to lift an engine during manufacturing. The hoist con-
sists of a horizontal bar
AB
and a cable
AC
, and the engine at
D
is supported
by a cable
DAE
that wraps around a frictionless pulley at point
A
and is driven
by an electric motor at
E
. The engine at
D
weighs
2500
N and other weights
in the system are negligible.
Determine the force supported by bar AB and cables AC and DAE.
Problem 3.128
The hoist shown is used to lift an engine during manufacturing. The hoist con-
sists of a horizontal bar
AB
and a cable
AC
, and the engine at
D
is supported
by a cable
DAE
that wraps around a frictionless pulley at point
A
and is driven
by an electric motor at
E
. The engine at
D
weighs
2500
N and other weights
in the system are negligible.
If the bar and cables have the strengths listed below, determine the factor of
safety for the hoist (factor of safety is defined in Eq. 3.23 on p. 184.)
Member Strength
AB 12;000 N tension & 9000 N compression
AC 8000 N
DAE 7000 N
Problem 3.129
To glue a strip of laminate to the edge of a circular table,
n
clamps are evenly
spaced around the perimeter of the table (the figure shows
nD8
). Each clamp
has a small pulley, and around all pulleys a cable is wrapped. A turnbuckle is
used to tighten the cable, producing a force
T
. Assuming the diameter of each
pulley is small, show that the force
R
each clamp applies to the edge of the
table is given by
RD2T cosŒ.n 2/180ı=.2n/
. Does this expression give
expected values when
nD2
and
nD 1
? Explain. Hint: The sum of the
interior angles of a polygon with mcorners is .m 2/180ı.
Problem 3.130
Spring
AC
is unstretched when
D0
. Force
F
is always perpendicular to bar
AB. Determine the value of Fneeded for equilibrium when D45ı.
Problem 3.131
If
WD100
N and
kD5N=mm
, determine
ı1
and
ı2
. Springs are unstretched
when ı1Dı2D0.
Problem 3.132
If
WD100
N and
kD5N=mm
, determine
ı1
and
ı2
. Springs are unstretched
when ı1Dı2D0.