Problem 6.86
For the ladder shown, if
WD800
N and
h
can have any value such that
0h0:9
m, determine the largest force supported by each of the spreader
bars
BG
and
DG
, and the value(s) of
h
for which this occurs. Neglect the
weight of the ladder and friction at points Aand E.
Solution
Problem 6.87
Stairs leading to a balcony are shown. For the
400 lb
and
600 lb
forces,
and if FD200 lb and PD0, determine the reaction at point Dand the
force supported by bar BE.
Solution
Problem 6.88
Repeat Prob. 6.87 if FD0and PD200 lb.
Problem 6.89
Stairs leading to a balcony are shown. For the
400 lb
and
600 lb
forces,
and if FD200 lb and PD0, determine the reaction at point Dand the
force supported by bar BE.
Problem 6.90
Repeat Prob. 6.89 if FD0and PD200 lb.
Problem 6.91
In the structure shown, cable segment
ED
and member
ECF
are horizontal. If
WD600 lb
, determine the force supported by members
ABCD
,
ECF
, and
GBF .
Problem 6.92
The structure shown consists of five members with pins at points
B
,
C
,
D
,
E
,
and
G
. Determine the force supported by members
BG
,
C G
, and
DG
due to
the 40 lb, 60 lb, and 80 lb loads.
Problem 6.93
A hydraulically powered lift supports the two boxes shown. Each box weighs
200 lb
with center of gravity in the middle of each box. Neglect the weight of
individual members.
(a)
Draw four FBDs, one each for members
AEF
,
ABC
,
ED
, and
BE
,
labeling all forces.
(b)
Determine the force in the hydraulic actuator
BE
required to keep the lift
in equilibrium.
Problem 6.94
The shovel of an end loader has pins at points
A
,
B
,
C
, and
D
. The scoop supports a downward vertical
load of 2000 lb, which is not shown in the figure, at point E.
(a)
Draw five FBDs, one each for parts
AB
and
AC
, hydraulic cylinder
AD
, shovel
CDE
, and member
BD, labeling all forces.
(b) Determine the force the hydraulic cylinder AD must generate to keep the shovel in equilibrium.
Problem 6.95
A backhoe is shown. Hydraulic cylinders
GF
and
BC
are horizontal and
vertical, respectively. Neglect the weights of members.
(a)
Draw six FBDs, one each for members
DEF
and
F CA
, shovel
AB
,
and hydraulic cylinders BC ,CE, and F G.
(b)
If each of the three hydraulic cylinders is capable of producing a
1000 lb
force (in both tension and compression), determine the largest
weight Wthat can be supported in the position shown.
Problem 6.96
The hand brake for a bicycle is shown. Portions
DE
and
F G
are free to rotate
on bolt
A
, which is screwed into the frame
BC
of the bicycle. The brake is
actuated by a shielded cable where
T1
is applied to point
E
and
T2
is applied
to point
G
. A spring having
50
N compressive force is placed between points
E
and
G
so that the brake stays open when it is not being used. Assume the
change in the spring’s force is negligible when the brake is actuated to produce
the 200 N forces at points Dand F.
(a)
Draw three FBDs, one each for
DE
and
F G
and bolt
A
, labeling all
forces.
(b) Determine the necessary cable forces T1and T2.
(c) Determine the forces exerted by DE and F G on bolt A.
Problem 6.97
A highchair for seating a child at a table is shown. The chair slips onto the
edge of the table and makes contact at points
C
and
G
, where friction at
G
is
negligible. To prevent the back of the chair from rotating counterclockwise,
there is a stop that makes frictionless contact at point
H
. Members
BF
and
EJ
are vertical. Hint: With negligible loss of accuracy, you may assume
that point Clies on the line connecting points Aand B.
(a) Determine the reactions at points Cand G.
(b)
Draw six FBDs, one each for members
ABC
,
DEF G
,
ADI
,
HIJ
,
BF , and EJ .
(c) Determine the forces supported by members BF and EJ .
Problem 6.98
The highchair in Prob. 6.97 can be collapsed (i.e., folded flat) so that it
may be easily transported and stored. To collapse the chair, the seatback
ADI
is rotated clockwise about hinge
I
. When designing the chair, it is
essential that it does not tend to collapse when a child is seated in it (as
modeled by the
16
N and
100
N loads shown). Determine if the chair is
safe from collapsing. Hint: If the reaction at point
H
is compressive, then
the chair will be safe, and if this reaction is tensile, then the chair will begin
to collapse.
NOTE: In the first printing of this book, the hint should refer to the reaction at point H(not point G). This
error is corrected in the second and subsequent printings of the book.
„ƒ‚…
16 N
D0)AxD 16 N;(6)
„ƒ‚…
165 N
Member DEFG:
XMDD0W Ey.22 cm/CBy
.28 cm/Gy
.62 cm/D0)EyD57:82 N;(8)
Problem 6.99
A bicycle is pedaled up a gentle incline. The rider and bicycle weigh
120 lb
with center of gravity at point
C
. For the position shown, determine the force
the rider must apply to the pedal at
F
for the bicycle to move at constant speed.
Assume the rider applies a force to the pedals using her right foot only, the
force applied by the rider to pedal
F
is perpendicular to the crank
EF
, and the
lower portion of the chain between sprockets Dand Eis slack.
Problem 6.100
The linkage shown is used on a garbage truck to lift a
2000 lb
dumpster. Points
A
–
G
are pins, and member
ABC
is horizontal. This linkage has the feature that as the dumpster is lifted and rotated, the front edge
A
of the dumpster is simultaneously lowered, placing it at a more convenient height for emptying.
(a)
Draw five FBDs, one each for members
ABC
,
CD
, and
EDG
, dumpster
H
, and hydraulic cylinder
CF , labeling all forces.
(b)
For the position shown, when the dumpster just fully lifts off the ground, determine the force in
hydraulic cylinder CF .