Statics 2e 1391
Problem 9.46
The structure consists of two uniform members AB and BC, each weighing
2kN
.
The members are pinned to one another at
B
, and the structure is supported
by surfaces at
A
and
C
having coefficients of static friction of 1.2 and 0.5,
respectively. Determine the largest positive value Pthe structure can support.
3)PD 0:5000 kN:(13)
Problem 9.47
The structure consists of two uniform members AB and BC, each weighing
2kN
and
P0
. Determine the minimum coefficient of static friction needed
at surface
A
and the minimum coefficient of static friction needed at surface
C
so that neither surface slips for any value of P(this is called self-locking).
Problem 9.48
A wrench is used to twist a pipe
C
. The wrench consists of jaw BD and handle-
jaw
ADE
, with a pin at
D
. The coefficient of static friction
s
for all contact
surfaces is the same. Determine the minimum value of
s
so that there is no
slip at Aor Bregardless of the value of force P(this is called self-locking).
Solution
The FBDs shown at the right have the directions of friction forces
F1
and
F2
such that if slip occurs at point
A
, then point
A
will move downward
relative to the fixed pipe, and if slip occurs at point
B
, then point
B
will
move upward relative to the fixed pipe.
Problem 9.49
A small lamp is clamped on a fixed circular bar
C
. The lamp assembly weighs
4lb
with center of gravity at point
G
, and the weights of all other members are
negligible. Determine the minimum moment the torsional spring at
D
must
produce so the lamp does not slip on the bar. The contact surfaces at
A
and
B
have coefficients of static friction of AD0:25 and BD0:35.
(7) and (10). Hence,
Problem 9.50
A bracket
ABCDEF
is clamped to a fixed circular bar. The bracket consists
of a horizontal member
ABC
that is pinned at
C
to member
CDEF
, and a
vertical bolt
BD
. The force
P
at point
F
is vertical, and the bracket makes
contact with the fixed bar at points
A
,
G
, and
E
. If all contact surfaces have the
same coefficient of static friction of 0.4, and if
PD50 lb
, determine the force
that bolt BD must support to prevent slip.
Problem 9.51
Two objects are connected by a weightless cord that is wrapped around a fixed cylindrical
surface. The coefficient of static friction between the cord and surface is 0.3. One of the
objects weighs
100 lb
, and the other has weight
W
. If the system is initially at rest, determine
the range of values for Wfor which there is no motion.
Problem 9.52
A
10
N weight is supported by a weightless cable where portion
AB
of the cable is
horizontal. The coefficients of static and kinetic friction are 0.5.
(a)
Determine the value of
P
so that downward motion of the
10
N weight is impend-
ing.
(b)
If
PD3
N, determine the force in portion CD of the cable. Is the system in
equilibrium or is there motion? Explain.
Problem 9.53
A
10
N weight is supported by a weightless cable where portion
AB
of the cable is
horizontal. A test is conducted where it is found that
PD4
N will cause impending
motion of the 10 N weight at D.
(a)
Determine the coefficient of static friction between the cable and cylindrical
surface.
(b)
Determine the tension in portion
BC
of the cable as a function of angular position
. Plot this function.
Problem 9.54
A hoist for lifting lightweight building materials is shown. The pulley at
B
is frictionless, and the pulley at
C
is driven by an electric motor rotating
counterclockwise at a speed high enough to always cause slip between the
cable and pulley
C
. The cable makes contact with one-fourth of the surface
of pulley
C
, and the coefficients of static and kinetic friction are 0.25 and 0.2,
respectively. If the cable has negligible weight and the building materials and
platform at
D
have a combined weight of
100 lb
, determine the force the worker
must apply to the cable to
(a) Raise the building materials at a uniform speed.
(b) Lower the building materials at a uniform speed.
(c) Hold the building materials in a fixed, suspended position.
Problem 9.55
In Prob. 9.54, if the cable were given an additional full wrap around the pulley
at
C
and if the worker can apply a force of
50 lb
to the cable, determine the
largest weight that may be lifted at D.
Problem 9.56
The machine shown is used to slowly lower and raise the object at point
D
.
Cable
BCD
is wrapped around the drum at
B
a large number of turns, and
cable segment
BC
is horizontal. The coefficients of static and kinetic friction
are 0.22 and 0.18, respectively. Let
P
be the force the operator applies to
point
A
of the machine, where this force is perpendicular to the crank
AB
. If
WD20 lb
, determine the range of values for
P
so that there is no motion of
the object at D.
Problem 9.57
In Prob. 9.56, if the person operating the machine can apply a maximum force
of
25 lb
to the handle
A
of the machine, where this force is perpendicular to the
crank
AB
, and if the cable has
50 lb
strength, determine the largest value of
W
that may be lowered, and the largest value of
W
that may be raised. Hint:
Lowering and raising motions will be initiated from at-rest conditions.
Problem 9.58
A brake for reducing the speed of a rotating drum is shown. The braking
moment is defined as the resultant moment the belt produces about the drum’s
bearing, point
A
. Determine the braking moment if the coefficient of kinetic
friction is 0.35 and: The drum rotates clockwise and PD90 N.
MADT2.20 cm/T1.20 cm/(6)
Problem 9.59
A brake for reducing the speed of a rotating drum is shown. The braking
moment is defined as the resultant moment the belt produces about the drum’s
bearing, point
A
. Determine the braking moment if the coefficient of kinetic
friction is 0.35 and: The drum rotates counterclockwise and PD90 N.
MADT2.20 cm/T1.20 cm/(6)
Problem 9.60
0.35 and: The drum rotates clockwise and PD20 lb.
MADT2.10 in:/ T1.10 in:/ (7)