Statics 2e 1427
Sliding analysis:
When sliding occurs, Coulomb’s law
FDN
, where the coefficient of static friction is
used, provides
BxD.0:28/By:(17)
Using Eq. (17), the equilibrium equations are
XMAD0WP .140 cm/.1000 N/.35 cm/CBy.70 cm/D0; (18)
Thus, motion is impending when
Problem 9.74
The cross section through a unidirectional clutch is shown. Member
ABC
is
attached to the input shaft, and when this shaft applies power to the output shaft,
the two shafts are locked together by members
AD
and
CE
. Both the input
and output shafts rotate clockwise. When the input shaft does not apply power
to the output shaft, members
AD
and
CE
disengage, allowing the output shaft
to rotate faster than the input shaft. If the coefficient of friction at
D
and
E
is
0.3, determine the largest value of
h
that prevents slip between the shafts when
power is transmitted. Assume the masses of members are small so that static
equilibrium may be assumed.
Problem 9.75
A roll of paper
C
with
8
N weight is supported by edges
A
and
B
. A horizontal force
P
is applied to pull a sheet of paper from the roll. Determine the value of
P
that
causes motion, and determine if the motion is rolling or tipping. The coefficient of
static friction between the roll of paper and edges Aand Bis: 0.1.
Problem 9.76
A roll of paper
C
with
8
N weight is supported by edges
A
and
B
. A horizontal force
P
is applied to pull a sheet of paper from the roll. Determine the value of
P
that
causes motion, and determine if the motion is rolling or tipping. The coefficient of
static friction between the roll of paper and edges Aand Bis: 0.3.
Problem 9.77
A car weighing
4000 lb
rests on a slope with coefficient of static friction of 0.4.
The car is disabled with its parking brake applied so that none of its wheels will
turn or roll. A tow truck applies a
y
direction force
P
to the car. Determine
the value of
P
that causes impending motion of the car, and determine the unit
vector that describes the direction in which the car will begin to slide.
Problem 9.78
A bicyclist descends a steep hill having uniform slope.
She does not pedal and she applies only the rear brake.
The rider and bicycle weigh
120 lb
with center of gravity
at point
C
. Is it possible to descend the hill with uniform
speed, and if so, what brake force
Q
is needed? The
coefficient of friction between the tire and pavement is
1.1, and between the brake pad and wheel rim is 0.7.
(a) ˛D20ı.
(b) ˛D10ı.
Problem 9.79
A model is shown for the nanotractor microelectromechanical machine pro-
duced at Sandia National Laboratory. This machine is very small (note that the
diameter of a human hair is about
100 m
). The forces
PA
,
PC
, and
PE
are
produced electronically, and the machine creeps (or inches) to the right along a
surface by alternately increasing and decreasing these forces in a synchronized
pattern, thus producing a force
Q
that can pull something. The weights of
all members are negligible, the coefficient of friction between the substrate
and blocks
A
and
E
is 0.35, and you may assume the blocks do not tip. If
PAD20 N
,
PED100 N
, and
QD25 N
, determine the value of
PC
that
will cause slip, and determine which of the blocks will slip.
Problem 9.80
To move a lathe weighing
1200 lb
with center of gravity at point
D
, a
machinist uses a steel pry bar as shown. The legs of the lathe are iron and
the floor is concrete. The coefficient of static friction for steel on iron is 0.3,
and for steel or iron on concrete is 0.35. If the force
P
applied to the pry
bar at
A
is vertical, determine the value of
P
necessary to cause impending
motion and describe the motion.
Problem 9.81
The wrench shown is used to twist a brass pipe. The wrench consists of a steel
handle
ABC
with a reinforced rubber belt that is pinned to the handle at points
A
and
B
. The steel handle makes contact with the brass pipe at point
A
, and
the coefficient of friction between steel and brass is 0.3. If a vertical force
PD50 lb
is applied at point
C
, determine the minimum coefficient of friction
needed between the rubber belt and brass pipe if the wrench is not to slip.
Problem 9.82
A conveyor belt for moving crushed rock is shown. The belt slides on a
straight roller bed with a coefficient of friction of 0.09. The belt is wrapped
around five pulleys where the pulley at
A
is powered by a motor that applies
a counterclockwise moment
MA
, and the other pulleys are frictionless. The
coefficient of friction between the belt and pulleys is 0.4. The belt is tensioned
by the weight
W
at point
G
, where cable segments
CD
and
DE
are vertical. If
the crushed stone weighs
4000 N=m
, determine the moment
MA
that the motor
must produce and the value of Wneeded so the belt does not slip.
Problem 9.83
The device shown allows for easy elevation adjustments of block
A
on the fixed ramp
E
. When the user applies a sufficient upward vertical force to the cable at
C
, block
A
is lowered. When the user applies a sufficient downward vertical force to the cable at
C
, block
A
is raised. The coefficients of static and kinetic friction between block
A
and the ramp, and between the cable and cylindrical surface at
B
, are 0.1. Block
A
has
40
N weight, the cable has negligible weight, cable segment AB is parallel to the ramp,
segment BCD is vertical, and assume block
A
does not tip. Determine the weight
WD
of the counterweight at
D
so that the value of the upward force the user must apply
to cause motion is the same as the value of the downward force the user must apply
to cause motion. Also, determine the value of the force the user must apply to cause
motion.
Problem 9.84
An electric motor at
A
is used to power an air compressor that requires a
200 in:lb
moment at pulley
B
to operate. When the motor is turned off, the
entire belt is at a uniform tensile force
T0
. When the motor is turned on, pulley
A
rotates clockwise, and the tensile forces in the upper and lower portions of
the belt change to
T0T
and
T0CT
, respectively. The lower portion of
the belt is horizontal, and the pulley radii and coefficients of static friction are
shown. Determine the initial belt tension T0so that neither pulley slips.
Problem 9.85
In Prob. 9.84, it was stated that when the motor is off, the tensile force in the belt is
T0
, and when the
motor is on, the tensile forces in the upper and lower portions of the belt change to
T0T
and
T0CT
,
respectively. Offer justification for why the increase in force in the high-tension portion of the belt is equal
to the decrease in force in the low-tension portion of the belt. Hint: Idealize the upper and lower portions
of the belt as springs, and consider the deformations they undergo when the motor is on.