Problem 9.92 Member BE of the frame has a turn-
buckle. (See Problem 9.90.) The threads have pitch pD
1 mm, their mean radius is rD6 mm, and the coeffi–
cient of static friction between the threads and the mating
grooves is 0.2. What couple must be exerted on the turn-
buckle to start loosening it?
600 N
ED
F
0.4 m 1.0 m
0.5 m
AB
C
0.4 m0.8 m
0.4
D51.3°
0.2
D68.2°
0.5
0.4
0.5
TBE
θ
φ
TBE FCF
Problem 9.93 In Problem 9.92, what couple must be
exerted on the turnbuckle to start tightening it?
pD0.001 mm
tan sDsD0.2
MD2.756 N-m
For two screws (turnbuckle)
746
Problem 9.94 Members CD and DG of the truss have
turnbuckles. (See Problem 9.90.) The pitch of the threads
is pD4 mm, their mean radius is rD10 mm, and the
coefficient of static friction between the threads and the
mating grooves is 0.18. What couple must be exerted on
the turnbuckle of member CD to start loosening it? A
2 m
CE
B
DF
H
G
8D2.5 kN.
FyDAyCH24D0,
from which AYD3.5 kN.
Joint E: ⊲7⊳0DEG CE,
⊲10⊳0DDG sin ˇCCD sin ˇCDE 4.
Joint C: ⊲11⊳0DCD cos ˇAC cos ˇCCE,
⊲12⊳0DCD sin ˇAC sin ˇBC.
2 m 2 m 2 m 2 m
EG
CD D2.12 kN,
BD D3.5kN,
AB D3.5kN.
The members of interest here are CD D2.12 kN and DG D3.54 kN.
Problem 9.95 In Problem 9.94, what couple must be
exerted on the turnbuckle of member DG to start loos-
ening it?
748
Problem 9.96* The load WD800 N can be raised or
lowered by rotating the threaded shaft. The distances
are bD75 mm and hD200 mm. The pinned bars are
each 300 mm in length. The pitch of the threaded shaft is
pD5 mm, the mean radius of the thread is rD15 mm,
and the coefficient of kinetic friction between the thread
and the mating groove is 0.2. When the system is in the
position shown, what couple must be exerted to turn the
threaded shaft at a constant rate, raising the load?
W
b
h
9.96 (Continued)
From ⊲1⊳ADWb
L.
From ⊲2⊳BDW1b
L.
From ⊲10⊳E
xD2
hWL.
From ⊲4⊳D
xD2
hWL
Check: This value of Gyis expected from the overall equilibrium
conditions. check. From (13)
GxD4WL
h.
600 2
from which
GxD2Wp6002h2
h.
The pitch angle is
Problem 9.97 In Active Example 9.6, suppose that the
placement of the winch at Ais changed so that the
angle between the rope from Ato Pand the horizontal
increases from 45°to 60°. If the suspended load weighs
1500 lb, what tension must the winch exert on the rope
to raise the load at a constant rate?
45⬚
P
750
Problem 9.98 The radius of the pulley is 4 in. The
pulley is rigidly attached to the horizontal shaft, which
is supported by two journal bearings. The radius of the
shaft is 1 in, and the combined weight of the pulley
and shaft is 20 lb. The coefficients of friction between
the shaft and the bearings are sD0.30 and kD0.28.
Determine the largest weight Wthat can be suspended
as shown without causing the stationary shaft to slip in
the bearings.
W
Solution:
Problem 9.99 In Problem 9.98, suppose that the
weight WD4 lb. What couple would have to be
applied to the horizontal shaft to raise the weight at a
constant rate?
Problem 9.100 The pulley is mounted on a horizontal
shaft supported by journal bearings. The coefficient of
kinetic friction between the shaft and the bearings is
kD0.3. The radius of the shaft is 20 mm, and the
radius of the pulley is 150 mm. The mass mD10 kg.
Neglect the masses of the pulley and shaft. What force
Tmust be applied to the cable to move the mass upward
at a constant rate?
m
Rsin k
Problem 9.101 In Problem 9.100, what force Tmust
be applied to the cable to lower the mass at a constant
rate?
16.7°, and MD⊲mg CT⊳r sin k. The applied moment is MD⊲mg
T⊳R. Substitute and reduce:
1r
Rsin k
Rsin k
Problem 9.102 The pulley of 8-in radius is mounted
on a shaft of 1-in radius. The shaft is supported by
Solution: (See Problem 9.100). The angle of static friction is sD
tan1⊲s⊳D8.53°. The moment required to start rotation for both
752
Problem 9.103 The pulley of 50-mm radius is
mounted on a shaft of 10-mm radius. The shaft is
supported by two journal bearings. The mass of the block
Ais 8 kg. Neglect the weights of the pulley and shaft.
If a force TD84 N is necessary to raise the block Aat
a constant rate, what is the coefficient of kinetic friction
between the shaft and the bearings?
20°
T
10 mm
50 mm
FDp107.22C78.92D133.13 N.
The moment required to raise the mass at constant rate for both
rF D0.276
1.33 D0.2073,
Problem 9.104 The mass of the suspended object is
4 kg. The pulley has a 100-mm radius and is rigidly
attached to a horizontal shaft supported by journal bear-
ings. The radius of the horizontal shaft is 10 mm and
the coefficient of kinetic friction between the shaft and
the bearings is 0.26. What tension must the person exert
on the rope to raise the load at a constant rate?
25°
100 mm
Solution:
RD0.1m
kD0.26
25°
T
MS
R = 0.1 m
Shaft radius 0.01 m
K (shaft) = 0.26
µ
K = 0.26
µ
OX
754
Problem 9.105 In Problem 9.104, what tension must
the person exert to lower the load at a constant rate?
TD37.6N
Also
MsD0.163 N-m
OyD55.1N
Problem 9.106 The radius of the pulley is 200 mm,
and it is mounted on a shaft of 20-mm radius. The coef-
ficient of static friction between the pulley and shaft is
sD0.18. If FAD200 N, what is the largest force FB
that can be applied without causing the pulley to turn?
FB
40°
y
Solution: The magnitude of the force on the shaft supporting the
pulley is
Problem 9.107 The masses of the boxes are mAD
15 kg and mBD60 kg. The coefficient of static friction
between boxes Aand Band between box Band the
inclined surface is 0.12. The pulley has a radius of
60 mm and is mounted on a shaft of 10-mm radius. The
coefficient of static friction between the pulley and shaft
is 0.16. What is the largest force Ffor which the boxes
will not slip?
F
A
B
f1D0.12N1,f
2D0.12N2
For the pulley sDtan1⊲0.16⊳, d D10 mm sin s
Thus 60 mm ⊲T1T2⊳D⊲T1CT2⊳d )FD283 N
20°
f1
N1
Problem 9.108 The two pulleys have a radius of 4 in
and are mounted on shafts of 1-in radius supported by
journal bearings. Neglect the weights of the pulleys and
shafts. The tension in the spring is 40 lb. The coefficient
of kinetic friction between the shafts and the bearings is
kD0.3. What couple Mis required to turn the left
pulley at a constant rate?
4 in
M
756
Problem 9.109 The weights of the boxes are WAD
65 lb and WBD130 lb. The coefficient of static friction
between boxes Aand Band between box Band the floor
is 0.12. The pulley has a radius of 4 in and is mounted on
a shaft of 0.8-in radius. The coefficient of static friction
between the pulley and shaft is 0.16. What is the largest
force Ffor which the boxes will not slip?
20⬚
F
A
B
Problem 9.110 The coefficient of kinetic friction
between the 100-kg box and the inclined surface is
0.35. Each pulley has a radius of 100 mm and is
mounted on a shaft of 5-mm radius supported by journal
bearings. The coefficient of kinetic friction between the
shafts and the journal bearings is 0.18. Determine the
tension Tnecessary to pull the box up the surface at a
constant rate.
T
60⬚
Solution: Working through the pulleys
f
T4
Problem 9.111 In Active Example 9.7, suppose that
the diameters DoD31
2in and DiD11
2in and the angle
˛D72°. What couple is required to turn the shaft at a
constant rate?
F
DiDo
a
758
Problem 9.112 The circular flat-ended shaft is pressed
into the thrust bearing by an axial load of 600 lb. The
weight of the shaft is negligible. The coefficients of fric-
tion between the end of the shaft and the bearing are
sD0.20 and kD0.15. What is the largest couple M
that can be applied to the stationary shaft without causing
it to rotate in the bearing?
600 lb
M
2 in
Problem 9.113 The circular flat-ended shaft is pressed
into the thrust bearing by an axial load of 600 lb. The
weight of the shaft is negligible. The coefficients of
friction between the end of the shaft and the bearing are
sD0.20 and sD0.15. What couple Mis required to
rotate the shaft at a constant rate?
600 lb
M
2 in
Problem 9.114 The disk Dis rigidly attached to the
vertical shaft. The shaft has flat ends supported by thrust
bearings. The disk and the shaft together have a mass
of 220 kg and the diameter of the shaft is 50 mm. The
vertical force exerted on the end of the shaft by the
upper thrust bearing is 440 N. The coefficient of kinetic
friction between the ends of the shaft and the bearings
is 0.25. What couple Mis required to rotate the shaft at
a constant rate?
M
M
DD
FLD2598.2N.
The couple necessary to turn Dat a constant rate is the sum of the
rD0.025 m
760
Problem 9.115 Suppose that the ends of the shaft
in Problem 9.114 are supported by thrust bearings of
the type shown in Fig. 9.14, where roD25 mm,r
iD
6mm,˛D45°, and kD0.25. What couple Mis
required to rotate the shaft at a constant rate?
Problem 9.116 The shaft is supported by thrust bear-
ings that subject it to an axial load of 800 N. The coef-
ficients of kinetic friction between the shaft and the left
and right bearings are 0.20 and 0.26, respectively. What
couple is required to rotate the shaft at a constant rate? 38 mm
15 mm
Solution: The left bearing: The parameters are
roD38 mm,
0.26, rD15 mm, and FD800 N. The moment required to sustain a
Problem 9.117 A motor is used to rotate a paddle for
mixing chemicals. The shaft of the motor is coupled
to the paddle using a friction clutch of the type shown
in Fig. 9.17. The radius of the disks of the clutch is
120 mm, and the coefficient of static friction between
the disks is 0.6. If the motor transmits a maximum torque
of 15 N-m to the paddle, what minimum normal force
between the plates of the clutch is necessary to prevent
slipping?
Clutch
Paddle
762
Problem 9.118 The thrust bearing is supported by
contact of the collar Cwith a fixed plate. The area
of contact is an annulus with an inside diameter D1D
40 mm and an outside diameter D2D120 mm. The
coefficient of kinetic friction between the collar and the
plate is kD0.3. The force FD400 N. What couple
Mis required to rotate the shaft at a constant rate? (See
F
F
M
C
M
C
Problem 9.119 An experimental automobile brake
design works by pressing the red annular plate against
the rotating wheel. If kD0.6, what force Fpressing
the plate against the wheel is necessary to exert a couple
of 200 N-m on the wheel?
F
Problem 9.120 In Problem 9.119, suppose that kD
0.65 and the force pressing the plate against the wheel
is FD2 kN.
(a) What couple is exerted on the wheel?
Solution: Use the results of the solution to Problem 9.119, with
parameters kD0.65, FD2 kN.
(a) The moment is
Problem 9.121 The coefficient of static friction
between the plates of the car’s clutch is 0.8. If the plates
are pressed together with a force FD2.60 kN, what
is the maximum torque the clutch will support without
slipping?
150 mm
75 mm
roD0.15 m
riD0.075 m
764