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PROBLEM 17.48
Knowing that the maximum allowable couple that can be applied to a shaft is 15.5 kip in., determine the
maximum horsepower that can be transmitted by the shaft at (a) 180 rpm, (b) 480 rpm.
PROBLEM 17.49
Three shafts and four gears are used to form a gear train which
will transmit 7.5 kW from the motor at A to a machine tool at F.
(Bearings for the shafts are omitted from the sketch.) Knowing
that the frequency of the motor is 30 Hz, determine the
magnitude of the couple which is applied to shaft (a) AB,
(b) CD, (c) EF.
D CD E EF EF
10.4167 rad/s
Power 7.5 kW
EF
(a) Shaft AB. Power : 7500 W (60 rad/s)
39.8 N m
EF EF EF
EF
PROBLEM 17.50
The shaft-disk-belt arrangement shown is used to transmit 2.4 kW from Point
A to Point D. Knowing that the maximum allowable couples that can be
applied to shafts AB and CD are 25 N m
and 80 N m, respectively,
determine the required minimum speed of shaft AB.
A
B
AB
AB
PROBLEM 17.51
The drive belt on a vintage sander transmits ½ hp to
a pulley that has a diameter of d = 4 in. Knowing
that the pulley rotates at 1450 rpm, determine the
tension difference T1 – T2 between the tight and
slack sides of the belt.
12
PROBLEM 17.52
The rotor of an electric motor has a mass of 25 kg, and it is observed that 4.2 min is required for the rotor to
coast to rest from an angular velocity of 3600 rpm. Knowing that kinetic friction produces a couple of
magnitude 1.2 Nm, determine the centroidal radius of gyration for the rotor.
1
2
(1.2 N m)(252 s)
120 rad/s
0.80214 kg m 0.1791 m
I
PROBLEM 17.53
A small grinding wheel is attached to the shaft of an electric motor
which has a rated speed of 3600 rpm. When the power is turned off, the
unit coasts to rest in 70 s. The grinding wheel and rotor have a combined
weight of 6 lb and a combined radius of gyration of 2 in. Determine the
average magnitude of the couple due to kinetic friction in the bearings
of the motor.
12
32.2 ft/s
0.02788 lb ft
M
PROBLEM 17.54
A bolt located 50 mm from the center of an automobile wheel is tightened
by applying the couple shown for 0.10 s. Assuming that the wheel is free to
rotate and is initially at rest, determine the resulting angular velocity of the
wheel. The wheel has a mass of 19 kg and has a radius of gyration of
250 mm.
SOLUTION
222
PROBLEM 17.55
A uniform 144-lb cube is attached to a uniform 136-lb circular shaft as shown and
a couple M of constant magnitude is applied to the shaft when the system is at
rest. Knowing that r 4 in., L 12 in., and the angular velocity of the system is
960 rpm after 4 s, determine the magnitude of the couple M.
20.97999 32
I
PROBLEM 17.56
A uniform 75-kg cube is attached to a uniform 70-kg circular shaft as shown and a
couple M of constant magnitude 20 N m
is applied to the shaft. Knowing that
r 100 mm and L 300 mm., determine the time required for the angular
velocity of the system to increase from 1000 rpm to 2000 rpm.
SOLUTION
22
22 2
11
PROBLEM 17.57
A disk of constant thickness, initially at rest, is placed in contact with a belt
that moves with a constant velocity
v
. Denoting by
k
the coefficient of
kinetic friction between the disk and the belt, derive an expression for the
time required for the disk to reach a constant angular velocity.
SOLUTION
2
1
PROBLEM 17.58
Disk A, of weight 5 lb and radius 3 in.,r is at rest when it is placed in
contact with a belt which moves at a constant speed 50 ft/s.v Knowing that
0.20
k
between the disk and the belt, determine the time required for the
disk to reach a constant angular velocity.
SOLUTION
2
1
PROBLEM 17.59
A cylinder of radius r and weight W with an initial counterclockwise angular
velocity
0
is placed in the corner formed by the floor and a vertical wall.
Denoting by
k
the coefficient of kinetic friction between the cylinder and the
wall and the floor derive an expression for the time required for the cylinder to
come to rest.
()(1)
AB k k
2(1 )
kk
PROBLEM 17.60
Each of the double pulleys shown has a centroidal mass moment of inertia
of 0.25
2
kg m ,
an inner radius of 100 mm, and an outer radius of 150
mm. Neglecting bearing friction, determine (a) the velocity of the cylinder
3 s after the system is released from rest, (b) the tension in the cord
connecting the pulleys.
SOLUTION
0.100
Principle of impulse and momentum for pulley B.
Syst momenta
+
Syst Ext Imp
=
Syst momenta
(1)
PROBLEM 17.60 (Continued)
PROBLEM 17.61
Each of the gears A and B has a mass of 675 g and has a radius of
gyration of 40 mm, while gear C has a mass of 3.6 kg and has a
radius of gyration of 100 mm. Assume that kinetic friction in the
bearings of gears A, B, and C produces couples of constant magnitude
0.15 N m,
0.15 N m,
and 0.3 N m,
respectively. Knowing that the
initial angular velocity of gear C is 2000 rpm, determine the time
required for the system to come to rest.
0.06
A
Gear A:
1
S
y
st Momenta 12
Syst Ext Imp
2
S
y
st Momenta
PROBLEM 17.61 (Continued)
Gear C:
1
S
y
st Momenta 12
Syst Ext Imp
2
S
y
st Momenta
Solving Equations (3) and (4) simultaneously,
PROBLEM 17.62
Disk B has an initial angular velocity
0
when it is brought into contact
with disk A which is at rest. Show that the final angular velocity of disk B
depends only on
0
and the ratio of the masses
A
m
and
B
m
of the two
disks.
1
B
m
PROBLEM 17.63
The 7.5-lb disk A has a radius
6
A
r
in. and is initially at rest. The
10-lb disk B has a radius
8
B
r
in. and an angular velocity
0
of 900
rpm when it is brought into contact with disk A. Neglecting friction in
the bearings, determine (a) the final angular velocity of each disk,
(b) the total impulse of the friction force exerted on disk A.
PROBLEM 17.63 (Continued)
PROBLEM 17.64
A tape moves over the two drums shown. Drum A weighs 1.4 lb and has
a radius of gyration of 0.75 in., while drum B weighs 3.5 lb and has a
radius of gyration of 1.25 in. In the lower portion of the tape the tension
is constant and equal to
0.75
A
T
lb. Knowing that the tape is initially at
rest, determine (a) the required constant tension T
B
if the velocity of the
tape is to be
10v
ft/s after 0.24 s, (b) the corresponding tension in the
portion of tape between the drums.
SOLUTION
Kinematics. Drums A and B rotate about fixed axes. Let v be the tape velocity in ft/s.
0.9
(8)(10) 80 rad/s
B
Drum A.
1
Syst. Momenta
12
Syst.Ext.Imp.
2
Syst. Momenta
