PROBLEM 16.50
A force P of magnitude 3 N is applied to a tape wrapped
around the body indicated. Knowing that the body rests
on a frictionless horizontal surface, determine the
acceleration of (a) Point A, (b) Point B.
A thin hoop of mass 2.4 kg.
SOLUTION
2
PROBLEM 16.51
A force P of magnitude 3 N is applied to a tape wrapped
around the body indicated. Knowing that the body rests
on a frictionless horizontal surface, determine the
acceleration of (a) Point A, (b) Point B.
A uniform disk of mass 2.4 kg.
PROBLEM 16.52
A 250–lb satellite has a radius of gyration of 24 in. with respect to the
y axis and is symmetrical with respect to the zx plane. Its orientation is
changed by firing four small rockets A, B, C, and D, each of which
produces a 4-lb thrust T directed as shown. Determine the angular
acceleration of the satellite and the acceleration of its mass center G
(a) when all four rockets are fired, (b) when all rockets except D are fired.
SOLUTION
12
PROBLEM 16.53
A rectangular plate of mass 5 kg is suspended from four
vertical wires, and a force P of magnitude 6 N is applied to
corner C as shown. Immediately after P is applied, determine
the acceleration of (a) the midpoint of edge BC, (b) corner B.
E
PROBLEM 16.53 (Continued)
(b)
/
2
2 22
(1.2 m/s ) (11.52 rad/s) [(0.2 m) +(0.15 m) ]
(1.2 m/s ) (2.304 m/s ) (1.728 m/s )
B BG
=+×
=+− ×
=++ +
aaαr
k ji k
kki
22
B
PROBLEM 16.54
A uniform semicircular plate of mass 6 kg is suspended from three
vertical wires at points A, B, and C, and a force P of magnitude 5 N
is applied to point B. Immediately after P is applied, determine the
acceleration of (a) the mass center of the plate, (b) point C.
x GG
2
or 0.833 m/s
G
a=i
( )
2
0.4
5 m 0.17273 kg m
G
MN
a
π
Σ= =
2
3.6856 rad/s
a
=
/C G CG
+
C
0.4
π
0.8333
C
=a
+
0.63641
2
2
or 0.1969 m/s
C
=a i
PROBLEM 16.55
A drum of 200-mm radius is attached to a disk of radius rA = 150 mm. The
disk and drum have a combined mass of 5 kg and a combined radius of
gyration of 120 mm and are suspended by two cords. Knowing that
TA = 35 N and TB = 25 N, determine the accelerations of points A and B on the
cords.
PROBLEM 16.56
A drum of 200-mm radius is attached to a disk of radius rA = 140 mm. The
disk and drum have a combined mass of 5 kg and are suspended by two cords.
Knowing that the acceleration of point B on the cord is zero, TA = 40 N, and
TB = 20 N, determine the combined radius of gyration of the disk and drum.
SOLUTION
0: 0.2
B
aa
a
= =
PROBLEM 16.57
The 12–lb uniform disk shown, of radius r = 3.2 in., rotates counterclockwise.
Its center C is constrained to move in a slot cut in the vertical member AB and
a 11–lb horizontal force P is applied at B to maintain contact at D between the
disk and the vertical wall. The disk moves downward under the influence of
gravity and the friction at D. Knowing that the coefficient of kinetic friction
between the disk and the wall is 0.12 and neglecting friction in the vertical
slot, determine (a) the angular acceleration of the disk, (b) the acceleration of
the center C of the disk.
PROBLEM 16.58
The steel roll shown has a mass of 1200 kg, a centroidal radius of
gyration of 150 mm, and is lifted by two cables looped around its
shaft. Knowing that for each cable
3100 N
A
T=
and TB
3300 N,=
determine (a) the angular acceleration of the roll, (b) the
acceleration of its mass center.
eff
G G BA
2( )
(2)(3300 3100)(0.050)
27
BA
T Tr
I
a
−
=
−
=
2
0.741 rad/s=a
(b) Acceleration of mass center.
1200
PROBLEM 16.59
The steel roll shown has a mass of 1200 kg, has a centriodal radius
of gyration of 150 mm, and is lifted by two cables looped around
its shaft. Knowing that at the instant shown the acceleration of the
roll is
2
150 mm/s
downward and that for each cable
3000 N,
A
T=
determine (a) the corresponding tension
,
B
T
(b) the angular
acceleration of the roll.
2 22
(1200)(0.150) 27 kg m
11
(0.100) 0.050 m
22
3000 N
A
I mk
rd
T
= = = ⋅
= = =
=
2
0.150 m/s=a
(a) Tension in cable B.
eff
( ):2 2
y y AB
F F T T mg maΣ=Σ + − =−
2
()
2
(1200)(9.81 0.150) 3000
2
BA
A
mg ma
TT
mg a T
−
= −
−
= −
−
= −
PROBLEM 16.60
A 15-ft beam weighing 500 lb is lowered by means of two
cables unwinding from overhead cranes. As the beam
approaches the ground, the crane operators apply brakes to slow
the unwinding motion. Knowing that the deceleration of cable A
is 20 ft/s2 and the deceleration of cable B is 2 ft/s2, determine
the tension in each cable.
2
1.2 rad/s=a
11
( ) (2 20)
22
AB
a aa= += +
2
11 ft/s=a
Kinetics:
2
2
2
2
1
12
1 500 (15 ft)
12 32.2 ft/s
291.15 lb ft s
I mL=
=
= ⋅⋅
B
B
PROBLEM 16.61
A 15-ft beam weighing 500 lb is lowered by means of two cables
unwinding from overhead cranes. As the beam approaches the
ground, the crane operators apply brakes to slow the unwinding
motion. Knowing that the deceleration of cable A is 20 ft/s2 and
the deceleration of cable B is
2
2 ft/s ,
determine the tension in each
cable.
SOLUTION
32.2
B
PROBLEM 16.62
Two uniform cylinders, each of weight W = 14 lb and radius r = 5 in.,
are connected by a belt as shown. If the system is released from rest,
determine (a) the angular acceleration of each cylinder, (b) the tension
in the portion of belt connecting the two cylinders, (c) the velocity of the
center of the cylinder A after it has moved through 3 ft.
SOLUTION
Kinematics
Let
AA
a=a
be the acceleration of the center of cylinder A,
AB AB
a=a
be acceleration of the cord between
the disks,
AA
a
=α
be the angular acceleration of disk A, and
BB
a
=α
be the angular acceleration of disk B.
eff
P P A AB A A A A
PROBLEM 16.62 (Continued)
Disk B:
eff
( ):
B B AB B B
M M rT I
a
Σ=Σ =
(6)
Add
2 Eq. (6)×
to Eq. (5) to eliminate TAB.
12
PROBLEM 16.62 (Continued)
(a) Angular accelerations.
2
32.2 ft/s 22.08 rad/s
2
0
22
0 (2)(9.20 ft/s)(3 ft) 55.2 ft /s
A A AA
=+=
7.43 ft/s
A
v=
7.43 ft/s
A
=v
PROBLEM 16.63
A beam AB of mass m and of uniform cross section is suspended
from two springs as shown. If spring 2 breaks, determine at that
instant (a) the angular acceleration of the beam, (b) the
acceleration of point A, (c) the acceleration of point B.
4
(c)
B=a
2
g+
0.75g
5
4
g
PROBLEM 16.64
A beam AB of mass m and of uniform cross section is suspended
from two springs as shown. If spring 2 breaks, determine at that
instant (a) the angular acceleration of the beam, (b) the
acceleration of point A, (c) the acceleration of point B.
3
B
PROBLEM 16.65
A uniform slender bar AB of mass m is suspended from two springs
as shown. If spring 2 breaks, determine at that instant (a) the angular
acceleration of the bar, (b) the acceleration of point A, (c) the
acceleration of point B.
1
eff
xx
x
0.866
x
g=a
: sin 30
F F W T ma= − °=
2
yg=a
PROBLEM 16.65 (Continued)
Accelerations of A and B
Bg=a
Translation with G + Rotation about
G