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PROBLEM 16.118
The 10-lb-uniform rod AB has a total length 2L = 2 ft and is
attached to collars of negligible mass that slide without friction
along fixed rods. If rod AB is released from rest when
30 ,
θ
= °
determine immediately after release (a) the angular acceleration of
the rod, (b) the reaction at A.
SOLUTION
2
10 lb 0.3106 slugs
32.2 ft/s
W
mg
= = =
1 ftL=
From P16.117
22
2
1
3
32.2 ft/s sin 30 27.600 rad/s
1.0 ft sin 30
a
°
= =
+°
or
2
27.6 rad/s
a
=
( )
( )
2
2
0.3106 slugs 32.2 ft/s
5.714 lbs
1 3sin 30
A= =
+°
or
5.714 lb=A
PROBLEM 16.119
A 40-lb ladder rests against a wall when the bottom begins to slide out. The
ladder is 30 ft long and the coefficient of kinetic friction between the ladder
and all surfaces is 0.2. For θ = 40°, determine (a) the angular acceleration of
the ladder, (b) the forces at A and B.
A
( )
( )
//
(4)
GA G A
A
A
a cd
ad c
a
aa
= ×+
=−+
i+ k i j
i j
AB
( )
( )
//
22
2 2 (5)
AB AB
AB
AB
aa cd
a d ac
a
aa
= + ×− −
= +−
i jk i j
i i j
PROBLEM 16.119 (Continued)
Solving the i components of (5): (6)
Substitute into (6)→(5): (7)
Substitute into (7)→(1): (8)
Substitute into (10), (11)→(3):
(a) Substitute in known values:
2
A
ad
a
=
dc
aa
= +a ij
B kA
N N md
µa
= −
2
1
Bk
k
µ
+
kk
mcg d cg d
a µa a µa
++ ++
( ) ( ) ( ) ( )
22
11
kk
kk
k kk
kk
mcd cd
I d c c dm d
aµµ
µ µµ
µµ
=
++
− − −+ −
++
2
-0.510 rad/s
a
=
A
6.24 lb.
kA
N
µ
=
B
2.70 lb.
kB
N
µ
=
B
PROBLEM 16.120
A beam AB of length L and mass m is supported by two cables as shown. If
cable BD breaks, determine at that instant the tension in the remaining cable as
a function of its initial angular orientation
θ
.
1 3sin
θ
PROBLEM 16.121
End A of the 6-kg uniform rod AB rests on the inclined surface, while end B is
attached to a collar of negligible mass which can slide along the vertical rod
shown. Knowing that the rod is released from rest when
θ
= 35° and neglecting the
effect of friction, determine immediately after release (a) the angular acceleration
of the rod, (b) the reaction at B.
SOLUTION
sin 60 sin 65 sin 65
°° °
PROBLEM 16.121 (Continued)
PROBLEM 16.122
End A of the 6-kg uniform rod AB rests on the inclined surface, while end B is
attached to a collar of negligible mass which can slide along the vertical rod
shown. When the rod is at rest a vertical force P is applied at B, causing end B of
the rod to start moving upward with an acceleration of 4 m/s2. Knowing that
θ
= 35°, determine the force P.
SOLUTION
2
sin 60 sin 65 sin 65
°° °
PROBLEM 16.122 (Continued)
PROBLEM 16.123
End A of the 8-kg uniform rod AB is attached to a collar that can
slide without friction on a vertical rod. End B of the rod is
attached to a vertical cable BC. If the rod is released from rest in
the position shown, determine immediately after release (a) the
angular acceleration of the rod, (b) the reaction at A.
23
2
L
PROBLEM 16.123 (Continued)
eff
( ) : sin
2
xx x
L
F F A ma m
aθ
Σ=Σ = =
3cos sin
Lg
PROBLEM 16.124
The 4-kg uniform rod ABD is attached to the crank BC and is fitted with
a small wheel that can roll without friction along a vertical slot. Knowing
that at the instant shown crank BC rotates with an angular velocity of 6
rad/s clockwise and an angular acceleration of 15 rad/s2
counterclockwise, determine the reaction at A.
0.1 mBC =
22
Bt
2
Bt
2 22
( ) ( ) (0.1 m)(6 rad/s) 3.6 m/s
Bn
a BC
ω
= = =
2
( ) 3.6 m/s
Bn
=a
11
0.1 m
BC
−−
PROBLEM 16.125
The 3-lb uniform rod BD is connected to crank AB and to a collar of
negligible weight. A couple (not shown) is applied to crank AB causing it to
rotate with an angular velocity of 12 rad/s counterclockwise and an angular
acceleration of 80 rad/s2 clockwise at the instant shown. Neglecting the effect
of friction, determine the reaction at D.
12
B AB
3 ft/s
0.5 ft
B
BD
v
BC
= =
ω
Accelerations:
PROBLEM 16.125 (Continued)
Translation with B and rotation about D = Planar motion
/D B DB
= +aaa
D
a
= 20 + 36
( )
/DB n
a+
( )
/DB t
a+
(1)
2
22
10 6 30 ft/s
PROBLEM 16.125 (Continued)
2
1 3 10 0.17361
PROBLEM 16.126
The 3-lb uniform rod BD is connected to crank AB and to a collar of
negligible weight. A couple (not shown) is applied to crank AB causing it to
rotate. At the instant shown, crank AB has an angular velocity of 12 rad/s and
an angular acceleration of 80 rad/s2, both counterclockwise. Neglecting the
effect of friction, determine the reaction at D.
2
BD
2
8.00 rad/s
BD
a
=
/is directed
DB t
2
8.00 rad/s
BD
=a
//
1
2
G B GB B DB
==+=+aa a a a a
130
2
1 10 8.00
2 12
PROBLEM 16.126 (Continued)
( ) ( )
2
43
20 15 3.333 10.00 ft/s
a=−+ =+
PROBLEM 16.127
The test rig shown was developed to perform fatigue testing
on fitness trampolines. A motor drives the 200-mm radius
flywheel AB, which is pinned at its center point, in a
counterclockwise direction with a constant angular velocity of
120 rpm. The flywheel is attached to slider CD by the 400-mm
connecting rod BC. The mass of the connecting rod BC is 5 kg
and the mass of the link CD and foot is 2 kg. At the instant
when
θ
= 0° and the foot is just above the trampoline,
determine the force exerted by pin C on rod BC.
SOLUTION
2
π
PROBLEM 16.127 (Continued)
xx
PROBLEM 16.127 (Continued)
2
2
16
π
PROBLEM 16.128
Solve Prob. 16.127 for
θ
= 90°.
PROBLEM 16.127 The test rig shown was developed to
perform fatigue testing on fitness trampolines. A motor drives
the 200-mm radius flywheel AB, which is pinned at its center
point, in a counterclockwise direction with a constant angular
velocity of 120 rpm. The flywheel is attached to slider CD by
the 400-mm connecting rod BC. The mass of the connecting rod
BC is 5 kg and the mass of the link CD and foot is 2 kg. At the
instant when
θ
= 0° and the foot is just above the trampoline,
determine the force exerted by pin C on rod BC.
SOLUTION
2
π
xx
