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Problem 18.112 A 2-kg box is subjected to a 40-N
horizontal force. Neglect friction.
(a) If the box remains on the floor, what is its accel-
eration?
(b) Determine the range of values of cfor which the
box will remain on the floor when the force is
applied.
40 N
BA
100 mm
c
100 mm
Solution:
Problem 18.113 The slender, 2-slug bar AB is 3 ft
long. It is pinned to the cart at Aand leans against it
at B.
(a) If the acceleration of the cart is a=20 ft/s2, what
normal force is exerted on the bar by the cart at B?
(b) What is the largest acceleration afor which the bar
will remain in contact with the surface at B?A
B
a
60°
546
Problem 18.114 To determine a 4.5-kg tire’s moment
of inertia, an engineer lets the tire roll down an inclined
surface. If it takes the tire 3.5 s to start from rest and
roll 3 m down the surface, what is the tire’s moment of
inertia about its center of mass?
330 mm
Problem 18.115 Pulley Aweighs 4 lb, IA=0.060
slug-ft2, and IB=0.014 slug-ft2. If the system is
released from rest, what distance does the 16-lb weight
fall in 0.5 s?
12 in
8 in
8 lb
16 lb
A
B
548
Problem 18.116 Model the excavator’s arm ABC as a
single rigid body. Its mass is 1200 kg, and the moment
of inertia about its center of mass is I=3600 kg-m2.If
point Ais stationary, the angular velocity of the arm is
zero, and the angular acceleration is 1.0 rad/s2counter-
clockwise, what force does the vertical hydraulic cylin-
der exert on the arm at B?
x
y
B
C
3.0 m
A
1.7 m 1.7 m
Solution: The distance from Ato the center of mass is
IA=I+d2m=28,270 kg-m2.
From the equation of angular motion: 1.7B−3.4mg =IAα.
Substitute α=1.0 rad/s2, to obtain B=40,170 N.
Problem 18.117 Model the excavator’s arm ABC as a
single rigid body. Its mass is 1200 kg, and the moment of
inertia about its center of mass is I=3600 kg-m2. The
angular velocity of the arm is 2 rad/s counterclockwise
and its angular acceleration is 1 rad/s2counterclockwise.
What are the components of the force exerted on the arm
at A?
Problem 18.118 To decrease the angle of elevation of
the stationary 200-kg ladder, the gears that raised it are
disengaged, and a fraction of a second later a second
set of gears that lower it are engaged. At the instant
the gears that raised the ladder are disengaged, what is
the ladder’s angular acceleration and what are the com-
ponents of force exerted on the ladder by its support
at O? The moment of inertia of the ladder about Ois
I0=14,000 kg-m2, and the coordinates of its center of
mass at the instant the gears are disengaged are x=3m,
y=4m.
y
x
O
550
Problem 18.119 The slender bars each weigh 4 lb and
are 10 in. long. The homogenous plate weighs 10 lb. If
the system is released from rest in the position shown,
what is the angular acceleration of the bars at that
instant?
45°
8 in
since ω=0 upon release.
The acceleration of the plate:
ijk
=10
12 sin θαi−10
12 cos θαj(ft/s2).
From which aPx =10
12 sin θα,aPy =−
10
12 cos θα.
Bx=4.42 lb, By=5.68 lb. α=30.17 rad/s2.
Problem 18.120 A slender bar of mass mis released
from rest in the position shown. The static and kinetic
friction coefficients of friction at the floor and the wall
have the same value µ. If the bar slips, what is its angu-
lar acceleration at the instant of release?
Solution: Choose a coordinate system with the origin at the inter-
section of wall and floor, with the xaxis parallel to the floor. Denote
the points of contact at wall and floor by P and N respectively, and
552
Problem 18.121 Each of the go-cart’s front wheels
weighs 5 lb and has a moment of inertia of 0.01 slug-ft2.
The two rear wheels and rear axle form a single rigid
body weighing 40 lb and having a moment of inertia of
0.1 slug-ft2. The total weight of the go-cart and driver
is 240 lb. (The location of the center of mass of the go-
cart and driver, not including the front wheels or the rear
wheels and rear axle, is shown.) If the engine exerts a
torque of 12 ft-lb on the rear axle, what is the go-cart’s
acceleration?
15 in
AB
6 in 4 in
Problem 18.122 Bar AB rotates with a constant angu-
lar velocity of 10 rad/s in the counterclockwise direc-
tion. The masses of the slender bars BC and CDE are
2 kg and 3.6 kg, respectively. The yaxis points upward.
Determine the components of the forces exerted on bar
BC by the pins at Band Cat the instant shown.
A
B
C
400 mm
10 rad/s D
700 mm
x
y
700 mm 400
mm
E
Solution: The velocity of point Bis
ij k
0.7−0.40
=−4i+0.4ωBCi+0.7ωBCj(m/s).
By
Bx
The acceleration of the center of mass of BC is
ijk
554
Problem 18.123 At the instant shown, the arms of the
robotic manipulator have the constant counterclockwise
angular velocities ωAB =−0.5 rad/s, ωBC =2 rad/s,
and ωCD =4 rad/s. The mass of arm CD is 10 kg, and
the center of mass is at its midpoint. At this instant, what
force and couple are exerted on arm CD at C?
x
D
C
y
B
30°
20°
A
250 mm
300 mm
250 mm
from which
Problem 18.124 Each bar is 1 m in length and has
a mass of 4 kg. The inclined surface is smooth. If the
system is released from rest in the position shown, what
are the angular accelerations of the bars at that instant?
A
B
45°
30°
O
the acceleration of Ato obtain the two equations:
(6)−Ax−Bsin β=maGABx ,
556
Problem 18.125 Each bar is 1 m in length and has
a mass of 4 kg. The inclined surface is smooth. If the
system is released from rest in the position shown, what
is the magnitude of the force exerted on bar OA by the
support at Oat that instant?
Problem 18.126 The fixed ring gear lies in the
horizontal plane. The hub and planet gears are bonded
together. The mass and moment of inertia of the
combined hub and planet gears are mHP =130 kg and
IHP =130 kg-m2. The moment of inertia of the sun gear
is Is=60 kg-m2. The mass of the connecting rod is
5 kg, and it can be modeled as a slender bar. If a 1 kN-
m counterclockwise couple is applied to the sun gear,
what is the resulting angular acceleration of the bonded
hub and planet gears?
240 mm
720 mm
340
mm
140
mm
Planet gear
Connecting
rod
Sun gear
Hub gear
Ring gear
Solution: The moment equation for the sun gear is
Problem 18.127 The system is stationary at the instant
shown. The net force exerted on the piston by the
exploding fuel-air mixture and friction is 5 kN to the
left. A clockwise couple M=200 N-m acts on the crank
AB. The moment of inertia of the crank about Ais
0.0003 kg-m2. The mass of the connecting rod BC is
0.36 kg, and its center of mass is 40 mm from Bon
the line from Bto C. The connecting rod’s moment
of inertia about its center of mass is 0.0004 kg-m2.
The mass of the piston is 4.6 kg. What is the piston’s
acceleration? (Neglect the gravitational forces on the
crank and connecting rod.)
40°
50 mm
A
M
B
C
125 mm
Solution: From the law of sines:
from which
558
Problem 18.128 If the crank AB in Problem 18.127
has a counterclockwise angular velocity of 2000 rpm at
the instant shown, what is the piston’s acceleration?
Solution: The angular velocity of AB is
