978-0073380308 Chapter 8 Solution Manual Part 16

subject Type Homework Help
subject Pages 9
subject Words 3610
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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Problem 8.90
A uniform disk
W
of radius
RWD7mm
and mass
mWD0:15 kg
is
connected to point
O
via the rotating arm
OC
. Disk
W
also rolls without
slip over the stationary cylinder
S
of radius
RSD15 mm
. Assuming that
!WD25 rad=s
, determine the angular momentum of
W
about its own
center of mass C, as well as about point O.
Solution
Recalling that in the component system shown
O
kDOurOu
, the angular
momentum of the the wheel Wabout its own mass center is
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permission of McGraw-Hill, is prohibited.
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Dynamics 2e 1809
Problem 8.91
A rotor
B
with center of mass
G
, weight
WD3000 lb
, and radius of gyration
kGD15 ft
is spinning with an angular speed
!BD1200 rpm
when a braking
system is applied to it, providing a time-dependent torque
MDM0.1 Cct/
,
with
M0D3000 ftlb
and
cD0:01 s1
. If
G
is also the geometric center of
the rotor and is a fixed point, determine the time
ts
that it takes to stop the rotor.
Photo credit: NASA
Solution
We use subscripts
1
and
2
to denote the time at which the braking moment
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permission of McGraw-Hill, is prohibited.
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Problem 8.92
The uniform bar
AB
has length
LD4:5 ft
and weight
WAB D14 lb
. At the
instant shown,
D67ı
and
vAD5:8 ft=s
. Determine the magnitude of the
linear momentum of
AB
, as well as the angular momentum of
AB
about its mass
center Gat the instant shown.
Solution
The linear momentum of the bar is
EpAB DmAB EvG
where
G
is the mass
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permission of McGraw-Hill, is prohibited.
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Dynamics 2e 1811
Problem 8.93
A uniform pipe section
A
of radius
r
, mass center
G
, and mass
m
is gently placed
(i.e., with zero velocity) on a conveyor belt moving with a constant speed
v0
to the right. Friction
between the belt and pipe causes the pipe to move to the right and eventually to roll without slip. If
k
is
the coefficient of kinetic friction between the pipe and the conveyor belt, find an expression for
tr
, the time
it takes for
A
to start rolling without slip. Hint: Using the methods of Chapter 7, we can show that the
force between the pipe section and the belt is constant.
Solution
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permission of McGraw-Hill, is prohibited.
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Computation. Substituting Eqs. (3)–(6) into Eqs. (1) and (2), we have
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
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Dynamics 2e 1813
Problem 8.94
An automobile wheel test rig consists of a uniform disk
A
, of mass
mAD5000 kg
and radius
rAD1:5
m, that can rotate freely about
its fixed center
C
and over which the wheel of an automobile is
made to roll. A wheel
B
, whose center and center of mass coincide
at D, is mounted on a shaft (not shown) that holds Dfixed while
it allows the wheel to rotate about
D
. The wheel has diameter
dD0:62
m, mass
mBD21:5 kg
, and mass moment of inertia
about its mass center
IDD44 kgm2
. Both
A
and
B
are initially
at rest when
B
is subject to a constant torque
M
that causes
B
to
roll without slip on A.
If
MD1500 Nm
, use the angular impulse-momentum prin-
ciple to determine how long it takes to reach conditions simulating
a car speed of 100 km=h.
Solution
We model the wheel and the disk as rigid bodies in fixed axis ro-
tations about
D
and
C
, respectively. We assume that wheel
B
is
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Force Laws. All forces are accounted for on the FBD.
Kinematic Equations.
Since the system starts from rest, we have
!A1 D0
and
!B1 D0
. Also, in order to
simulate a car moving at a speed
vs
, the speed of point
D
relative to the point on the wheel in contact with
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf8
Dynamics 2e 1815
Problem 8.95
An automobile wheel test rig consists of a uniform disk
A
, of mass
mAD5000 kg
and radius
rAD1:5
m, that can rotate freely about
its fixed center
C
and over which the wheel of an automobile is
made to roll. A wheel
B
, whose center and center of mass coincide
at D, is mounted on a shaft (not shown) that holds Dfixed while
it allows the wheel to rotate about
D
. The wheel has diameter
dD0:62
m, mass
mBD21:5 kg
, and mass moment of inertia
about its mass center
IDD44 kgm2
. Both
A
and
B
are initially
at rest when
B
is subject to a constant torque
M
that causes
B
to
roll without slip on A.
Use the angular impulse-momentum principle and determine
M
if it takes 15 seconds to achieve conditions simulating a car
speed of 60 km=h.
t1
where
ID
is the mass moment of inertia of
B
about
D
, and where
E!BD!BO
k
is the angular velocity of
B
. Choosing the fixed
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pf9
Force Laws. All forces are accounted for on the FBD.
Kinematic Equations.
Since the system starts from rest, we have
!A1 D0
and
!B1 D0
. Also, in order to
simulate a car moving at a speed
vs
, the speed of point
D
relative to the point on the wheel in contact with
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
page-pfa
Dynamics 2e 1817
Problem 8.96
A spool of mass
msD150 kg
and inner and outer radii
D0:8
m
and
RD1:2
m, respectively, is connected to a counterweight
A
of
mass
mAD50 kg
by a pulley system whose cord, at one end, is
wound around the inner hub of the spool. The center
G
and the
center of mass of the spool coincide, and the radius of gyration of
the spool is
kGD1
m. The system is at rest when the counterweight
is released, causing the spool to move to the right. The spool rolls
without slip, and the cord unwinds from the spool without slip.
Neglecting the inertia of the pulley system, use the impulse-
momentum principles to determine the angular speed of the spool
3
s
after release.
Solution

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