978-0073380308 Chapter 8 Solution Manual Part 14

subject Type Homework Help
subject Pages 9
subject Words 2917
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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Problem 8.77
The rear-wheel-drive car can go from rest to
60 mph
in
tD8
s.
Assume that the wheels are all identical and that their geometric
centers coincide with their mass centers. Let
Mrear
be the average
moment applied to one of the rear wheels during
t
and computed
relative to the wheel’s center. Finally, let
Mfront
be the average mo-
ment applied to one of the front wheels during
t
and computed
relative to the wheel’s center. Modeling the wheels as rigid bod-
ies, determine which of the following statements is true and why:
(a)
ˇˇMrearˇˇ<ˇˇMfrontˇˇ
, (b)
ˇˇMrearˇˇDˇˇMfrontˇˇ
, (c)
ˇˇMrearˇˇ>
ˇˇMfrontˇˇ.
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 1789
Problem 8.78
The rear-wheel-drive car can go from rest to
60 mph
in
tD8
s.
Assume that its wheels are identical, with their geometric centers
coinciding with their mass centers. Let
Favg
be the average friction
force acting on the system during
t
due to contact with the
ground. Modeling the car and the wheels as rigid bodies, does the
value of
Favg
change whether or not we account for the rotational
inertia of the wheels? Why?
Solution
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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Problem 8.79
A uniform disk of mass
m
and radius
R
rolls to the right without slip, such
that the speed of the center of mass is
vG
. Provide an expression for the linear
momentum of the disk in terms of the given quantities. In addition, provide
an expression for the angular momentum of the disk relative to
O
, the point of
contact with the ground. Express your answers using the component system
shown.
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 1791
Problem 8.80
At the instant shown, the eccentric wheel with center at
O
and center of mass
at
G
is rotating counterclockwise without slip with an angular speed
!wD
10 rad=s
. The weight of the wheel is
WD90 lb
. In addition, let
RD2ft
,
hD1ft
, and the radius of gyration
kGD1:45 ft
. At the instant shown,
determine the linear momentum of the disk and the angular momentum about
C
, the point of contact with the ground. Express your answers in the component
system shown.
Solution
Let
EvG
and
Epw
denote the velocity of
G
and the linear momentum of the wheel, respectively. The linear
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Problem 8.81
The top of the Space Needle in Seattle, Washington, hosts a revolving
restaurant that goes through one full revolution every
47 min
under
the action of a motor with a power output of
1:5 hp
. The portion
of the restaurant that rotates is a ring-shaped turntable with internal
and external radii
riD33:3 ft
and
roD47:3 ft
, respectively, and
approximate weight
WD125 tons
(
1ton D2000 lb
). Use the given
values of power output and angular speed to estimate the torque
M
that the engine provides. Then, assuming that the motor can provide
a constant torque equal to
M;
neglecting all friction, and modeling
the turntable as a uniform body, determine the time
ts
that it takes
to spin up the revolving restaurant from rest to its working angular
speed.
Solution
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 1793
Computation. Substituting Eq. (2), the first of Eqs. (3), and Eqs. (4) into Eq. (1), 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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Problem 8.82
A rotor, spinning freely about the fixed point
O
, consists of a thin uniform bar
AB
that functions as a hub
and two identical blades pinned at
A
and
B
, respectively. The dimensions of the system are:
dD0:5
m,
`D5
m, and
wD0:3
m. The bar
AB
has a mass
mAB D30 kg
, and each of the blades has a mass
mbD20 kg
. Each blade can be modeled as a uniform thin plate. The angular speed is
!rD100 rpm
when
the angle
is equal to
90ı
. At some point, an internal mechanism causes the blades to change orientation
relative to
AB
in such a way that
becomes constant and equal to
180ı
. Neglecting aerodynamic forces
and friction at the bearings at O, determine the angular speed of the rotor after D180ı.
Solution
Referring to the figure below, since the rotor is spinning freely in the horizontal plane, the system is not acted
upon by any force or moment that would promote or hinder its rotation. Hence, the system can be considered
isolated. This implies that the angular momentum of the system about any point is conserved. We denote
Force Laws. All forces are accounted for on the FBD.
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 1795
Kinematic Equations. The initial angular velocity is known:
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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1796 Solutions Manual
A uniform disk of mass
mD20 kg
and radius
RD0:75
m is being pulled
to the left with a constant horizontal force
P
by the cord wrapped around it.
Assume that the disk starts from rest and that it rolls without slip.
If
PD30
N, apply the impulse-momentum principles to determine the
angular speed of the disk after 4s.
Solution
We model the disk as a rigid body subject only to its own weight
mg
, the force
P
,
and the components
F
and
N
of the contact force between the disk and the ground.
We denote by
t1D0
the initial time and by
t2D4
s, the time at which the answer
to the problem needs to be provided. We select
G
as the moment center for the
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Dynamics 2e 1797
Eliminating the time integral of Ffrom the above two equations, 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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