Problem 8.17
A door
AB
weighing
80 lb
is pinned at
A
and swings in the horizontal
plane. The spring
CD
has stiffness
k
and is unstretched when
✓D0ı
. Let
LD1:5 ft and hD0:5 ft.
If the door is released from rest when
✓D45ı
and
kD50 lb=ft
,
determine the speed of Bwhen ✓D0.
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Dynamics 2e 1679
Problem 8.18
A uniform thin bar
AB
of length
LD4ft
is released from rest at an angle
✓D✓1
. As
the bar slides, the ends
A
and
B
maintain contact with the surfaces on which they slide.
Neglecting friction and knowing that the end
A
has a speed of
18 ft=s
right before hitting
the floor, determine ✓1.
Solution
We model the bar as a thin rigid body. We assume that the bar is
1680 Solutions Manual
A uniform thin bar
AB
of length
LD3ft
is released from rest at an angle
✓D30ı
. As the bar slides, the ends
A
and
B
maintain contact with the surfaces
on which they slide. The inclination of the wall is
D50ı
. Neglecting friction,
determine the angular speed of the bar right before the end Ahits the floor.
Solution
We model the bar as a thin rigid body. We assume that the bar is
subject only to its own weight
mg
, which is a conservative force,
Dynamics 2e 1681
Using the above result, we can then determine the velocity of the mass center in ¡as follows:
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permission of McGraw-Hill, is prohibited.
Problem 8.20
The disk
D
, which has mass
m
, center of mass
G
, and radius of
gyration
kG
, is at rest on a flat horizontal surface when the constant
moment
M
is applied to it. The disk is attached at its center to a
vertical wall by a linear elastic spring of constant
k
. The spring is
unstretched when the system is at rest. Assuming that the disk rolls
without slipping and that it has not yet come to a stop, determine an
expression for the angular velocity of the disk after its center
G
has
moved a distance
d
. After doing so, determine the distance
ds
that
the disk moves before it comes to a stop.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1683
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permission of McGraw-Hill, is prohibited.
1684 Solutions Manual
An automobile wheel test rig consists of a uniform disk
A
, of mass
mAD
5000 kg
and radius
rAD1:5
m, that can rotate freely about its fixed center
C
and over which the wheel
B
of an automobile is made to roll. The wheel
B
, with center and center of mass at
D
, is mounted on a shaft (not shown)
that holds
D
fixed while allowing 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 Mthat causes Bto roll without slip over A.
If
MD1500 Nm
, determine the number of revolutions of
B
needed to
reach conditions simulating a car speed of 100 km=h.
Solution
We consider the system consisting of
A
and
B
modeled as rigid
bodies in fixed axis rotations about
C
and
D
, respectively. We
Dynamics 2e 1685
Kinematic Equations.
The system starts from rest. Also, denoting by
vs
the speed of the intended
simulation, due to the fact that
A
(with radius equal to
rA
) and
B
(with diameter equal to
d
) are in fixed
axis rotations about their respective centers, we have that
A
and
B
will eventually rotate with angular speeds
vs=r
Aand 2vs=d , respectively. So, summarizing,
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permission of McGraw-Hill, is prohibited.
Problem 8.22
An automobile wheel test rig consists of a uniform disk
A
, of mass
mAD
5000 kg
and radius
rAD1:5
m, that can rotate freely about its fixed center
C
and over which the wheel
B
of an automobile is made to roll. The wheel
B
, with center and center of mass at
D
, is mounted on a shaft (not shown)
that holds
D
fixed while allowing 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 Mthat causes Bto roll without slip over A.
Determine
M
if it takes
100
revolutions of the wheel
B
to achieve condi-
tions simulating a car speed of 60 km=h.
1and 2to denote quantities at ¿and ¡, respectively.
Balance Principles.
Applying the work-energy principle, we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1687
Kinematic Equations.
The system starts from rest. Also, denoting by
vs
the speed of the intended
simulation, due to the fact that
A
(with radius equal to
rA
) and
B
(with diameter equal to
d
) are in fixed
axis rotations about their respective centers, we have that
A
and
B
will eventually rotate with angular speeds
vs=r
Aand 2vs=d , respectively. So, summarizing,
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permission of McGraw-Hill, is prohibited.