978-0073380308 Chapter 7 Solution Manual Part 20

subject Type Homework Help
subject Pages 9
subject Words 3651
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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page-pf1
Problem 7.97
An SUV is pushing a large drum to the right with force
P
, using
its front bumper. The drum has mass
m
and radius of gyration
kG
. The static and kinetic friction coefficients between the drum
and the ground and between the drum and the SUV are
s
and
k
,
respectively.
(a)
Assuming that there is no slipping between the drum and
the ground, determine the acceleration of the drum and the
minimum value of sthat is consistent with this motion.
(b)
Determine the acceleration of point
G
and the angular accel-
eration of the drum if
P
is increased so that the drum slips
relative to the ground.
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permission of McGraw-Hill, is prohibited.
page-pf2
Dynamics 2e 1607
Computation.
Substituting Eqs. (4), (5), and (7) into the Newton-Euler equations yields the following
Part (b)
When there is slipping between the ground and the drum, then we must enforce the following kinetic friction
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-pf3
Problem 7.98
The disk
A
rolls without slipping on a horizontal surface. End
B
of
bar
BC
is pinned to the edge of the disk
A
, and end
C
of the bar
BC
can slide freely along the horizontal surface. In addition, bar
BC
is pushed by the force
PDmg
at its left end. The mass of
bar
BC
is
mBC
, and the mass of the disk
A
is
mA
. The system is
initially at rest.
Determine the acceleration of the center of the disk
A
and the
angular acceleration of bar
BC
immediately after the force
P
is
applied if mADmBC Dm.
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-pf4
Dynamics 2e 1609
Kinematic Equations. Since the disk rolls without slip on a horizontal surface, we have
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permission of McGraw-Hill, is prohibited.
page-pf5
Problem 7.99
The disk
A
rolls without slipping on a horizontal surface. End
B
of
bar
BC
is pinned to the edge of the disk
A
, and end
C
of the bar
BC
can slide freely along the horizontal surface. In addition, bar
BC
is pushed by the force
PDmg
at its left end. The mass of
bar
BC
is
mBC
, and the mass of the disk
A
is
mA
. The system is
initially at rest.
Determine the acceleration of the center of disk
A
and the angu-
lar acceleration of bar
BC
immediately after force
P
is applied if
mBC Dmand the mass of the disk mAis negligible.
2ByCNC2
3RDIG˛b;(6)
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-pf6
Dynamics 2e 1611
where we have used the fact that, at the instant of release, all velocities are zero. Relating the acceleration of
point Cto that of B, we obtain
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-pf7
Problem 7.100
The crank
AB
in the slider-crank mechanism is rotating counterclockwise with constant angular velocity
!AB
. The crankshaft radius is
R
, the length of the connecting rod
BC
is
L
, and the distance from the
mass center of the connecting rod
D
to the end of the crank at
B
is
d
. The mass of the connecting rod is
mD, the mass moment of inertia of the connecting rod is ID, and the mass of the piston is mC.
(a)
Using the component system shown, determine the
x
and
y
components of the forces on the
connecting rod at Band Cas functions of the crank angle .
(b)
Using
!AB D5700 rpm
,
RD48:5 mm
,
LD141 mm
,
dD36:4 mm
,
mDD0:439 kg
,
IDD
0:00144 kgm2
, and
mCD0:434 kg
, plot each of the four force components, the magnitude of the
forces at
B
and
C
, and the moment acting on the connecting rod about point
D
, all as a function of
, for one full rotation of the crank.
Hint: The kinematics of this problem have been considered in Example 6.10 on p. 480.
Solution
Part (a)
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 1613
R2cos23
R2cos2
Computation.
Now that we have the accelerations of
C
,
D
and the angular acceleration of
BC
in terms of
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permission of McGraw-Hill, is prohibited.
page-pf9
Substituting Eqs. (6), (7), (9), and (11) into Eqs. (12)–(15), after simplification, we have
AB cos
<
AB "RL2R2cos2
.L2R2cos /3=2 sin Rsin2
Part (b)
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
1#%L
R&2
%% L
R&2#Cos!Θ"2&
3
2
Sin!Θ"2
%L
R&2#Cos!Θ"2
%L
R&2#Cos!Θ"2
1#%L
Sin!Θ"2
The Mathematica code defining the angular acceleration, the problem’s parameters, and the plotting com-
mands is as follows:
This solutions manual, in any print or electronic form, remains the property of McGraw-Hill, Inc. It may be used and/or possessed only by permission
July 6, 2012

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