978-0073380308 Chapter 8 Solution Manual Part 8

subject Type Homework Help
subject Pages 9
subject Words 3830
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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1728 Solutions Manual
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
of the spool
is also the center of mass of the spool, 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. Assume that the
spool rolls without slip.
Neglecting the inertia of the pulley system, determine the angular
speed of the spool after the counterweight has dropped 0:5 m.
Solution
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Dynamics 2e 1729
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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1730 Solutions Manual
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
of the spool
is also the center of mass of the spool, 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. Assume that the
spool rolls without slip.
Assume that the inertia of the cord and of pulleys
B
and
D
can be
neglected, but model pulley
C
as a uniform disk of mass
mCD15 kg
and radius
rCD0:3
m. If the cord does not slip relative to pulley
C
,
determine the angular speed of the spool after Adrops 0:5 m.
Solution
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Dynamics 2e 1731
Kinematic Equations. Denoting by Lthe length of the cord, 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 8.48
The uniform slender bar
AB
has length
LD1:45 ft
and weight
WAB D20 lb
. Rollers
D
and
E
, which are pinned at
A
and
B
,
respectively, can be modeled as two identical uniform disks, each with
radius
rD1:5 in:
and weight
WrD0:35 lb
. Rollers
D
and
E
roll
without slip on the surface of a cylindrical bowl with center at
O
and
radius
RD1ft
. Determine the system’s kinetic energy when
G
(the
center of mass of bar AB) moves with a speed vD7ft=s.
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 1733
Problem 8.49
The Charpy impact test is one test that measures the resistance of a material
to fracture. In this test, the fracture toughness is assessed by measuring the
energy required to break a specimen of a given geometry. This is done by
releasing a heavy pendulum from rest at an angle
i
and then measuring
the maximum swing angle
f
reached by the pendulum after the specimen
is broken.
Consider a test rig in which the striker
S
(the pendulum’s bob) can
be modeled as a uniform disk of mass
mSD19:5 kg
and radius
rSD
150 mm
, and the arm can be modeled as a thin rod of mass
mAD2:5 kg
and length
LAD0:8
m. Neglecting friction and noting that the striker
and the arm are rigidly connected, determine the fracture energy (i.e.,
the kinetic energy lost in breaking the specimen) in an experiment where
iD158ıand
fD43ı.
Solution
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Computation. Substituting Eqs. (2)–(6) 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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Dynamics 2e 1735
Problem 8.50
The Charpy impact test is one test that measures the resistance of a material
to fracture. In this test, the fracture toughness is assessed by measuring the
energy required to break a specimen of a given geometry. This is done by
releasing a heavy pendulum from rest at an angle
i
and then measuring
the maximum swing angle
f
reached by the pendulum after the specimen
is broken.
Consider a test rig in which the striker
S
(the pendulum’s bob) can be
modeled as a uniform disk of weight
WSD40 lb
and radius
rSD6in:
,
if the striker impacts the specimen when the pendulum’s arm is vertical,
determine the speed of the point
Q
on the striker immediately before the
striker impacts with the specimen. Neglect friction, and observe that the
striker and the arm are rigidly connected.
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
Computation. Substituting Eqs. (2), and (4)–(5) into Eq. (1), we have
v2
Q2
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 1737
Problem 8.51
A crate, with weight
WD155 lb
and mass center
G
, is placed on
a slide and released from rest as shown. The lower part of the slide
is circular, with radius
RD6ft
. Model the crate as a uniform body
with
bD3:6 ft
and
hD2ft
. Take into account the gap between
the crate and the slide when the crate is in its lowest position, and
assume that when the crate is in its lowest position on the slide, the
crate’s center of mass is moving to the left with a speed
vGD12 ft=s
.
Determine the work done by friction on the crate as the crate moves
from the release point to the lowest point on the slide.
Solution
Referring to the
FBD
on the left in the figure below, we model the crate as a rigid body subject to its own

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