Problem 7.74
The uniform thin rod
AB
couples the slider
A
, which moves along a
frictionless guide, to the wheel
B
, which rolls without slip over a horizon-
tal surface. While not required, the use of computer algebra software is
recommended for Probs. 7.74–7.76.
Assuming that
A
has negligible mass,
B
is a uniform disk of mass
mB
, the mass of
AB
is
mAB
, and the system is released from rest at the
angle
, determine, immediately after release, the angular acceleration
of the rod
AB
, the acceleration of the center of the wheel at
B
, and the
angular acceleration of the wheel.
Solution
The FBD of each element of the system is shown
on the right. Since the slider
A
is assumed to have
negligible mass, its weight has been neglected.
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Dynamics 2e 1557
where
˛w
is the angular acceleration of the wheel and its mass moment of inertia with respect to its center at
Bis
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1558 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1559
Problem 7.75
The uniform thin rod
AB
couples the slider
A
, which moves along a
frictionless guide, to the wheel
B
, which rolls without slip over a horizon-
tal surface. While not required, the use of computer algebra software is
recommended for Probs. 7.74–7.76.
Assuming that
AB
has negligible mass, the mass of
A
is
mA
,
B
is
a uniform disk of mass
mB
, and the system is released from rest at the
angle
, determine, immediately after release, the angular acceleration
of the rod
AB
, the acceleration of the center of the wheel at
B
, and the
angular acceleration of the wheel.
Solution
The FBD of each element of the system is shown
on the right. Since the bar
AB
is assumed to have
negligible mass, its weight has been neglected.
Balance Principles.
Based on these FBDs, the
Newton-Euler equations for the slider Aare
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permission of McGraw-Hill, is prohibited.
Force Laws. All forces have been accounted for on the FBD.
Kinematic Equations.
Observing that
A
is constrained to move vertically (
aAx D0
), that
B
is constrained
to move horizontally (aBy D0), and that the system is released from rest (all velocities are zero), we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1561
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.
Problem 7.76
The uniform thin rod
AB
couples the slider
A
, which moves along a
frictionless guide, to the wheel
B
, which rolls without slip over a horizon-
tal surface. While not required, the use of computer algebra software is
recommended for Probs. 7.74–7.76.
Assuming that the mass of
A
is
mA
,
B
is a uniform disk of mass
mB
,
the mass of
AB
is
mAB
, and that the system is released from rest at the
angle
, determine, immediately after release, the angular acceleration
of the rod
AB
, the acceleration of the center of the wheel at
B
, and the
angular acceleration of the wheel.
2sin CAyByL
2cos DIG˛AB :(5)
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.
Dynamics 2e 1563
where
˛w
is the angular acceleration of the wheel and its mass moment of inertia with respect to its center at
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.
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.
Dynamics 2e 1565
Problem 7.77
A spool of mass
mD220 kg
, inner and outer radii
D1:75
m and
RD
2:25
m, respectively, and radius of gyration
kGD1:9
m, is being lowered
down an incline with
D29ı
. There is no slip between the spool and the
cable as the spool moves down the incline. If the static and kinetic friction
coefficients between the incline and the spool are
sD0:4
and
kD0:35
,
respectively, determine the acceleration of
G
, the angular acceleration of
the spool, and the tension in the cable if the system is released from rest.
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permission of McGraw-Hill, is prohibited.