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Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1709
Problem 8.36
A
400 lb
uniform disk with center
G
and radius
rD3ft
is connected
by a pulley system to a counterweight
A
weighing
75 lb
. The system
is initially at rest when
A
is allowed to drop, thus causing the disk to
roll without slipping to the right.
Neglecting the inertia of the pulley system, determine the speed of
Gafter Ahas dropped 2ft.
Solution
Referring to the figure at the right, we consider a
FBD
of the system
Computation. Substituting Eqs. (2)–(4) and Eqs. (6) into Eq. (1), we have
Agh
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1711
Problem 8.37
A
400 lb
uniform disk with center
G
and radius
rD3ft
is connected
by a pulley system to a counterweight
A
weighing
75 lb
. The system
is initially at rest when
A
is allowed to drop, thus causing the disk to
roll without slipping to the right.
Neglect the inertia of pulley
B
and the cord, but model pulley
C
as a uniform disk with radius
rCD0:8 ft
and weight
WCD50 lb
.
Assuming the cord does not slip relative to pulley
C
, determine the
speed of Gafter Ahas dropped 2ft.
Solution
Kinematic Equations. Letting Ldenote the length of the cord, we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1713
Problem 8.38
In a contraption built by a fraternity, a person sits at the center of
a swinging platform with mass
mD400 kg
and length
LD4
m
suspended by two identical arms of length HD3m.
Neglecting the mass of the arms and of the person, neglecting
friction, and assuming that the platform is released from rest when
✓D180ı
, compute the speed of the person as a function of
✓
for
0ı✓180ı. In addition, find the speed of the person for ✓D0ı.
Solution
1714 Solutions Manual
In a contraption built by a fraternity, a person sits at the center of
a swinging platform with mass
mD400 kg
and length
LD4
m
suspended by two identical arms of length HD3m.
Neglecting the mass of the person, neglecting friction, letting the
mass of each arm be
mAD150 kg
, and assuming that the platform is
released from rest when
✓D180ı
, compute the speed of the person
as a function of
✓
for
0ı✓180ı
. In addition, find the speed of
the person for ✓D0ı.
Solution
Dynamics 2e 1715
Computation. Substituting Eqs. (2)–(5) into Eq. (1), we have
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permission of McGraw-Hill, is prohibited.
Problem 8.40
The weights of the uniform thin pin-connected bars
AB
,BC, and CD are
WAB D4lb
,
WBC D6:5 lb
, and
WCD D10 lb
, respectively. Letting
D47ı
,
RD2ft
,
LD3:5 ft
, and
HD4:5 ft
, and knowing that
bar
AB
rotates at an angular velocity
!AB D4rad=s
, compute the kinetic energy
T
of the system at the
instant shown.
Solution
The kinetic energy of the system is the sum of the kinetic energies of each individual component, i.e.,
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1717
where we have used the following numerical data:
!AB D4rad=s
,
RD2ft
,
LD3:5 ft
, and
D47ı
. Then,
using the first of Eqs. (10), we have that the velocity of Gis
cos
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permission of McGraw-Hill, is prohibited.
