1688 Solutions Manual
An electric motor drawing
15 kW
and with an efficiency of
85
% lifts a
400 kg
crate
B
with a constant speed
vc
. Pulley
A
has radius
rpD15 cm
,
and the center of mass of
A
is also the center of
A
. The cord is inextensible
and does not slip relative to the pulley. Assume that the friction at the pulley
bearings results in a moment about the pulley’s center with magnitude
ˇj!pj
opposing the rotation of the pulley, where
ˇ
is a constant and
j!pj
is the
angular speed of the pulley. Hint: Review Example 4.16 on p. 300. Also
note that friction in the pulley bearings causes the tension in the cord to be
different on the two sides of the pulley.
Determine ˇif vcD3m=s.
Solution
rpD15 cm D15
100 m we can evaluate ˇto obtain
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permission of McGraw-Hill, is prohibited.
Problem 8.24
An electric motor drawing
15 kW
and with an efficiency of
85
% lifts a
400 kg
crate
B
with a constant speed
vc
. Pulley
A
has radius
rpD15 cm
,
and the center of mass of
A
is also the center of
A
. The cord is inextensible
and does not slip relative to the pulley. Assume that the friction at the pulley
bearings results in a moment about the pulley’s center with magnitude
ˇj!pj
opposing the rotation of the pulley, where
ˇ
is a constant and
j!pj
is the
angular speed of the pulley. Hint: Review Example 4.16 on p. 300. Also
note that friction in the pulley bearings causes the tension in the cord to be
different on the two sides of the pulley.
Determine vcif ˇD2kgm2=s.
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permission of McGraw-Hill, is prohibited.
where we have selected the only root for
vc
compatible with the fact that
vc
is a speed. Recalling that
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1692 Solutions Manual
An eccentric wheel with weight
WD250 lb
, mass center
G
, and radius
of gyration
kGD1:32 ft
is initially at rest in the position shown. Letting
RD1:75 ft
and
hD0:8 ft
, and assuming that the wheel is gently nudged to
the right and rolls without slip, determine the speed of Owhen Gis closest to
the ground.
Solution
Dynamics 2e 1693
Problem 8.26
A cord is wound around a uniform disk of mass
mD2:5 kg
and radius
RD
10 cm
. A person pulls on the cord to the right with a constant horizontal force
P
. The disk is initially at rest and rolls without slip. Determine
P
if the center
of the disk has a speed of
0:5 m=s
after the hand pulling the cord displaces
horizontally to the right by 20 cm.
Solution
We model disk as a rigid body rolling without slip on a flat horizontal surface while
1694 Solutions Manual
The pendulum consists of a thin bar of length
LD1:5
m and mass
mbD2kg
, at the
end of which is rigidly attached a uniform solid sphere of radius
rD0:25
m and mass
msD3kg
. The pendulum is pinned at the top end
O
of the bar. The pendulum is
initially at
✓D0
when the center of the sphere
C
is given a speed
v1D4m=s
to the
right. The quantity
d
denotes the distance between
O
and the center of mass of the
bar G. Neglect friction.
If the bar is uniform (i.e., dDL=2), determine the maximum swing angle of the
pendulum.
Solution
We model the entire pendulum as a rigid body in a fixed axis rotation
Balance Principles.
Applying the work-energy principle as a statement of conservation of energy, we have
T1CV1DT2CV2;(1)
where
V
is the potential energy of the pendulum, and where, denoting by
IO
the mass moment of inertia of
Dynamics 2e 1695
Computation. Substituting Eqs. (2), (4), and Eqs. (5) into Eq. (1), we have
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permission of McGraw-Hill, is prohibited.
Problem 8.28
The pendulum consists of a thin bar of length
LD1:5
m and mass
mbD2kg
, at the
end of which is rigidly attached a uniform solid sphere of radius
rD0:25
m and mass
msD3kg
. The pendulum is pinned at the top end
O
of the bar. The pendulum is
initially at
✓D0
when the center of the sphere
C
is given a speed
v1D4m=s
to the
right. The quantity
d
denotes the distance between
O
and the center of mass of the
bar G. Neglect friction.
If the radius of gyration of the bar is
kGD0:35
m, determine
d
so that the
maximum swing angle is 55ı.
1
and
2
. We observe that the weight of the pendulum is the only force
doing work and that this force is conservative.
Balance Principles.
Applying the work-energy principle as a statement of conservation of energy, we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1697
Computation. Substituting Eqs. (2), (4), and Eqs. (5) into Eq. (1), we have
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permission of McGraw-Hill, is prohibited.