Dynamics 2e 817
Problem 4.110
The motor
B
is used to raise and lower the crate
C
by a pulley system. At the
instant shown, the cable is being retracted by the motor with the constant speed
vcD5ft=s. The weight of the crate is WCD450 lb.
If the overall efficiency of the system is 0.82, determine the power input to
the motor that the meter at Awould read.
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818 Solutions Manual
Problem 4.111
Assuming that the motor shown has an efficiency
✏D0:80
, determine the
power to be supplied to the motor if it is to pull a
250 lb
crate up the incline
with a constant speed
vD7ft=s
. Assume that the kinetic friction coefficient
between the slide and the crate is kD0:25 and that ✓D28ı.
Solution
We model the crate as a particle subject to its own weight
mg
, the normal reaction
from the incline N, the friction force Fand the tension in the cord Fc.
Dynamics 2e 819
Problem 4.112
Assume that the motor shown has an efficiency
✏D0:82
and that it draws
6hp
.
Determine the constant speed with which the motor can pull a
300 lb
crate up
the incline if the kinetic friction coefficient between the slide and the crate is
kD0:45 and ✓D32ı.
Solution
We model the crate as a particle subject to its own weight
mg
, the normal reaction
from the incline N, the friction force Fand the tension in the cord Fc.
820 Solutions Manual
Problem 4.113
Rubber bumpers are commonly used in marine applications to keep boats and ships from getting damaged
by docks. Consider a boat with a mass of
35;000 kg
and a bumper with a force compression profile
given by
FBDˇx3
, where
ˇ
is a constant and
x
is the compression of the bumper. Treating the boat
C
as a particle, neglecting its vertical motion, and neglecting the drag force between the water and the
boat
C
, determine
ˇ
so that if the boat were to impact the bumper with a speed of
4m=s
, the maximum
compression of the bumper would be 18 cm.
Solution
We model
C
as a particle subject only to its own weight
mg
, the force
of the bumper
FB
, and the force of the water
FW
. We neglect vertical
Dynamics 2e 821
Problem 4.114
The crates
A
and
B
of mass
mAD50 kg
and
mBD75 kg
, respec-
tively, are connected by a pulley system. The system is released from
rest on the inclined surfaces for which
✓D30ı
. Friction between
A
and the inclined surface on which it slides is insufficient to prevent
slipping, and friction between
B
and the incline on which it slides
is negligible. The cables in the pulley system are inextensible, and
the coefficient of kinetic friction between crate
A
and the horizontal
surface is k.
Letting
kD0
, determine the speed of
B
after
A
slides
5
m up
the incline.
Solution
We model
A
and
B
as a system of particles subject to the weights of
A
and
B
,
mAg
and
mBg
, respectively, the reaction with the ground
822 Solutions Manual
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 823
Problem 4.115
The crates
A
and
B
of mass
mAD50 kg
and
mBD75 kg
, respec-
tively, are connected by a pulley system. The system is released from
rest on the inclined surfaces for which
✓D30ı
. Friction between
A
and the inclined surface on which it slides is insufficient to prevent
slipping, and friction between
B
and the incline on which it slides
is negligible. The cables in the pulley system are inextensible, and
the coefficient of kinetic friction between crate
A
and the horizontal
surface is k.
Determine the required value of
k
so that the speed of
B
is
7m=s
after it slides 5m down the incline.
Solution
NOTE: the given value of the speed of Bshould be 7m=s instead of 10 m=s.
824 Solutions Manual
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 825
Problem 4.116
The crates
A
and
B
of mass
mAD50 kg
and
mBD75 kg
, respec-
tively, are connected by a pulley system. The system is released from
rest on the inclined surfaces for which
✓D30ı
. Friction between
A
and the inclined surface on which it slides is insufficient to prevent
slipping, and friction between
B
and the incline on which it slides
is negligible. The cables in the pulley system are inextensible, and
the coefficient of kinetic friction between crate
A
and the horizontal
surface is k.
Letting
kD0:25
, determine the speed of
A
after
B
slides
5
m
down the incline.
Solution
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permission of McGraw-Hill, is prohibited.
826 Solutions Manual
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.