930 Solutions Manual
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Dynamics 2e 931
Problem 5.56
The
135 lb
woman
A
sits atop the
90 lb
cart
B
, both of which are initially at rest. If the woman slides
down the frictionless incline of length
LD11 ft
, determine the velocity of both the woman and the cart
when she reaches the bottom of the incline. Ignore the mass of the wheels on which the cart rolls and any
friction in their bearings. The angle ✓D26ı.
Solution
932 Solutions Manual
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Dynamics 2e 933
Problem 5.57
An Apollo Lunar Module
A
and Command and Service Module
B
are moving through space far from any
other bodies (so that their gravitational effects can be ignored). When
✓D30ı
, the two craft are separated
using an internal linear elastic spring whose constant is
kD200;000 N=m
and is precompressed
0:5
m.
Noting that the mass of the Command and Service Module is about
29;000 kg
and that the mass of the
Lunar Module is about
15;100 kg
, determine their postseparation velocities if their common preseparation
velocity is 11;000 m=s.
Solution
We model
A
and
B
as particles. We denote by
¿
the position of the system
with the spring fully compressed. We denote by
¡
the position of the
934 Solutions Manual
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Dynamics 2e 935
Problem 5.58
In the ride shown, a person Asits in a seat that is attached by a cable of
length
L
to a freely moving trolley
B
of mass
mB
. The total mass of
the person and the seat is
mA
. The trolley is constrained by the beam
to move only in the horizontal direction. The system is released from
rest at the angle
✓D✓0
, and it is allowed to swing in the vertical plane.
Neglect the mass of the cable and treat the person and the seat as a single
particle.
Determine expressions for the velocities of the trolley and the rider
the first time that
✓D0ı
. Evaluate your solution for
WAD100 lb
,
WBD20 lb, LD15 ft, and ✓0D70ı.
Solution
We model
A
and
B
as a system of particles subject to their respective
weights
mAg
and
mBg
.
B
is also subject to the normal reaction from
936 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 937
Problem 5.59
In the ride shown, a person Asits in a seat that is attached by a cable of
length
L
to a freely moving trolley
B
of mass
mB
. The total mass of
the person and the seat is
mA
. The trolley is constrained by the beam
to move only in the horizontal direction. The system is released from
rest at the angle
✓D✓0
, and it is allowed to swing in the vertical plane.
Neglect the mass of the cable and treat the person and the seat as a single
particle.
Determine expressions for the velocities of the trolley and the rider
the first time that
✓D0ı
. After doing so, for given
g
,
L
,
mA
, and
✓0
,
determine the maximum speed achievable by the rider at
✓D0ı
and the
corresponding value of
mB
. Evaluate your solution for
WAD100 lb
,
LD15 ft
, and
✓0D70ı
. What would be the motion of
B
for this value
of mB?
Solution
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938 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 939
Problem 5.60
In the ride shown, a person Asits in a seat that is attached by a cable of
length
L
to a freely moving trolley
B
of mass
mB
. The total mass of
the person and the seat is
mA
. The trolley is constrained by the beam
to move only in the horizontal direction. The system is released from
rest at the angle
✓D✓0
, and it is allowed to swing in the vertical plane.
Neglect the mass of the cable and treat the person and the seat as a single
particle.
Determine the velocity of the trolley and the speed of the rider for
any arbitrary value of ✓.
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