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606 Solutions Manual
Problem 3.127
The double pendulum shown consists of two particles with masses
m1D7:5 kg
and
m2D12 kg
connected by two inextensible cords of length
L1D1:4
m and
L2D2
m and negligible mass. If the system is released from rest when
✓D10ı
and D20ı, determine the tension in the two cords at the instant of release.
Solution
Referring to the figure at the right, we model the two pendulum bobs
as particles of mass
m1
and
m2
subject to their respective weights,
m1g
Dynamics 2e 607
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.
608 Solutions Manual
Problem 3.128
Two small spheres
A
and
B
, each of mass
m
, are attached at either end of
a rod of length
d
. The system is released from rest in the position shown.
Neglect friction, treat the spheres as particles (assume that their diameter
is negligible), neglect the mass of the rod, assume the rod is rigid, and
assume that
d<R
.Hint: The force that the rod exerts on either ball has
the same direction as the rod itself.
Using the angle
✓
as the dependent variable, derive the equation of
motion for the particle system from the moment of release until particle
Breaches point D.
Solution
Following the problem statement, we model
A
and
B
as particles subject to their
weight
mg
, the normal reactions from the slide
NA
and
NB
, and the force
T
Dynamics 2e 609
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.
610 Solutions Manual
Problem 3.129
Two small spheres
A
and
B
, each of mass
m
, are attached at either end of
a rod of length
d
. The system is released from rest in the position shown.
Neglect friction, treat the spheres as particles (assume that their diameter
is negligible), neglect the mass of the rod, assume the rod is rigid, and
assume that
d<R
.Hint: The force that the rod exerts on either ball has
the same direction as the rod itself.
Determine the expression for the speed of the spheres immediately
before Breaches point D.
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 611
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.
612 Solutions Manual
Problem 3.130
A
62 kg
woman
A
sits atop the
60 kg
cart
B
, both of which are
initially at rest. The cart is rigidly attached to a wall by the rope
CD
. If the woman slides down the frictionless incline of length
LD3:5
m, determine the tension in the rope
CD
as she slides
down the incline. Ignore the mass of the wheels on which the cart
can roll. The angle ✓D26ı.
Solution
Dynamics 2e 613
Problem 3.131
A
62 kg
woman
A
sits atop the
60 kg
cart
B
, both of which are
initially at rest. If
✓D26ı
and the woman slides down the incline
of length
LD3:5
m, 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 friction in their
bearings, and neglect friction between the woman and the incline.
Solution
614 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 615
Problem 3.132
Two blocks Aand Bweighing 123 and 234 lb, respectively, are released
from rest as shown. At the moment of release the spring is unstretched. In
solving these problems, model
A
and
B
as particles, neglect air resistance,
and assume that the cord is inextensible. Hint: If
B
hits the ground, then
its maximum displacement is equal to the distance between the initial
position of Band the ground.
Determine the maximum displacement and the maximum speed of
block
B
if
˛D0ı
, the contact between
A
and the surface is frictionless,
and the spring constant is kD30 lb=ft.
Solution
We model
A
and
B
as particles subject only to their respective weights,
mAg
