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546 Solutions Manual
Problem 3.89
A pendulum with cord length
LD6ft
and a bob weighing
3lb
is released
from rest at an angle
✓i
. Once the pendulum has swung to the vertical position
(i.e.,
✓D0
), its cord runs into a small fixed obstacle. In solving this problem,
neglect the size of the obstacle; model the pendulum’s bob as a particle and the
pendulum’s cord as massless and inextensible; and let gravity and the tension in
the cord be the only relevant forces.
If the bob is released from rest at
✓iD90ı
, at what angle
does the cord go
slack?
Solution
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 547
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.
548 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 549
Problem 3.90
A spherical pendulum is suspended from point
O
and put in motion.
Derive the pendulum’s equations of motion using Cartesian
coordinates.
Solution
Referring to the figure at the right, we model the pendulum bob as a particle subject
only to its own weight
mg
and the tension in the cord
Fc
. We use the Cartesian
550 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 551
Problem 3.91
A spherical pendulum is suspended from point
O
and put in motion.
Derive the pendulum’s equations of motion using cylindrical
coordinates.
Solution
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.
552 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 553
Problem 3.92
A spherical pendulum is suspended from point
O
and put in motion.
Derive the pendulum’s equations of motion using spherical co-
ordinates.
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.
554 Solutions Manual
Problem 3.93
A spherical pendulum is suspended from point
O
and put in motion.
At the lowest point on its trajectory, the pendulum in the figure
has a speed
v0D2:5 ft=s
while
0D15ı
. Letting
LD2ft
, plot
the trajectory of the pendulum bob for 5s.
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 555
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.
