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496 Solutions Manual
Problem 3.61
Continue Prob. 3.60 and using mathematical software, numerically
solve the equations of motion. Use the same parameters and initial
conditions that were used in Example 3.10, and compare your
results with those presented in that example.
Solution
Referring to the FBD on the right, we model the disk as a particle moving in
the horizontal plane and subject only to the spring force
Fs
. We adopt the
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.
498 Solutions Manual
Problem 3.62
Derive the equations of motion for the pendulum supported by a linear spring of
constant
k
and unstretched length
ru
. Neglect friction at the pivot
O
, the mass of
the spring, and air resistance. Treat the pendulum bob as a particle of mass
m
, and
use polar coordinates.
Solution
Dynamics 2e 499
Problem 3.63
Using mathematical software, solve the equations of motion for the pendulum
supported by a linear spring of constant
k
(derived in Prob. 3.62). Plot the trajectory
of the mass
m
in the vertical plane for a number of different values of
k=m
. The
unstretched length of the spring is
0:25
m, and the mass is released when the
pendulum is vertical, the spring is stretched
0:75
m, and the mass is moving to the
right at 1m=s.
Solution
Referring to the FBD on the right, we model the pendulum bob as a particle subject only
to its own weight
mg
and to the spring force
Fs
. To study the motion of the pendulum
500 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 501
Problem 3.64
The system shown is initially at rest when the bent bar starts to rotate about the vertical axis
AB
with
constant angular acceleration
˛0D3rad=s2
. The coefficient of static friction between the collar of mass
mD2kg and the bent bar is sD0:35, and the collar is initially dD70 cm from the spin axis AB.
Assuming the motion starts at
tD0
, determine the time at which the collar starts to slip relative to the
bent bar.
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.
502 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 503
Problem 3.65
The system shown is initially at rest when the bent bar starts to rotate about the vertical axis
AB
with
constant angular acceleration
˛0D3rad=s2
. The coefficient of static friction between the collar of mass
mD2kg and the bent bar is sD0:35, and the collar is initially dD70 cm from the spin axis AB.
Determine the number of rotations undergone by the bent bar when the collar starts to slip relative to it.
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.
504 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 505
Problem 3.66
Revisiting Example 3.7, assume that the drag force in the
x
direction is proportional to the square of the
x
component of velocity, but that the ball’s trajectory is shallow enough to neglect the drag force in the
y
direction. Using this assumption, letting
O
be the initial position of the ball, and letting the ball’s initial
velocity have a magnitude
v0
and letting it form an angle
✓0
with the
x
axis, determine an expression for
the trajectory of the ball of the form yDy.x/.
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.
