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556 Solutions Manual
Problem 3.94
Consider a collar with mass
m
that is free to slide with no friction
along a rotating arm, which has negligible mass. The system is
initially rotating with an angular velocity
!0
while the collar is kept
a distance
r0
away from the
´
axis. At some point, the restraint
keeping the collar in place is removed so that the collar is allowed to
slide.
Derive the collar’s equations of motion when M´D0.
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 557
Problem 3.95
Consider a collar with mass
m
that is free to slide with no friction
along a rotating arm, which has negligible mass. The system is
initially rotating with an angular velocity
!0
while the collar is kept
a distance
r0
away from the
´
axis. At some point, the restraint
keeping the collar in place is removed so that the collar is allowed to
slide.
If no external forces and moments are applied to the system, what
are the radial speed and the total speed of the collar when it reaches
the end of the arm? Use
mD2kg
,
!0D1rad=s
,
r0D0:5
m, and
dD1m.
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.
558 Solutions Manual
P
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 559
Problem 3.96
Consider a collar with mass
m
that is free to slide with no friction
along a rotating arm, which has negligible mass. The system is
initially rotating with an angular velocity
!0
while the collar is kept
a distance
r0
away from the
´
axis. At some point, the restraint
keeping the collar in place is removed so that the collar is allowed to
slide.
Compute the moment
M´
that you would need to apply to the
arm, as a function of
r
, to keep the arm rotating at a constant angular
velocity
!0
. In addition, determine the radial speed, as well as the
total speed with which the collar would reach the end of the arm
with this moment applied. Hint: The moment
M´
applied to the
arm of negligible mass is equivalent to a force
M´=r
applied to the
collar in the plane of motion and perpendicular to the arm.
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.
560 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 561
Problem 3.97
Consider a collar with mass
m
that is free to slide with no friction
along a rotating arm, which has negligible mass. The system is
initially rotating with an angular velocity
!0
while the collar is kept
a distance
r0
away from the
´
axis. At some point, the restraint
keeping the collar in place is removed so that the collar is allowed to
slide.
Compute and plot the collar’s trajectory from the moment of
release until the collar reaches the end of the arm. Use the parameters
and initial conditions given in Prob. 3.95.
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.
562 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 563
Problem 3.98
The radar station at
O
is tracking the meteor
P
as it moves through the atmosphere. The data measured by
the radar station indicates that the acceleration vector of
P
is almost exactly in the opposite direction of
the velocity vector. Explain why this is what we should expect.
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.
564 Solutions Manual
Problem 3.99
The particle
P
is placed on the turntable, and both are initially at rest. The turntable is then turned on so
that the disk starts spinning. Assuming that there is no friction between the turntable disk and the particle,
what will be the motion of the particle after the disk starts spinning? Explain.
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 565
Problem 3.100
The conveyor belt moves parts, each with mass
m
, at a constant speed
v0
. When the parts get to
A
, they
begin moving over a circular path of radius
⇢
. If the coefficient of static friction between the belt and the
parts is
s
, determine the angle
✓
at which the parts will start to slide on the belt. Neglect the size of
the parts. After determining
✓
in terms of
s
,
v0
,
⇢
, and
g
, evaluate
✓
for
sD0:6
,
v0D3mph
, and
⇢D14 in.
Solution
Referring to the FBD at the right, we model each part on the belt as a particle subject
to its own weight
mg
, the normal reaction
N
with the belt and the friction force
F
.
