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Problem 7.26
The system shown lies in the vertical plane. The trolley
A
is
moving to the right with a constant acceleration
aA
. Attached
to the trolley by a pin is a thin uniform bar
AB
of mass
m
and
length
L
. Attached to the end of the bar
AB
by a pin is a thin
uniform bar
BC
of mass
m
and length
L
. When the trolley
A
is accelerating at constant
aA
, the angles
and
are both
constant. Determine these two constant angles in this steady
state as functions of one or more of the given quantities (i.e.,
L
,
m, and aA). Note that cos.
2x/ Dsin x.
Solution
Separating the two bars, their FBDs are shown at the right, where
D
is the
mass center of bar AB and Eis the mass center of bar BC .
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 1467
In addition, since neither bar is rotating, the
x
component of acceleration of the mass center of each of the
bars must equal the acceleration of point A, that is
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permission of McGraw-Hill, is prohibited.
Problem 7.27
Following up on Example 7.5 on p. 542, now assume that the pivot point
O
is close to the center of mass
of the batter so that it is a distance
ıD3in:
from the knob of the bat at
A
. Determine the location of the
center of percussion
P
relative to the knob at
A
, and show that the position of
P
is independent of the
location of point
C
at which the batter grips the bat. Recall that
P
is the point at which the ball should
be hit so that, no matter how large the force applied at
P
to the bat by the ball, the lateral force (i.e.,
perpendicular to the bat) felt by the batter at the grip
C
is zero. Assume the bat has mass
m
, its mass
center is at
G
, and
IG
is its mass moment of inertia. Evaluate your answer for a typical bat used in Major
League Baseball whose weight is
32 oz
and whose length is
34 in:
,
`D22:5 in:
,
mD0:0630 slug
, and
IGD0:0413 slugft2. Ignore the weight force on the bat.
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.
12 ft
12 ft
12 in:D1ft to obtain the numerical results.
We see that the location of the center of percussion, which is determined by
d
, is independent of
h
, and
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permission of McGraw-Hill, is prohibited.
Problem 7.28
For the centrifuge rotor and test tube given in Example 7.6 on
p. 544, assume that all the test tubes are locked into their horizontal
position and that the rotor is uniformly accelerated from rest to
60;000 rpm
in
9:5 min
. Determine, as a function of time, the
forces and moments on one of the test tubes during this spin-up
phase of motion. Assume that each test tube and its contents can
be modeled as a uniform circular cylinder with a mass of
10
g,
and ignore gravity.
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 1471
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.
Problem 7.29
The spool is pinned at its center at
O
, about which it can spin freely. The radius of the
spool is
RD0:15
m, its radius of gyration is
kOD0:11
m, and the mass of the spool
is
msD5kg
. The mass
B
is suspended from the periphery of the spool by a chain of
negligible mass that moves over the spool without slip. The mass of Bis mBD7kg.
If the system is released from rest, determine the angular acceleration of the spool
and the tension in the chain.
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 1473
Solving these four equations for the four unknowns, we obtain
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permission of McGraw-Hill, is prohibited.
Problem 7.30
The spool is pinned at its center at
O
, about which it can spin freely. The radius of the
spool is
RD0:15
m, its radius of gyration is
kOD0:11
m, and the mass of the spool
is
msD5kg
. The mass
B
is suspended from the periphery of the spool by a chain of
negligible mass that moves over the spool without slip. The mass of Bis mBD7kg.
If the system is released from rest, determine the number of revolutions of the spool
and the time it takes for mass Bto achieve a speed of 10 m=s.
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 1475
Solving these four equations for the four unknowns, we obtain
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