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PROBLEM 18.68 (Continued)
PROBLEM 18.69
After attaching the 18-kg wheel shown to a balancing machine and
making it spin at the rate of 15 rev/s, a mechanic has found that to balance
the wheel both statically and dynamically, he should use two corrective
masses, a 170-g mass placed at B and a 56-g mass placed at D. Using a
right-handed frame of reference rotating with the wheel (with the z axis
perpendicular to the plane of the figure), determine before the corrective
masses have been attached (a) the distance from the axis of rotation to the
mass center of the wheel and the products of inertia
x
y
I and ,
zx
I (b) the
force-couple system at C equivalent to the forces exerted by the wheel on
the machine.
PROBLEM 18.69 (Continued)
PROBLEM 18.70
When the 18-kg wheel shown is attached to a balancing machine and
made to spin at a rate of 12.5 rev/s, it is found that the forces exerted by
the wheel on the machine are equivalent to a force-couple system
consisting of a force (160 N)
Fj applied at C and a couple
(14.7 N m) ,
CMk
where the unit vectors form a triad which rotates
with the wheel. (a) Determine the distance from the axis of rotation to the
mass center of the wheel and the products of inertia
x
y
I and .
zx
I (b) If
only two corrective masses are to be used to balance the wheel statically
and dynamically, what should these masses be and at which of the Points
A, B, D, or E should they be placed?
PROBLEM 18.70 (Continued)
PROBLEM 18.71
Knowing that the assembly of Problem 18.65 is initially at rest
(
0) when a couple of moment 00
MMj
is applied to shaft CD,
determine (a) the resulting angular acceleration of the assembly,
(b) the dynamic reactions at C and D immediately after the couple is
applied.
PROBLEM 18.71 (Continued)
PROBLEM 18.72
Knowing that the plate of Problem 18.66 is initially at rest
(0)
when a couple
of moment
0
(0.75 ftM
lb)
j
is applied to it, determine (a) the resulting
angular acceleration of the plate, (b) the dynamic reactions A and B immediately
after the couple has been applied.
PROBLEM 18.66
A thin homogeneous triangular plate of weight 10 pounds
is welded to a light vertical axle supported by bearings at A and B. Knowing
that the plate rotates at the constant rate
8rad/s,
determine the dynamic
reactions at A and B.
PROBLEM 18.72 (Continued)
PROBLEM 18.73
The assembly of Problem 18.67 is initially at rest (
0)
when a couple
0
M
is applied to axle AB. Knowing that the
resulting angular acceleration of the assembly is
2
(150 rad/s ) ,αi
determine (a) the couple
0
,M
(b) the
dynamic reactions at A and B immediately after the couple is
applied.
