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Problem 2.314
A bar
ABC
revolves in a horizontal plane about a
vertical axis at the midpoint
C
(see figure). The bar, which has length
2
L
and crosssectional area
A
, revolves at constant angular speed
v
.
Each half of the bar (
AC
and
BC
) has weight
W
1
and supports a weight
W
2
at its end.
Derive the following formula for the elongation of onehalf of the
bar (that is, the elongation of either
AC
or
BC
):
d
5
}
3
L
g
2
E
v
A
2
}
(
W
1
1
3
W
2
)
in which
E
is the modulus of elasticity of the material of the bar and
g
is the acceleration of gravity.
Solution 2.314
Rotating bar
SECTION 2.3
Changes in Lengths under Nonuniform Conditions
85
AC
B
v
LL
W
2
W
1
W
1
W
2
C
B
v
L
W
1
W
2
x
F(x)
dx
d
j
j
v
5
angular speed
A
5
crosssectional area
E
5
modulus of elasticity
g
5
acceleration of gravity
F
(
x
)
5
axial force in bar at distance
x
from point
C
Consider an element of length
dx
at distance
x
from
point
C
.
To find the force
F
(
x
) acting on this element, we
must find the inertia force of the part of the bar from
distance
x
to distance
L
, plus the inertia force of the
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.
 Spring '08
 Armanios

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