Problem 6.124
A flood gate is controlled by the hydraulic cylinder
AB
. If the length of
the cylinder is increased with a constant time rate of
2:5 ft=s
, determine
the angular acceleration of the gate when
D0ı
. Let
`D10 ft
,
hD2:5 ft, and dD5ft.
Solution
For any position of the gate, we have the following constraint equations
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Dynamics 2e 1321
Problem 6.125
At the instant shown, bar
CD
is rotating with an angular velocity
20 rad=s
and with angular acceleration
2rad=s2
in the directions shown. Furthermore,
at this instant
D45ı
. If
LD2:25 ft
, determine the angular accelerations
of bars AB and BC .
Solution
First finding the velocity of C, we obtain
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permission of McGraw-Hill, is prohibited.
where we have used the expressions for
!AB
and
!BC
determined above. Equating components, we have
two equations for ˛AB and ˛BC :
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Dynamics 2e 1323
Problem 6.126
The bucket of a backhoe is the element
AB
of the four-bar linkage
system
ABCD
. Assume that the points
A
and
D
are fixed and that
the bucket rotates with a constant angular velocity
!AB D0:25 rad=s
.
In addition, suppose that, at the instant shown, point
B
is aligned
vertically with point
A
, and
C
is aligned horizontally with
B
. Deter-
mine the acceleration of point
C
at the instant shown, along with the
angular accelerations of the elements
BC
and
CD
. Let
hD0:66 ft
,
eD0:46 ft, `D0:9 ft, and wD1:0 ft.
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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 1325
Problem 6.127
At the instant shown, bars
AB
and
CD
are vertical. In addition, point
C
is moving
to the left with an increasing speed of
4m=s
, and the magnitude of the acceleration
of
C
is
55 m=s2
. If
LD0:5
m and
HD0:2
m, determine the angular accelerations
of bars AB and BC .
)L˛AB O{Cv2
LO|D.aCx C2L˛BC /O{C.aCy H˛BC /O|
where we have used the fact that
!BC D0
. This corresponds to the following two scalar equations in the two
unknowns ˛AB and ˛BC :
C
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where we will choose the minus sign on the final result for
aCx
since
C
is moving to the left and its speed is
increasing. Substituting these results for
aCx
and
aCy
into the solutions for
˛BC
and
˛AB
determined above,
Using vCD4m=s, aCD55 m=s2,LD0:5 m, and HD0:2 m, these become
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Dynamics 2e 1327
Problem 6.128
For the slider-crank mechanism shown, let
RD1:9 in:
,
LD6:1 in:
, and
HD1:2 in:
Assuming that !AB D4850 rpm and is constant, determine the angu-
lar acceleration of the connecting rod
BC
and the acceleration of point
C
at the instant when D27ı.
Relating the acceleration of Bto that of A, we have
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Since point Ccan only move in the vertical direction, aCx D0, which implies
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Dynamics 2e 1329
Problem 6.129
For the slider-crank mechanism shown, let
RD1:9 in:
,
LD6:1 in:
, and
HD1:2 in:
Assuming that
!AB D4850 rpm
and is constant, determine the accel-
eration of point Dat the instant when D10ı.
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permission of McGraw-Hill, is prohibited.