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Problem 6.161
At the instant shown, the wheel
D
rolls without slipping over a flat
surface with an angular velocity
!DD14 rad=s
and an angular
acceleration
˛DD1:1 rad=s2
. The
X Y Z
frame shown is inertial,
whereas the
xy´
frame is attached to
D
. At the instant shown, the
collar
C
is sliding along the bar
AB
with a velocity
vCD4ft=s
and
acceleration
aCD7ft=s2
, both relative to the
xy´
frame. Letting
`D
0:25 ft
and
RD1ft
, determine the inertial velocity and acceleration
of
C
when
D25ı
and the
xy´
frame is parallel to the
X Y Z
frame
as shown. Express your result in both the xy´ and the X Y Z frames.
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.
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 6.162
The manually operated road barrier shown has a total length
lD15:7 ft
and has a counterweight
C
whose
position is identified by the distances
dD2:58 ft
and
ıD1:4 ft
. The barrier is pinned at
O
and can move
in the vertical plane. If the barrier is raised and then released so that the end
B
of the barrier hits the
support with a speed vBD1:5 ft=s, determine the speed of the counterweight Cwhen Bhits A.
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 1393
Problem 6.163
Bar
AB
rotates about point
A
with angular speed
!1
and angular
acceleration
˛1
, both in the directions shown. Bar
BC
rotates
about the pin at
B
relative to bar
AB
with angular speed
!2
and
angular acceleration
˛2
, both in the directions shown. The position
of collar
D
relative to bar
BC
is given by the coordinate
s
, which
is a known function of time. Express your answers in the
xy´
frame that is attached to bar
BC
with its origin at
B
.Hint: As we
will see in Eq. (10.14), E!BC D E!AB C E!BC=AB D E!1C E!2.
Determine an expression for the Coriolis acceleration of the
collar D.
Solution
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permission of McGraw-Hill, is prohibited.
Problem 6.164
Bar
AB
rotates about point
A
with angular speed
!1
and angular
acceleration
˛1
, both in the directions shown. Bar
BC
rotates
about the pin at
B
relative to bar
AB
with angular speed
!2
and
angular acceleration
˛2
, both in the directions shown. The position
of collar
D
relative to bar
BC
is given by the coordinate
s
, which
is a known function of time. Express your answers in the
xy´
frame that is attached to bar
BC
with its origin at
B
.Hint: As we
will see in Eq. (10.14), E!BC D E!AB C E!BC =AB D E!1C E!2.
Determine an expression for the acceleration of the collar
D
in terms of
d
,
!1
,
!2
,
˛1
,
˛2
, and the position coordinate
s
and its
time derivatives.
EvDrel D PsO{;
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1395
Problem 6.165
At the instant shown, the hammer head
H
is moving to the right
with a speed
vHD45 ft=s
and the angle
D20ı
. Assuming that
the belt does not slip relative to wheels
A
and
B
and assuming that
wheel
A
is mounted on the shaft of the motor shown, determine the
angular velocity of the motor at the instant shown. The diameter of
wheel
A
is
dD0:25 ft
, the radius of wheel
B
is
RD0:75 ft
, and
point
C
is at a distance
`D0:72 ft
from
O
, which is the center of
the wheel
B
. Finally, let
CD
have a length
LD2ft
, and assume
that, at the instant shown, D25ı.
2!AD RP
dP
d
`sin. C/ D480:6 rad=s
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permission of McGraw-Hill, is prohibited.
Problem 6.166
The bar
AB
is pinned to the ground at
A
, and its angle
with respect to the
vertical is a known function of time. The bar
BC
is pinned to the bar
AB
at
B
, and its orientation
is measured with respect to the bar
AB
. The position
of the collar
D
is measured relative to the bar
BC
by the coordinate
s
, which
is also a known function of time. The length of the bar
AB
is
dD2ft
. At the
instant shown,
D30ı
,
D30ı
,
P
D5rad=s
,
R
D3rad=s2
,
P
D 5rad=s
,
R
D4rad=s2
,
sD2:5 ft
,
PsD10 ft=s
, and
RsD 15 ft=s2
. Express all your
answers in the
xy´
frame that is attached to the bar
BC
and whose origin is at
B.Hint: As we will see in Eq. (10.14), E!BC D E!AB C E!BC =AB .
Determine the velocity of the collar Dat this instant.
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 1397
Problem 6.167
The bar
AB
is pinned to the ground at
A
, and its angle
with respect to the
vertical is a known function of time. The bar
BC
is pinned to the bar
AB
at
B
, and its orientation
is measured with respect to the bar
AB
. The position
of the collar
D
is measured relative to the bar
BC
by the coordinate
s
, which
is also a known function of time. The length of the bar
AB
is
dD2ft
. At the
instant shown,
D30ı
,
D30ı
,
P
D5rad=s
,
R
D3rad=s2
,
P
D 5rad=s
,
R
D4rad=s2
,
sD2:5 ft
,
PsD10 ft=s
, and
RsD 15 ft=s2
. Express all your
answers in the
xy´
frame that is attached to the bar
BC
and whose origin is at
B.Hint: As we will see in Eq. (10.14), E!BC D E!AB C E!BC =AB .
Determine the acceleration of the collar Dat this instant.
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.
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 1399
Problem 6.168
Assuming that the rope does not slip relative to any of the pulleys in the system,
determine the velocity and acceleration of
A
and
D
, knowing that the angular
velocity and acceleration of pulley
B
are
!BD7rad=s
and
˛BD3rad=s2
,
respectively. The diameters of pulleys
B
and
C
are
dD25 cm
and
`D34 cm
,
respectively.
Solution
Referring to the figure at the right, let
Q
be the point of contact between the pulley
B
and the rope on the right side of pulley
B
. Since the rope to the right of pulley
B
is attached to the ceiling, its velocity must be zero. Because the pulley
B
rolls
without slipping on the rope at
Q
, we must have that the speed of the center of
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.
