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Computation.
Substituting Eqs. (6) and (5) into Eqs. (1), (2), and (4), and taking into account Eq. (3), we
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Dynamics 2e 1869
Problem 8.124
A uniform bar
A
with a hook
H
at the end is dropped from rest as shown
from a height
dD3ft
over a fixed pin
B
. Letting the weight and length
of
A
be
WD100 lb
and
`D7ft
, respectively, determine the angle
✓
that
the bar will sweep through if the bar becomes hooked with
B
and does not
rebound. Although bar
A
becomes hooked with
B
, assume that there is no
friction between the hook and the pin.
Solution
First, we determine the impact speed between the bar and the pin
B
. Second, we determine the postimpact
angular velocity of the bar. Third, we determine of the angle swept by the bar.
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permission of McGraw-Hill, is prohibited.
Force Laws.
Since the bar does not rebound away from the obstacle, we do not have a
COR
equation in
this problem.
Kinematic Equations.
Using the result from the work-energy part of the solution and using the parallel
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Dynamics 2e 1871
Problem 8.125
A drawbridge of length
`D30 ft
and weight
WD600 lb
is released in the position
shown and freely pivots clockwise until it strikes the right end of the moat. If the
COR
for the collision between the bridge and the ground is
eD0:45
and if the contact
point between the bridge and the ground is effectively
`
away from the bridge’s pivot
point, determine the angle to which the bridge rebounds after the collision. Neglect
any possible source of friction.
Solution
First, we determine the angular speed with which the bridge hits the ground. Second, we analyze the impact
between the bridge and the ground. Third, we determine the rebound angle.
To determine the angular speed of the bridge right before impact, we define
¿
and
¡
to be the positions at release and when the bridge first strikes the
ground respectively. We observe that, between
¿
and
¡
, the bridge is in a
We now proceed to determine the postimpact angular velocity of the bridge.
Balance Principles.
The impact-relevant
FBD
of the bridge illustrates the fact
that this is a constrained impact in which no momentum conservation principle can
be invoked.
Force Laws.
The only governing equation that can be written for this impact is the coefficient of restitution
equation long the
LOI
. Let
Q
be the point on the bridge that comes into contact with the ground. Then,
accounting for the fact that the ground does not move, we have
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Dynamics 2e 1873
Problem 8.126
A stick
A
with length
`D1:55
m and mass
mAD6kg
is in static equilibrium as
shown when a ball
B
with mass
mBD0:15 kg
traveling at a speed
v0D30 m=s
strikes the stick at distance
dD1:3
m from the lower end of the stick. If the COR for
the impact is
eD0:85
, determine the velocity of the mass center
G
of the stick, as
well as the stick’s angular velocity right after the impact.
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permission of McGraw-Hill, is prohibited.
Computation.
Substituting Eq. (5), Eqs. (7), and the last of Eqs. (8) into Eqs. (1)–(4) and Eq. (6) we have
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Dynamics 2e 1875
Problem 8.127
A gymnast on the uneven parallel bars has a vertical speed
v0
and no angular speed when she grasps the
upper bar. Model the gymnast as a single uniform rigid bar
A
of weight
WD92 lb
and length
`D6ft
.
Neglecting all friction, letting
ˇD12ı
, and assuming that the upper bar
B
does not move after the
gymnast grasps it, determine the minimum speed
v0
for the gymnast to swing (counterclockwise) into the
horizontal position on the other side of the bar. Assume that, during the motion, the friction between the
gymnast’s hands and the upper bar is negligible.
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Balance Principles.
Applying the work-energy principle as a statement of conservation of energy, we have
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1877
Problem 8.128
A uniform thin ring
A
of mass
mD7kg
and radius
rD0:5
m is released
from rest as shown and rolls without slip until it meets a step of height
`D0:45
m. Letting
ˇD12ı
and assuming that the ring does not
rebound off the step or slip relative to it, determine the distance
d
, such
that the ring barely makes it over the step.
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