Force Laws. Due to our choice of datum,
rand v
Computation.
Substituting Eqs. (10) and (11) into Eq. (9) and solving
for !C
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 1879
Balance Principles.
Applying the work-energy principle as a statement of conservation of energy, we have
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Problem 8.129
Two identical uniform bars
AB
and BD are pin-connected at
B;
and bar BD has a hook at the free end.
The two bars are dropped as shown from a height
dD3ft
over a fixed pin
E
(shown in cross section).
Letting the weight and length of each bar be
WD100 lb
and
`D7ft
, respectively, determine the angular
velocities of
AB
and BD immediately after bar BD becomes hooked on
E
and does not rebound. Hint:
The angular momentum of bar AB is conserved about Bduring impact.
Solution
The figure below shows the impact-relevant FBDs of the system and of bar AB.
These FBDs imply that the angular momentum of the system about
E
and the angular momentum of bar
AB
about Bare conserved through the impact.
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Dynamics 2e 1881
Computation.
Substituting Eqs. (3)–(5) into Eqs. (1) and (2), we obtain a system of two equations in the
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1882 Solutions Manual
Cars
A
and
B
collide as shown. Determine the angular velocities of
A
and
B
immediately after impact if
the
COR
is
eD0:35
. In solving the problem, let
C
and
D
be the mass centers of
A
and
B
, respectively.
In addition, enforce assumption 3 on p. 640 and use the following data:
WAD3130 lb
(weight of
A
),
kCD34:5 in:
(radius of gyration of
A
),
vCD12 mph
(speed of the mass center of
A
),
WBD3520 lb
(weight of
B
),
kDD39:3 in:
(radius of gyration of
B
),
vDD15 mph
(speed of the mass center of
B
),
dD19 in:,`D79 in:,ıD7:1 in:,⇢D65 in:, and ˇD12ı.
Solution
We model the impact as an unconstrainted oblique eccentric impact of two rigid bodies. The figure below
BDE
BD!C
BO
v
Qx DvDcos ˇ; vC
Qx DvC
Dx C!C
B.d cos ˇ`sin ˇ/; (17)
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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.
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 8.131
Consider the collision of two rigid bodies
A
and
B
, which, referring to
Example 8.10 on p. 627, models the docking of the Space Shuttle (body
A
) to the International Space Station (body
B
). As in Example 8.10,
we assume that
B
is stationary relative to an inertial frame of reference
and that
A
translates as shown. In contrast to Example 8.10, here
we assume that
A
and
B
join at point
Q
but, due to the flexibility of
the docking system, can rotate relative to one another. Determine the
angular velocities of
A
and
B
right after docking if
v0D0:03 m=s
.
In solving the problem, let
C
and
D
be the centers of mass of
A
and
B
, respectively. In addition, let the mass and mass moment of inertia
of
A
be
mAD120 ⇥103kg
and
ICD14⇥106kgm2
, respectively,
and the mass and mass moment of inertia of
B
be
mBD180⇥103kg
and
IDD34 ⇥106kgm2
, respectively. Finally, use the following
dimensions: `D24 m, dD8m, ⇢D2:6 m, and ıD2:4 m.
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mAD120⇥103kg
,
ICD14⇥106kgm2
,
mBD180⇥103kg
,
IDD34⇥106kgm2
,
`D24
m,
dD8
m,
⇢D2:6 m, and ıD2:4 m, we can rewrite Eqs. (1)–(4) and Eqs. (8) and (9) as follows:
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permission of McGraw-Hill, is prohibited.