576 Solutions Manual
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 577
Problem 3.110
Revisit Example 3.14 and assume that the static coefficient of fric-
tion between the two books is
s2 D0:55
, while all other parame-
ters stay as specified in the example. Determine the acceleration of
each of the books.
Solution
As discussed in Example 3.14, if
S2 >
k1
the books do not slide relative
to each other. Therefore, referring to the figure at the right, we can model the
578 Solutions Manual
Problem 3.111
As seen in Fig. P3.111(a), a window washing platform is controlled by the two pulley systems at
AB
and
CD
. The workers
E
and
F
can raise and lower the platform
P
by pulling on the cables
H
and
I
,
respectively. The weight of each of the workers is
185 lb
, and the platform
P
weighs
200 lb
. A schematic
representation of the pulley system is shown in Fig. P3.111(b). If the workers start from rest and, in
1:5
s,
uniformly start pulling the cable in at
2:5 ft=s
, determine the force each worker must exert on the cables
H
and
I
during that
1:5
s. Neglect the mass of the pulleys, friction in the pulleys, and the mass of the cable.
Assume each worker pulls with the same force, and ignore the departure from vertical of segments
H
and
I.
Solution
The FBD at the right shows the system of three masses with
Dynamics 2e 579
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
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580 Solutions Manual
Problem 3.112
A man
A
is trying to keep his balance while on a metal wedge
B
that is
sliding down an icy incline. Letting
mAD78 kg
and
mBD25 kg
be the
masses of
A
and
B
, respectively, and assuming that there is enough friction
between
A
and
B
for
A
not to slide with respect to
B
, determine the value
of the normal reaction force between
A
and
B
, as well as the magnitude of
their acceleration if
✓D20ı
. Friction between the wedge and the incline is
negligible.
Solution
Referring to the figure at the right, to determine the normal reaction force
Dynamics 2e 581
Problem 3.113
A man
A
is trying to keep his balance while on a metal wedge
B
that is
sliding down an icy incline. The weights of
A
and
B
are
WAD181 lb
and
WBD50 lb
, respectively. Determine the minimum coefficient of static
friction
s
between
A
and
B
required for
A
not to slide with respect to
B
if
✓D23ı. Friction between the wedge and the incline is negligible.
Referring to the figure at the right, we sketch individual FBDs for
A
and
B
modeled as particles. The relevant forces on
A
are its weight
mAg
, the normal
582 Solutions Manual
Problem 3.114
A force
F0
of
400 lb
is applied to block
A
. Letting the weights of
A
and
B
be 55 and
73 lb
, respectively, and letting the static and kinetic friction
coefficients between blocks
A
and
B
be
1D0:25
, and the static and
kinetic friction coefficients between block
B
and the ground be
2D0:45
,
determine the accelerations of both blocks.
Solution
Dynamics 2e 583
Problem 3.115
A force
F0
of
400 lb
is applied to block
B
. Letting the weights of
A
and
B
be 55 and
73 lb
, respectively, and letting the static and kinetic
friction coefficients between blocks
A
and
B
be
1D0:25
, and the
static and kinetic friction coefficients between block
B
and the ground be
2D0:45, determine the accelerations of both blocks.
Solution
Referring to the figure at the right, we sketch individual FBDs for
A
and
B
, each modeled as a particle. We model
A
as subject to its own
584 Solutions Manual
Blocks
A
and
B
are connected by a pulley system. The coefficient
of kinetic friction between the block
A
and the incline is
kD0:25
,
and static friction is insufficient to prevent slipping. The mass of
A
is
mAD7kg
, the mass of
B
is
mBD20 kg
, and the angle between the
incline and the horizontal is
✓D30ı
. Determine the acceleration of
A
, the acceleration of
B
, and the tension in the rope after the system is
released.
Solution
As shown at the right, we model
A
and
B
as particles. We neglect the
inertia and the friction of the pulley system. At the outset we do not
Dynamics 2e 585
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permission of McGraw-Hill, is prohibited.