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Dynamics 2e 657
Problem 3.155
A crate of mass
m
is thrown horizontally with speed
vc
onto an inextensible
conveyor belt that is moving to the right at a constant speed
vb
. Treating the
crate as a particle, knowing that
vb>v
c
, and assuming that the coefficients
of static and kinetic friction between the crate and conveyor are
s
and
k
,
respectively, determine:
(a) the distance the crate slides before it stops slipping relative to the belt,
(b) the time it takes for the crate to stop sliding, and
(c) the distance the crate moves relative to the belt.
Solution
We model the crate as a particle subject to its own weight
mg
, the normal reaction
N
with the conveyor, and the friction force
F
due to the belt. The direction of
F
658 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 659
Problem 3.156
A man
A
is trying to keep his balance while on a metal wedge
B
that is sliding
down an icy incline. Let
mAD78 kg
and
mBD25 kg
be the masses of
A
and
B
, respectively. In addition, let the static and kinetic friction coefficients
between
A
and
B
be
sD0:4
and
kD0:35
, respectively. Determine the
acceleration of
A
if
✓D23ı
. Friction between the wedge and the incline is
negligible.
Solution
We sketch individual FBDs for
A
and
B
modeled as particles. The relevant
forces on
A
are its weight
mAg
, the normal force
NAB
between
A
and
B
, and
660 Solutions Manual
AmBgcos2✓
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 661
Problem 3.157
Derive the equations of motion for the double pendulum shown.
Solution
Referring to the figure at the right, we model the two pendulum bobs as
particles of mass
m1
and
m2
subject to their respective weights,
m1g
and
662 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 663
Problem 3.158
Derive the equations of motion for the double pendulum shown. After doing
so, let
L1D1:4
m,
L2D2
m,
m1D7:5 kg
, and
m2D12 kg
, and release the
pendulum from rest with
✓.0/ D25ı
and
.0/ D37ı
. Integrate the equations
of motion, and plot the trajectory of each of the particles for at least 5s.
Solution
Referring to the figure at the right, we model the two pendulum bobs as
particles of mass
m1
and
m2
subject to their respective weights,
m1g
and
664 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.
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.
666 Solutions Manual
Problem 3.159
Blocks
A
and
B
are connected by the pulley system shown. Friction between
the block
A
and the incline is negligible. The weight of
A
is
WAD12 lb
, the
weight of
B
is
WBD30 lb
, 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. We also neglect friction
Dynamics 2e 667
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.
