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90 Solutions Manual
Problem 2.50
Approximately 1 h 15 min into the movie King Kong (the one
directed by Peter Jackson), there is a scene in which Kong is
holding Ann Darrow (played by the actress Naomi Watts) in his
hand while swinging his arm in anger. A quick analysis of the
movie indicates that at a particular moment Kong displaces Ann
from rest by roughly
10 ft
in a span of four frames. Knowing that
the DVD plays at 24 frames per second and assuming that Kong
subjects Ann to a constant acceleration, determine the acceleration
Ann experiences in the scene in question. Express your answer
in terms of the acceleration due to gravity
g
. Comment on what
would happen to a person really subjected to this acceleration.
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.
Dynamics 2e 91
Problem 2.51
A car travels on a rectilinear stretch of road at a constant speed
v0D65 mph
. At
sD0
the driver applies
the brakes hard enough to cause the car to skid. Assume that the car keeps sliding until it stops, and assume
that throughout this process the car’s acceleration is given by
RsDkg
, where
kD0:76
is the kinetic
friction coefficient and gis the acceleration of gravity. Compute the car’s stopping distance and time.
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.
92 Solutions Manual
Problem 2.52
If the truck brakes and the crate slides to the right relative to the truck, the horizontal acceleration of the
crate is given by
RsDgk
, where
g
is the acceleration of gravity,
kD0:87
is the kinetic friction
coefficient, and
s
is the position of the crate relative to a coordinate system attached to the ground (rather
than the truck).
Assuming that the crate slides without hitting the right end of the truck bed, determine the time it takes
to stop if its velocity at the start of the sliding motion is v0D55 mph.
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 93
Problem 2.53
If the truck brakes and the crate slides to the right relative to the truck, the horizontal acceleration of the
crate is given by
RsDgk
, where
g
is the acceleration of gravity,
kD0:87
is the kinetic friction
coefficient, and
s
is the position of the crate relative to a coordinate system attached to the ground (rather
than the truck).
Assuming that the crate slides without hitting the right end of the truck bed, determine the distance it
takes to stop if its velocity at the start of the sliding motion is v0D75 km=h.
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.
94 Solutions Manual
Problem 2.54
A sphere is dropped from rest at the free surface of a thick polymer fluid. The
acceleration of the sphere has the form
aDg⌘v
, where
g
is the acceleration due
to gravity, ⌘is a constant, and vis the sphere’s velocity.
The sphere is observed to reach a constant sinking velocity equal to
0:1 m=s
.
Determine ⌘.
Solution
If the sphere achieves what appears to be a constant velocity, then the corresponding acceleration is equal to
Dynamics 2e 95
Problem 2.55
A sphere is dropped from rest at the free surface of a thick polymer fluid. The
acceleration of the sphere has the form
aDg⌘v
, where
g
is the acceleration due
to gravity, ⌘is a constant, and vis the sphere’s velocity.
If
⌘D50 s1
determine the velocity of the sphere after
0:02
s. Express the
result in feet per second.
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.
96 Solutions Manual
Problem 2.56
The motion of a peg sliding within a rectilinear guide is controlled by an actuator in such a way that
the peg’s acceleration takes on the form
RxDa0.2 cos 2!t ˇsin !t/
, where
t
is time,
a0D3:5 m=s2
,
!D0:5 rad=s, and ˇD1:5.
Determine the expressions for the velocity and the position of the peg as functions of time if
Px.0/ D
0m=s and x.0/ D0m.
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 97
Problem 2.57
The motion of a peg sliding within a rectilinear guide is controlled by an actuator in such a way that
the peg’s acceleration takes on the form
RxDa0.2 cos 2!t ˇsin !t/
, where
t
is time,
a0D3:5 m=s2
,
!D0:5 rad=s, and ˇD1:5.
Determine the total distance traveled by the peg during the time interval
0
s
t5
s if
Px.0/ Da0ˇ=!
.
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.
98 Solutions Manual
Problem 2.58
A package is pushed up an incline at
xD0
with an initial speed
v0
. The incline is coated with a thin
viscous layer so that the acceleration of the package is given by
aD.g sin ✓C⌘v/
, where
g
is the
acceleration due to gravity, ⌘is a constant, and vis the velocity of the package.
If
✓D30ı
,
v0D10 ft=s
, and
⌘D8s1
, determine the time it takes for the package to come to a stop.
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.
Dynamics 2e 99
Problem 2.59
A package is pushed up an incline at
xD0
with an initial speed
v0
. The incline is coated with a thin
viscous layer so that the acceleration of the package is given by
aD.g sin ✓C⌘v/
, where
g
is the
acceleration due to gravity, ⌘is a constant, and vis the velocity of the package.
If
✓D25ı
,
v0D7m=s
, and
⌘D8s1
, determine the distance
d
traveled by the package before it
comes to a stop.
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.
