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476 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 477
Problem 3.46
The force on the mass for the device in Prob. 3.43 and the force on the mass in the Duffing equation
obtained from the device equation of motion (and defined by Eqs. (2) and (3)) can be plotted as a function
of
x
. The nature of that force depends on whether or not the springs are initially stretched (
L>L
0
) or
initially compressed (
L<L
0
). The figure shows the elastic restoring force on the mass
m
as a function of
the displacement xfor four different cases:
Force for device with LD2and L0D1.
Force for device with LD1and L0D2.
Force for the Duffing equation with LD2and L0D1.
Force for the Duffing equation with LD1and L0D2.
For small
x
, the force given by the Duffing equation is a good approximation to the force in the device.
Explain which of the curves corresponds to a “hardening” spring (a spring that gets stiffer as you pull
it) and which corresponds to a “softening” spring (a spring that gets less stiff as you pull it), and explain
physically why we see this behavior.
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.
478 Solutions Manual
Problem 3.47
A train is traveling with constant speed
v0
along the level track
OAB
, which lies in the horizontal plane.
The section between points
O
and
A
is straight, and the section between points
A
and
B
is circular with
radius of curvature
⇢
. The train starts at point
O
at time
tD0
, reaches point
A
at time
tA
, and reaches
point
B
at time
tB
. For this motion, sketch the magnitude of the acceleration vector as a function of time.
Would you want to design a train track with this shape?
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 479
Problem 3.48
A plane is turning along a horizontal path at constant speed. What is the component of force in the direction
of the path acting on the plane?
3
3
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.
480 Solutions Manual
Problem 3.49
Body
D
is in equilibrium when cable
AC
suddenly breaks. If
B
is fixed, does the tension in the inextensible
cable BC increase or decrease at the instant of release?
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 481
Problem 3.50
Body
D
is in equilibrium when cable
AC
suddenly breaks. If
B
is fixed, does the tension in the inextensible
cable BC increase or decrease at the instant of release?
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.
482 Solutions Manual
Problem 3.51
An aircraft carrier is turning with a constant speed
v
along a circular path with radius
⇢
and center
O
.
During the maneuver, a forklift is being driven across the deck of the ship at a constant speed
v0
, relative
to the deck. Does the friction force between the forklift and the deck have a component perpendicular to
the relative velocity of the forklift with respect to the deck?
Solution
The situation depicted in the figure is conceptually identical to “Case 3” in Example 3.11. The forklift must
Dynamics 2e 483
Problem 3.52
A jet is coming out of a dive, and a sensor in the pilot’s seat measures
a force of
800 lb
for a pilot whose weight is
180 lb
. If the jet’s
instruments indicate that the plane is traveling at
850 mph
, determine
the radius of curvature of the plane’s path at this instant.
Solution
484 Solutions Manual
Problem 3.53
A partial cross section of an amusement park ride is shown. While the
ride spins up to the angular speed
!c
, there is a small platform at
F
on
which the person
P
stands. Once the ride reaches the desired angular
speed, the platform falls away and only friction keeps the person from
sliding to the floor of the ride. The wall, against which the person lies,
is inclined at the angle
✓D15ı
with respect to the vertical. Model the
person as a particle that is a distance
dD20 ft
from the spin axis
AB
and let the coefficient of static friction between the person and the wall
be sD0:7.
Determine the minimum value of
!c
at which the platform at
F
can
be withdrawn.
Solution
Dynamics 2e 485
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.
