Dynamics 2e 687
Problem 4.18
Two identical cars travel at a speed of
60 mph
, one along a newly asphalt-paved straight and horizontal
road and the other on a straight and horizontal dirt road. If brakes are applied and if the second car slips
during the braking process, what difference will there be in the amount of work done to stop each car?
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Problem 4.19
Two identical locomotives
A
and
B
are coupled with one and two passenger cars, respectively. Suppose
that each passenger car is identical to the others in all respects. If each train (locomotive plus cars) starts
from rest, each locomotive exerts the maximum tractive effort (traction force), and assuming that gravity
and the tractive effort are the only relevant forces acting on the trains, which of the two trains will have
greater kinetic energy after the locomotives have moved 50 m along a horizontal and rectilinear stretch?
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Dynamics 2e 689
Problem 4.20
The crate
A
of weight
WD30 lb
is being pulled to the right by the winch at
B
. The crate starts from rest
at
xD0
and is pulled a total distance of
15 ft
over the rough surface for which the coefficient of kinetic
friction is
kD0:3
. The force
P
in the cable due to the winch varies according to the plot, where
P
is in
lb, bis in lb=pft, and xis in ft. The coefficient of static friction is insufficient to prevent slipping.
Using the work-energy principle, determine the speed of the block when
bD11 lb=pft
and
xD15 ft
.
Solution
Referring to the figure at the right, we model the crate as a
particle subject to its own weight
mg
, the normal reaction
690 Solutions Manual
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Dynamics 2e 691
Problem 4.21
The crate
A
of weight
WD30 lb
is being pulled to the right by the winch at
B
. The crate starts from rest
at
xD0
and is pulled a total distance of
15 ft
over the rough surface for which the coefficient of kinetic
friction is
kD0:3
. The force
P
in the cable due to the winch varies according to the plot, where
P
is in
lb, bis in lb=pft, and xis in ft. The coefficient of static friction is insufficient to prevent slipping.
Using the work-energy principle, determine the value of
b
so that the block is moving at
35 ft=s
when
xD10 ft.
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692 Solutions Manual
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Dynamics 2e 693
Problem 4.22
The crate
A
of weight
WD30 lb
is being pulled to the right by the winch at
B
. The crate starts from rest
at
xD0
and is pulled a total distance of
15 ft
over the rough surface for which the coefficient of kinetic
friction is
kD0:3
. The force
P
in the cable due to the winch varies according to the plot, where
P
is in
lb, bis in lb=pft, and xis in ft. The coefficient of static friction is insufficient to prevent slipping.
Determine how far the crate slides before its speed becomes 20 ft=s with bD11 lb=pft.
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694 Solutions Manual
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Dynamics 2e 695
Problem 4.23
Many advanced materials consist of fibers (e.g., made of glass, Kevlar, or carbon) placed within a matrix
(such as epoxy, a titanium alloy, etc.). For these materials it is important to assess the bond strength
between fibers and matrix, and this is often done with a pullout test, in which the tip of a fiber is exposed,
the material sampled is properly clamped, and the fiber is pulled out of the matrix. The data collected often
consists of a graph like the one shown, in which the force exerted on the fiber is recorded as a function of
pullout displacement. With this in mind, the interface toughness assessment process may require a measure
of the energy expended to pull out the fiber. Use the force-displacement graph shown, which is typical for
a glass-fiber reinforced epoxy, to measure the total pullout energy. Hint: The work of the pullout force is
given by the area under the curve.
Solution
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Problem 4.24
Components subjected to large contact forces (e.g., brake disks) are often made of high-grade steel coated
with a thin film of a very hard material, such as diamond. A common test to assess the mechanical
properties (hardness, elastic moduli, etc.) of the coating is the nanoindentation test, which consists of
making a controlled dent in the film using a nail-like object, called an indentor. During the test, the force
applied to the indentor and the indentation depth are measured. The graph shows the curves interpolating
the loading and unloading data for a diamond film on steel. Since the unloading curve does not go back
to the origin of the plot, the film is permanently deformed during the indentation process. Determine the
energy lost to permanent deformation if the indentation force is given by
FID(25
4xC5
32 x2during loading;
300 145
6xC7
18 x2during unloading;
where FIis expressed in N and the indentation depth xis given in nm.
Solution
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