210 Solutions Manual
Problem 2.151
The position of the piston
C
, as a function of the crank angle
and the
lengths of the crank
AB
and connecting rod
BC
, is given by
yCDRcos C
Lp1.R sin =L/2
and
xCD0
. Using the component system shown, express
Out
, the unit vector tangent to the trajectory of
C
, as a function of the crank angle
for 02⇡rad.
Solution
OutDO|
for
0<<⇡rad
.
OutDO|
for
⇡<< 2⇡rad
.
Out
is undefined at
D0
and
D2⇡rad
Dynamics 2e 211
Problem 2.152
An aerobatics plane initiates the basic loop maneuver such that, at the bottom of the loop, the plane is going
140 mph
, while subjecting the plane to approximately
4g
of acceleration. Estimate the corresponding
radius of the loop.
Solution
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permission of McGraw-Hill, is prohibited.
212 Solutions Manual
Problem 2.153
The portion of a race track between points
A
(corresponding to
xD0
) and
B
is part of a parabolic curve
described by the equation yDx2, where is a constant. Let gdenote the acceleration due to gravity.
Determine
such that a car driving at constant speed
v0D180 mph
experiences at
A
an acceleration
with magnitude equal to 1:5g.
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 213
Problem 2.154
The portion of a race track between points
A
(corresponding to
xD0
) and
B
is part of a parabolic curve
described by the equation yDx2, where is a constant. Let gdenote the acceleration due to gravity.
If
D0:4⇥103ft1
, determine
d
such that a car driving at constant speed
v0D180 mph
experiences
at Ban acceleration with magnitude equal to g.
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.
214 Solutions Manual
Problem 2.155
The portion of a race track between points
A
(corresponding to
xD0
) and
B
is part of a parabolic curve
described by the equation yDx2, where is a constant. Let gdenote the acceleration due to gravity.
Suppose a car travels from Ato Bwith a constant speed v0D180 mph. Let jEajmin and jEajmax denote
the minimum and maximum values of the magnitude of the acceleration, respectively. Determine
jEajmin
if
dD1200 ft and jEajmax D1:5g.
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 215
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.
216 Solutions Manual
Problem 2.156
An airplane is flying straight and level at a constant speed
v0
when it starts climbing along a path described
by the equation yDhCˇx3, where hand ˇare constants. Let gdenote the acceleration due to gravity.
Determine the acceleration of the airplane at xD0.
Solution
Referring to the figure on the right, at
xD0
the tangent and normal di-
rections to the trajectory are parallel to the
x
and the
y
axes, respectively.
Dynamics 2e 217
Problem 2.157
An airplane is flying straight and level at a constant speed
v0
when it starts climbing along a path described
by the equation yDhCˇx3, where hand ˇare constants. Let gdenote the acceleration due to gravity.
If
ˇD0:05⇥103m2
and
v0
remains constant, find
v0
such that the magnitude of the acceleration
of the airplane is equal to 3g for xD300 m.
Solution
The expression of the acceleration in normal-tangential components is
218 Solutions Manual
Problem 2.158
An airplane is flying straight and level at a constant speed
v0
when it starts climbing along a path described
by the equation yDhCˇx3, where hand ˇare constants. Let gdenote the acceleration due to gravity.
If
v0D600 km=h
and
ˇD0:025⇥104m2
, determine the acceleration of the airplane for
xD350
m
and express it in the Cartesian component system shown.
Solution
The expression of the acceleration in normal-tangential components is
EaDPvOutC.v2=⇢/Oun;(1)
Dynamics 2e 219
Problem 2.159
A jet is flying at a constant speed
v0D750 mph
while performing a constant
speed circular turn. If the magnitude of the acceleration needs to remain constant
and equal to
9g
, where
g
is the acceleration due to gravity, determine the radius
of curvature of the turn.
3
3
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.