978-0073380308 Chapter 2 Solution Manual Part 33

subject Type Homework Help
subject Pages 9
subject Words 3459
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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350 Solutions Manual
Problem 2.271
A golfer chips the ball on a flat, level part of a golf course as shown. Letting
˛D23ı
,
ˇD41ı
, and the initial speed be
v0D6m=s
, determine the
x
and
y
coordinates of the place where the ball will land.
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.
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Dynamics 2e 351
Problem 2.272
Relative to the cylindrical coordinate system shown, with origin at
O
, the radial and
´
coordinates of point
G
are
RDdC.L=2/ cos ˇ
and
´D.L=2/ sin ˇ
, respectively, where
dD0:5
m and
LD
0:6
m. The shaft
CD
rotates as shown with a constant angular velocity
!sD10 rad=s
, and the angle
ˇ
varies with time as follows:
ˇD
ˇ0sin.2!t/
, where
ˇ0D0:3 rad
,
!D2rad=s
, and
t
is time in
seconds. Determine the velocity and the acceleration of
G
for
tD3
s
(express the result in the cylindrical component system
.OuR;Ou;Ou´/
,
with OuDOu´OuR).
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.
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352 Solutions Manual
P
R
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.
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Dynamics 2e 353
Problem 2.273
An airplane is traveling at a constant altitude of
10;000 ft
, with
a constant speed of
450 mph
, within the plane whose equation is
given by
xCyD10 mi
and in the direction of increasing
x
. Find
the expressions for
Pr
,
P
,
P
,
Rr
,
R
, and
R
that would be measured
when the airplane is closest to the radar station.
Solution
The figure at the right shows the trace of the path of the airplane on the
xy
plane. Since the airplane is moving along a straight line with constant
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354 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.
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Dynamics 2e 355
Problem 2.274
A carnival ride called the octopus consists of eight arms that rotate about the
´
axis at the constant angular
velocity
P
D6rpm
. The arms have a length
LD22 ft
and form an angle
with the
´
axis. Assuming that
varies with time as
.t/ D0C1sin !t
with
0D70:5ı
,
1D25:5ı
, and
!D1rad=s
, determine
the magnitude of the acceleration of the outer end of an arm when achieves its maximum value.
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.
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356 Solutions Manual
Problem 2.275
A particle is moving over the surface of a right cone with angle
ˇ
and under the constraint that
R2P
DK
, where
K
is a constant. The
equation describing the cone is
RD´tan ˇ
. Determine the expressions
for the velocity and the acceleration of the particle in terms of
K
,
ˇ
,
´
,
and the time derivatives of ´.
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.
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Dynamics 2e 357
Problem 2.276
Solve Prob. 2.275 for general surfaces of revolution; that is,
R
is no
longer equal to
´tan ˇ
, but is now an arbitrary function of
´
, that is,
RDf .´/
. The expressions you need to find will contain
K
,
f .´/
,
derivatives of
f .´/
with respect to
´
, and derivatives of
´
with respect to
time.
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.
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358 Solutions Manual
Problem 2.277
In a racquetball court, at point
P
with coordinates
xPD35 ft
,
yPD16 ft
, and
´PD1ft
, a ball is imparted a speed
v0D90 mph
and a direction defined by the angles
D63ı
and
ˇD8ı
(
ˇ
is the
angle formed by the initial velocity vector and the
xy
plane). The
ball bounces off the left vertical wall to then hit the front wall of
the court. Assume that the rebound off the left vertical wall occurs
such that (1) the component of the ball’s velocity tangent to the
wall before and after rebound is the same and (2) the component of
velocity normal to the wall right after impact is equal in magnitude
and opposite in direction to the same component of velocity right
before impact. Accounting for the effect of gravity, determine the
coordinates of the point on the front wall that will be hit by the ball
after rebounding off the left wall.
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.
page-pfa
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.

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