978-0073380308 Chapter 2 Solution Manual Part 22

subject Type Homework Help
subject Pages 9
subject Words 2138
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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240 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 241
Problem 2.177
Recalling that a circle of radius
R
and center at the origin
O
of a Cartesian
coordinate system with axes
x
and
y
can be expressed by the formula
x2Cy2D
R2
, use Eq. (2.59) to verify that the radius of curvature of this circle is equal to
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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242 Solutions Manual
Problem 2.178
A particle
P
is moving along a path with the velocity shown. Discuss in detail whether or not there are
incorrect elements in the sketch of the polar component system at P.
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 243
Problem 2.179
A particle
P
is moving along a path with the velocity shown. Discuss in detail whether or not there are
incorrect elements in the sketch of the polar component system at P.
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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244 Solutions Manual
Problem 2.180
A particle
P
is moving along a path with the velocity shown. Discuss in detail whether or not there are
incorrect elements in the sketch of the polar component system at P.
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 245
Problem 2.181
A particle
P
is moving along a circle with center
C
and radius
R
in the direction shown. Letting
O
be the
origin of a polar coordinate system with the coordinates
r
and
shown, discuss in detail whether or not
there are incorrect elements in the sketch of the polar component system at P.
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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246 Solutions Manual
Problem 2.182
A radar station is tracking a plane flying at a constant altitude with
a constant speed v0D550 mph. If at a given instant rD7mi and
D32ı, determine the corresponding values of Pr,P
,Rr, and R
.
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 247
Problem 2.183
A basketball moves along the trajectory shown. Modeling the motion of the ball as a projectile motion,
determine the radial and transverse components of the acceleration when
D65ı
. Express your answer in
SI units.
Solution
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248 Solutions Manual
Problem 2.184
At a given instant, the merry-go-round is rotating with an angular velocity
!D20 rpm
while the child is
moving radially outward at a constant rate of
0:7 m=s
. Assuming that the angular velocity of the merry-go-
round remains constant, i.e., ˛D0, determine the magnitudes of the speed and of the acceleration of the
child when he is 0:8 m away from the spin axis.
Solution
The child’s velocity is
EvDPrOurCrP
Ou
, where
PrD0:7 m=s
and
P
D!D20 rpm D20.2=60/ rad=s
.
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Dynamics 2e 249
Problem 2.185
At a given instant, the merry-go-round is rotating with an angular
velocity
!D18 rpm
, and it is slowing down at a rate of
0:4 rad=s2
.
When the child is
2:5 ft
away from the spin axis, determine the
time rate of change of the child’s distance from the spin axis so
that the child experiences no transverse acceleration while moving
along a radial line.
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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