200 Solutions Manual
Problem 2.141
A particle
P
is moving along the curve
C
, whose equation is given
by
y2x2.x 1/.2x 3/ D4x2Cy22x2;
at a constant speed
vc
. For any position on the curve
C
for
which the radius of curvature is defined (i.e., not equal to infinity),
what must be the angle
between the velocity vector
Ev
and the
acceleration vector Ea?
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 201
Problem 2.142
A particle
P
is moving along a path with the velocity shown. Is the sketch of the normal-tangential
component system at Pcorrect?
Solution
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permission of McGraw-Hill, is prohibited.
202 Solutions Manual
Problem 2.143
A particle
P
is moving along a path with the velocity shown. Is the sketch of the normal-tangential
component system at Pcorrect?
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 203
Problem 2.144
A particle
P
is moving along a straight line with the velocity and acceleration shown. What is wrong with
the unit vectors shown in the figure?
Solution
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permission of McGraw-Hill, is prohibited.
204 Solutions Manual
Problem 2.145
A particle
P
is moving along some path with the velocity and acceleration shown. Can the path of
P
be
the straight line shown?
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 205
Problem 2.146
The water jet of a fountain is let out at a speed
v0D80 ft=s
and at an angle
ˇD60ı
. Determine the radius
of curvature of the jet at its highest point.
Solution
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permission of McGraw-Hill, is prohibited.
206 Solutions Manual
Problem 2.147
A telecommunications satellite is made to orbit the Earth in such a way as to appear to
hover in the same point in the sky as seen by a person standing on the surface of the
Earth. Assuming that the satellite’s orbit is circular with radius
rgD1:385 ⇥108ft
and
knowing that the speed of the satellite is constant and equal to
vgD1:008 ⇥104ft=s
, determine the
magnitude of the acceleration of the satellite.
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 207
Problem 2.148
A car travels along a city roundabout with radius
⇢D30
m. At the instant shown, the speed of the car
is
vD35 km=h
and the magnitude of the acceleration of the car is
4:5 m=s2
. If the car is increasing its
speed, determine the time rate of change of the speed of the car at the instant shown.
Solution
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permission of McGraw-Hill, is prohibited.
208 Solutions Manual
Problem 2.149
A car travels along a city roundabout with radius
⇢D100 ft
. At the instant shown, the speed of the car is
vD25 mph
and the speed is decreasing at the rate
8ft=s2
. Determine the magnitude of the acceleration of
the car at the instant shown.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 209
Problem 2.150
Making the same assumptions stated in Example 2.15, consider the map of the Formula 1 circuit at
Hockenheim in Germany and estimate the radius of curvature of the curves Südkurve and Nordkurve (at
the locations indicated in gold).
Photo credit: Courtesy of FIA
Solution
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permission of McGraw-Hill, is prohibited.