220 Solutions Manual
Problem 2.160
Particles
A
and
B
are moving in the plane with the same constant speed
v
, and their
paths are tangent at
P
. Do these particles have zero acceleration at
P
? If not, do
these particles have the same acceleration 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.
Dynamics 2e 221
Problem 2.161
Uranium is used in light water reactors to produce a controlled nuclear reaction for the generation of power.
When first mined, uranium comes out as the oxide U3O8, 0.7% of which is the isotope U-235 and 99.3%
the isotope U-238. For it to be used in a nuclear reactor, the concentration of U-235 must be in the 3–5%
range. The process of increasing the percentage of U-235 is called enrichment, and it is done in a number
of ways. One method uses centrifuges, which spin at very high rates to create artificial gravity. In these
centrifuges, the heavy U-238 atoms concentrate on the outside of the cylinder (where the acceleration is
largest), and the lighter U-235 atoms concentrate near the spin axis. Before centrifuging, the uranium is
processed into gaseous uranium hexafluoride or
UF6
, which is then injected into the centrifuge. Assuming
that the radius of the centrifuge is 20 cm and that it spins at 70;000 rpm, determine
(a) The velocity of the outer surface of the centrifuge.
(b)
The acceleration in
g
experienced by an atom of uranium that is on the inside of the outer wall of the
centrifuge.
Photo credit: Courtesy of the Department of Energy
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.
222 Solutions Manual
Problem 2.162
Treating the center of the Earth as a fixed point, determine the magnitude of the
acceleration of points on the surface of the earth as a function of the angle
shown. Use RD6371 km as the radius of the Earth.
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 223
Problem 2.163
An airplane is flying straight and level at a speed
v0D150 mph
and with a constant time rate of increase
of speed
PvD20 ft=s2
, when it starts to climb along a circular path with a radius of curvature
⇢D2000 ft
.
The airplane maintains Pvconstant for about 30 s.
Determine the acceleration of the airplane right at the start of the climb and express the result in the
Cartesian component system shown.
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.
224 Solutions Manual
Problem 2.164
An airplane is flying straight and level at a speed
v0D150 mph
and with a constant time rate of increase
of speed
PvD20 ft=s2
, when it starts to climb along a circular path with a radius of curvature
⇢D2000 ft
.
The airplane maintains Pvconstant for about 30 s.
Determine the acceleration of the airplane
25
s after the start of the climb and express the result in the
Cartesian component system shown.
Solution
Using normal-tangential components, the acceleration can be expressed as
Dynamics 2e 225
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.
226 Solutions Manual
Problem 2.165
An airplane is flying straight and level at a speed
v0D150 mph
and with a constant time rate of increase
of speed
PvD20 ft=s2
, when it starts to climb along a circular path with a radius of curvature
⇢D2000 ft
.
The airplane maintains Pvconstant for about 30 s.
Determine the acceleration of the airplane after it has traveled
150 ft
along the path and express the
result in the Cartesian component system shown.
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 227
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.
228 Solutions Manual
Problem 2.166
Suppose that a highway exit ramp is designed to be a circular
segment of radius
⇢D130 ft
. A car begins to exit the highway at
A
while traveling at a speed of
65 mph
and goes by point
B
with a
speed of
25 mph
. Compute the acceleration vector of the car as a
function of the arc length
s
, assuming that the tangential component
of the acceleration is constant between points Aand B.
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 229
Problem 2.167
Suppose that a highway exit ramp is designed to be a circular
segment of radius
⇢D130 ft
. A car begins to exit the highway at
A
while traveling at a speed of
65 mph
and goes by point
B
with
a speed of
25 mph
. Compute the acceleration vector of the car as
a function of the arc length
s
, assuming that between
A
and
B
the
speed was controlled so as to maintain constant the rate dv=ds.
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.