978-0073380308 Chapter 2 Solution Manual Part 16

subject Type Homework Help
subject Pages 9
subject Words 3998
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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180 Solutions Manual
Problem 2.124
Consider the four points whose positions are given by the vectors
ErAD
2O{C0O
km
,
ErBD2O{C1O
km
,
ErCD2O{C2O
km
, and
ErDD2O{C3O
km
.
Knowing that the magnitude of these vectors is constant and that the angular
velocity of these vectors at a given instant is
E!D5O
krad=s
, apply Eq. (2.48)
to find the velocities
EvA
,
EvB
,
EvC
, and
EvD
. Explain why all the velocity vectors
are the same even though the position vectors are not.
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 181
Problem 2.125
A child on a merry-go-round is moving radially outward at a
constant rate of
4ft=s
. If the merry-go-round is spinning at
30 rpm
,
determine the velocity and acceleration of point
P
on the child
when the child is 0.5 and
2:3 ft
from the spin axis. Express the
answers using the component system shown.
Solution
Let
ErP
denote the position of
P
relative to the origin of the
rq´
coordinate system shown in the problem’s
figure. The origin in question is on the
´
axis, which is fixed. Therefore the velocity and acceleration of
P
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182 Solutions Manual
Problem 2.126
When a wheel rolls without slipping on a stationary surface, the point
O
on the wheel that is in contact
with the rolling surface has zero velocity. With this in mind, consider a nondeformable wheel rolling
without slip on a flat stationary surface. The center of the wheel
P
is traveling to the right with a constant
speed
v0D23 m=s
. Letting
RD0:35
m, determine the angular velocity of the wheel, using the stationary
component system shown.
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 183
Problem 2.127
The radar station at
O
is tracking the meteor
P
as it moves through the
atmosphere. At the instant shown, the station measures the following data
for the motion of the meteor:
rD21;000 ft
,
D40ı
,
PrD22;440 ft=s
,
and
P
D2:935 rad=s
. Use Eq. (2.48) to determine the magnitude and
direction (relative to the
xy
coordinate system shown) of the velocity
vector at this instant.
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-pf5
184 Solutions Manual
Problem 2.128
The radar station at
O
is tracking the meteor
P
as it moves through the
atmosphere. At the instant shown, the station measures the following data
for the motion of the meteor:
rD21;000 ft
,
D40ı
,
PrD22;440 ft=s
,
P
D2:935 rad=s
,
RrD187;500 ft=s2
, and
R
D5:409 rad=s2
. Use the
equation derived in Prob. 2.122 to determine the magnitude and direction
(relative to the
xy
coordinate system shown) of the acceleration vector at
this instant.
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 185
Problem 2.129
A plane
B
is approaching a runway along the trajectory shown while the
radar antenna
A
is monitoring the distance
r
between
A
and
B
, as well
as the angle
. If the plane has a constant approach speed
v0
as shown,
use Eq. (2.48) to determine the expressions for
Pr
and
P
in terms of
r
,
,
v0, and .
Solution
The position of the airplane
B
can be written as
ErDrOur
. Differentiating
Er
with respect to time according to
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186 Solutions Manual
Problem 2.130
A plane
B
is approaching a runway along the trajectory shown with
D15ı
, while the radar antenna
A
is monitoring the distance
r
between
A
and
B
, as well as the angle
. The plane has a constant approach
speed
v0
. In addition, when
D20ı
, it is known that
PrD216 ft=s
and
P
D0:022 rad=s
. Use Eq. (2.48) to determine the corresponding values
of v0and of the distance between the plane and the radar antenna.
Solution
The position of the airplane
B
can be written as
ErDrOur
. Differentiating
Er
with respect to time according to
Eq. (2.48) on p. 81 of the textbook, we obtain the velocity of the airplane as
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Dynamics 2e 187
Problem 2.131
The end
B
of a robot arm is being extended with the constant rate
PrD4ft=s
.
Knowing that
P
D0:4 rad=s
and is constant, use Eq. (2.48) and the equation
derived in Prob. 2.122 to determine the velocity and acceleration of
B
when
rD2ft. Express your answer using the component system shown.
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-pf9
188 Solutions Manual
Problem 2.132
The end
B
of a robot arm is moving vertically down with a constant speed
v0D2m=s
. Letting
dD1:5
m, apply Eq. (2.48) to determine the rate at which
rand are changing when D37ı.
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
Dynamics 2e 189
Problem 2.133
The end
B
of a robot arm is moving vertically down with a constant speed
v0D6ft=s
. Letting
dD4ft
, use Eq. (2.48) and the equation derived in
Prob. 2.122 to determine Pr,P
,Rr, and R
when D0ı.
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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