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1110 Solutions Manual
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FRD270:4 kN:
Dynamics 2e 1111
Problem 5.173
Let
pA
and
pB
be given static pressure measurements at the cross sections
A
and
B
in the air duct shown.
Assume that any cross section between
A
and
B
is circular with diameter
d
. Assume that the flow is steady
and that the mass density
⇢A
at
A
is known along with
vA
, the speed of the flow at
A
, and
vB
, the speed of
the flow at
B
. Determine the expression of mass density at
B
and the expression of the force
F
acting on
the fan.
Solution
The flow under consideration is steady and therefore we will solve this problem applying concepts pertaining
to steady flows systems. We begin with observing that since the mass flow rate
Pm
f
is constant and the cross
sectional area at Aand Bare equal, we must have
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Problem 5.174
A rope with weight per unit length of
0:1 lb=ft
is lifted at a constant
upward speed
v0D8ft=s
. Treating the rope as inextensible, deter-
mine the force applied to the top end of the rope after it is lifted
9ft
.
Assume that the top end of the rope is initially at rest and on the
floor. In addition, disregard the horizontal motion associated with
the uncoiling of the rope.
Solution
To solve this problem we model the portion of the rope that has been lifted as a variable mass
system gaining mass. Hence, referring to the FBD shown to the right, using the appropriate
force balance for variable mass systems and focusing only on the vertical motion, we have
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Dynamics 2e 1113
Problem 5.175
A rope with mass per unit length of
0:05 kg=m
is lifted at a constant
upward acceleration
a0D6m=s2
. Treating the rope as inextensible,
determine the force that must be applied at the top end of the rope
after it is lifted
3
m. Assume that the top end of the rope is initially
at rest and on the floor. In addition, disregard the horizontal motion
associated with the uncoiling of the rope.
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.
Problem 5.176
A rope with mass per unit length of
0:05 kg=m
is lifted by applying a
constant vertical force
FD10
N. Treating the rope as inextensible,
plot the velocity and position of the top end of the string as a function
of time for
0t3
s. Assume that the top end of the rope is
initially at rest and
1mm
off the floor. In addition, disregard the
horizontal motion associated with the uncoiling of the rope.
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.
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.
Problem 5.177
An amateur rocket with a body weight of
6:5 lb
is equipped with a rocket engine
holding
2:54 lb
of solid propellant with a burnout time (time required to burn all
the fuel) of
5:25
s (this is the typical data made available by amateur rocket engine
manufacturers). The initial thrust is
68 lb
. Assuming that the mass flow rate and the
speed of the exhaust relative to the rocket remain constant, determine the exhaust
mass flow rate
Pmo
and the speed relative to the rocket
vo
. In addition, determine
the maximum speed achieved by the rocket
vmax
if the rocket is launched from rest.
Neglect air resistance, and assume that gravity does not change with elevation.
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Dynamics 2e 1117
Letting
vmax
be the speed at burnout, multiplying both sides of the above equation by
dt
and integrating, we
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Problem 5.178
Continue Prob. 5.177 and determine the maximum height reached by the rocket, again
neglecting air resistance and changes of gravity with elevation. Hint: For
0<t<t
0
,
Zln✓1t
t0◆dt D.t0t/1ln✓1t
t0◆CC:
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to time from tD0to tDtbo as follows:
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