978-0077687342 Chapter 14 Part 7

subject Type Homework Help
subject Pages 14
subject Words 1513
subject Authors Brian Self, E. Johnston, Ferdinand Beer, Phillip Cornwell

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PROBLEM 14.89
A toy car is propelled by water that squirts from an internal
tank at a constant 6 ft/s relative to the car. The weight of the
empty car is 0.4 lb and it holds 2 lb of water. Neglecting other
tangential forces, determine the top speed of the car.
SOLUTION
Consider a time interval .t Let m be the mass of the car plus the water in the tank at the beginning of the
interval and
()mm
the corresponding mass at the end of the interval.
0
m
is the initial value of m. Let
v
be
max
max
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PROBLEM 14.90
A toy car is propelled by water that squirts from an internal
tank. The weight of the empty car is 0.4 lb and it holds 2 lb of
water. Knowing the top speed of the car is 8 ft/s, determine the
relative velocity of the water that is being ejected.
SOLUTION
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PROBLEM 14.91
The main propulsion system of a space shuttle consists of three identical
rocket engines which provide a total thrust of 6 MN. Determine the rate at
that the hydrogen-oxygen propellant is burned by each of the three
engines, knowing that it is ejected with a relative velocity of 3750 m/s.
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PROBLEM 14.92
The main propulsion system of a space shuttle consists of three identical
rocket engines, each of which burns the hydrogen-oxygen propellant at
the rate of 750 lb/s and ejects it with a relative velocity of 12000 ft/s.
Determine the total thrust provided by the three engines.
SOLUTION
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PROBLEM 14.93
A rocket sled burns fuel at the constant rate of 120
lb/s. The initial weight of the sled is 1800 lb,
including 360 lb of fuel. Assume that the track is
lubricated and the sled is aerodynamically designed
so that air resistance and friction are negligible. (a)
Derive a formula for the acceleration a of the sled as
a function of time t and the exhaust velocity vex of the
burned fuel relative to the sled. Plot the ratio a/vex
versus time t for the range 0 < t < 4 s, and check the
slope of the graph at t = 0 and t = 4 s using the
formula for a. (b) Determine the ratio of the velocity
vb of the sled at burnout to the exhaust velocity vex.
SOLUTION
dm

55.90 3.727
ex
Plot of a/vex vs. time:
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PROBLEM 14.93 (Continued
ex
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PROBLEM 14.94
A space vehicle describing a circular orbit at a speed of 3
24 10 km/h
releases its front end, a capsule that has a gross mass of 600 kg,
including 400 kg of fuel. If the fuel is consumed at the rate of 18 kg/s
and ejected with a relative velocity of 3000 m/s, determine (a) the
tangential acceleration of the capsule as the engine is fired, (b) the
maximum speed attained by the capsule.
135.9 10 km/hv 
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PROBLEM 14.95
A 540-kg spacecraft is mounted on top of a rocket with a mass of 19 Mg, including 17.8 Mg of fuel.
Knowing that the fuel is consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600
m/s, determine the maximum speed imparted to the spacecraft if the rocket is fired vertically from the
ground.
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PROBLEM 14.96
The rocket used to launch the 540-kg spacecraft of Problem 14.95 is redesigned to include two
stages A and B, each of mass 9.5 Mg, including 8.9 Mg of fuel. The fuel is again consumed at a rate
of 225 kg/s and ejected with a relative velocity of 3600 m/s. Knowing that when stage A expels its
last particle of fuel its casing is released and jettisoned, determine (a) the speed of the rocket at that
instant, (b) the maximum speed imparted to the spacecraft.
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PROBLEM 14.97
The weight of a spacecraft, including fuel, is 11,600 lb when the rocket engines are
fired to increase its velocity by 360 ft/s. Knowing that 1000 lb of fuel is consumed,
determine the relative velocity of the fuel ejected.
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PROBLEM 14.98
The rocket engines of a spacecraft are fired to increase its velocity by 450 ft/s.
Knowing that 1200 lb of fuel is ejected at a relative velocity of 5400 ft/s, determine
the weight of the spacecraft after the firing.
SOLUTION
Apply conservation of momentum to the rocket plus the fuel.
1
W
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PROBLEM 14.99
Determine the distance traveled by the spacecraft of Prob. 14.97 during the rocket
engine firing, knowing that its initial speed was 7500 ft/s and the duration of the
firing was 60 s.
0
qmqt


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PROBLEM 14.99 (Continued)
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PROBLEM 14.100
A rocket weighs 2600 lb, including 2200 lb of fuel, which is consumed at the rate of 25 lb/s and ejected with
a relative velocity of 13000 ft/s. Knowing that the rocket is fired vertically from the ground, determine (a) its
acceleration as it is fired, (b) its acceleration as the last particle of fuel is being consumed, (c) the altitude at
which all the fuel has been consumed, (d) the velocity of the rocket at that time.
SOLUTION
00
mm q
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PROBLEM 14.100 (Continued)
0
0
22
00
2
00 0 0 0
00 00
2
00
11
ln [( ln )]
22
1
ln 1 ln 1 2
1
zz
z
z
mu mu
h z dz gt z z z gt
qq
mu m qt m qt m m
g
t
qm m mm
mu m qt
qt gt











 
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PROBLEM 14.101
Determine the altitude reached by the spacecraft of Problem 14.95 when all the fuel of its launching
rocket has been consumed.
SOLUTION
0
qmqt


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PROBLEM 14.101 (Continued)
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PROBLEM 14.102
For the spacecraft and the two-stage launching rocket of Problem 14.96, determine the altitude at
which (a) stage A of the rocket is released, (b) the fuel of both stages has been consumed.
0
qm


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PROBLEM 14.102 (Continued)
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PROBLEM 14.103
In a jet airplane, the kinetic energy imparted to the exhaust gases is wasted as far as propelling the airplane is
concerned. The useful power is equal to the product of the force available to propel the airplane and the speed
of the airplane. If v is the speed of the airplane and u is the relative speed of the expelled gases, show that the
mechanical efficiency of the airplane is 2/( ).vu v
 Explain why 1
when uv
.

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