EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 28, Problem 44P
Repeat the falling parachutist problem (Example 1.2), but with the upward force due to drag as a second-order rate:
where
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An object is shot upward from the ground with an initial velocity of 640 ft/sec, and
experiencés a constant deceleration of 32 ft/sec² due to gravity as well as a deceleration of
(v(t) / 10) ft/sec due to air resistance, where v(t) is the object's velocity in ft/sec.
(a) Set up and solve an initial-value problem to determine the object's velocity v(t) at time
t.
(b) At what time does the object reach its highest point?
1.
F3
The lateral-direction equations of motion of an aircraft in steady, straight and level
flight are
v=-0.243v-136.25r+9.80-0.7595 +4.825
p+0.0557r=-0.195v-1.695p+0.913r+16.535 +6.995
0.0152p+ 0.106v+0.039p-0.624r +0.3195-6.43%
O=P
(a)
4 €
Consider the state-space representation of the equations of motion given by.
Xlat Alat Alat + Blatulat '
and
where
and
with
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Ylat
5
= Clat Xlat + Dlat lat
Xlat = (V, p, r, $)T
Ylat = (Y1, Y2, 3),
Y₁ =B=V/VR,
Determine the matrices Alat Blat, Clat, and Dlat-
10
F5
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Y2 = r,
6
1)
F6
H
y3 = (ay) eg
7
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F7
= V +136.25r.
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End
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PgUp
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Based on your equations for the above problem, solve for the extension of the spring (in meters) when the variables have values as follows:
angle A is 74.79 degrees
angle B is 44.36 degrees
spring constant k is 123.77 N/m
mass m2 is 2.52 kg
Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 28 - 8.1 Perform the first computation in Sec. 28.1,...Ch. 28 - 28.2 Perform the second computation in Sec. 28.1,...Ch. 28 - A mass balance for a chemical in a completely...Ch. 28 - 28.4 If, calculate the outflow concentration of a...Ch. 28 - 28.5 Seawater with a concentration of 8000 g/m3...Ch. 28 - 28.6 A spherical ice cube (an “ice sphere”) that...Ch. 28 - The following equations define the concentrations...Ch. 28 - 28.8 Compound A diffuses through a 4-cm-long tube...Ch. 28 - In the investigation of a homicide or accidental...Ch. 28 - The reaction AB takes place in two reactors in...
Ch. 28 - An on is other malbatchre actor can be described...Ch. 28 - The following system is a classic example of stiff...Ch. 28 - 28.13 A biofilm with a thickness grows on the...Ch. 28 - 28.14 The following differential equation...Ch. 28 - Prob. 15PCh. 28 - 28.16 Bacteria growing in a batch reactor utilize...Ch. 28 - 28.17 Perform the same computation for the...Ch. 28 - Perform the same computation for the Lorenz...Ch. 28 - The following equation can be used to model the...Ch. 28 - Perform the same computation as in Prob. 28.19,...Ch. 28 - 28.21 An environmental engineer is interested in...Ch. 28 - 28.22 Population-growth dynamics are important in...Ch. 28 - 28.23 Although the model in Prob. 28.22 works...Ch. 28 - 28.25 A cable is hanging from two supports at A...Ch. 28 - 28.26 The basic differential equation of the...Ch. 28 - 28.27 The basic differential equation of the...Ch. 28 - A pond drains through a pipe, as shown in Fig....Ch. 28 - 28.29 Engineers and scientists use mass-spring...Ch. 28 - Under a number of simplifying assumptions, the...Ch. 28 - 28.31 In Prob. 28.30, a linearized groundwater...Ch. 28 - The Lotka-Volterra equations described in Sec....Ch. 28 - The growth of floating, unicellular algae below a...Ch. 28 - 28.34 The following ODEs have been proposed as a...Ch. 28 - 28.35 Perform the same computation as in the first...Ch. 28 - Solve the ODE in the first part of Sec. 8.3 from...Ch. 28 - 28.37 For a simple RL circuit, Kirchhoff’s voltage...Ch. 28 - In contrast to Prob. 28.37, real resistors may not...Ch. 28 - 28.39 Develop an eigenvalue problem for an LC...Ch. 28 - 28.40 Just as Fourier’s law and the heat balance...Ch. 28 - 28.41 Perform the same computation as in Sec....Ch. 28 - 28.42 The rate of cooling of a body can be...Ch. 28 - The rate of heat flow (conduction) between two...Ch. 28 - Repeat the falling parachutist problem (Example...Ch. 28 - 28.45 Suppose that, after falling for 13 s, the...Ch. 28 - 28.46 The following ordinary differential equation...Ch. 28 - 28.47 A forced damped spring-mass system (Fig....Ch. 28 - 28.48 The temperature distribution in a tapered...Ch. 28 - 28.49 The dynamics of a forced spring-mass-damper...Ch. 28 - The differential equation for the velocity of a...Ch. 28 - 28.51 Two masses are attached to a wall by linear...
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