Welding: Principles and Applications (MindTap Course List)
8th Edition
ISBN: 9781305494695
Author: Larry Jeffus
Publisher: Cengage Learning
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Chapter 26, Problem 22R
What other properties can a metal's hardness reveal?
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 26 Solutions
Welding: Principles and Applications (MindTap Course List)
Ch. 26 - What gives metals their desirable properties?Ch. 26 - What is heat?Ch. 26 - What are the basic units of measure for heat?Ch. 26 - What is sensible heat?Ch. 26 - Prob. 5RCh. 26 - What does the color of light given off from a hot...Ch. 26 - Prob. 7RCh. 26 - In steel-making, what is ore combined with in the...Ch. 26 - Prob. 9RCh. 26 - What is an alloy?
Ch. 26 - Using Figure 26-18, answer the following...Ch. 26 - What is a eutectic composition?Ch. 26 - Using Table 26-3, what are the lowest and highest...Ch. 26 - Approximately how many degrees wide is the...Ch. 26 - Referring to Figure 26-20, what color would...Ch. 26 - Referring to Figure 26-20, what is the approximate...Ch. 26 - Prob. 17RCh. 26 - Referring to Figure 26-20, above what temperature...Ch. 26 - Prob. 19RCh. 26 - What is known as the critical temperature of...Ch. 26 - Can a metal have all the mechanical properties at...Ch. 26 - What other properties can a metal's hardness...Ch. 26 - Which property, brittleness or ductility, will let...Ch. 26 - What is toughness?Ch. 26 - What are the common types of strength...Ch. 26 - Prob. 26RCh. 26 - What are the three steps in precipitation...Ch. 26 - How do ferrite and cementite work together to form...Ch. 26 - Why is brine quenching faster than water...Ch. 26 - What can be done to speed up the quenching rate in...Ch. 26 - Why is the formation of martensite a problem when...Ch. 26 - How can the effects of cold working be removed?Ch. 26 - Prob. 33RCh. 26 - Referring to Figure 26-20, what would the preheat...Ch. 26 - Why must the stress-relieving temperature be kept...Ch. 26 - What properties can annealing produce in metals?Ch. 26 - How long does it take the weld metal to go through...Ch. 26 - What are some sources of hydrogen that can...Ch. 26 - How can nitrogen get into an SMA weld?Ch. 26 - What are some of the problems that oxygen can...Ch. 26 - When do cold cracks develop?Ch. 26 - What is carbide precipitation?
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