DeGarmo's Materials and Processes in Manufacturing
12th Edition
ISBN: 9781118987674
Author: J. T. Black, Ronald A. Kohser
Publisher: WILEY
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Chapter 1, Problem 21RQ
In Figure 1.8, what do the lines connecting the processes represent?
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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 1 Solutions
DeGarmo's Materials and Processes in Manufacturing
Ch. 1 - What role does manufacturing play relative to the...Ch. 1 - Arent all goods really consumer goods, depending...Ch. 1 - The Subway sandwich shop is an example of a job...Ch. 1 - How does a system differ from a process? From a...Ch. 1 - Is a cutting tool the same thing as a machine...Ch. 1 - What are the major classifications of basic...Ch. 1 - Casting is often used to produce a...Ch. 1 - In the lost�wax casting process, what happens to...Ch. 1 - In making a gold medal, what do we mean by a...Ch. 1 - How is a railroad station like a station on an...
Ch. 1 - Because no work is being done on a part when it is...Ch. 1 - What forming processes are used to make a paper...Ch. 1 - What is tooling in a manufacturing system?Ch. 1 - It is acknowledged that chipâ€�type machining is...Ch. 1 - Compare Figures 1.1 and 1.16. What are the...Ch. 1 - In a modern safety razor with three or four blades...Ch. 1 - List three purposes of packaging operations.Ch. 1 - Assembly is defined as the putting together of...Ch. 1 - What are the physical elements in a manufacturing...Ch. 1 - In the production system, who usually figures out...Ch. 1 - In Figure 1.8, what do the lines connecting the...Ch. 1 - Characterize the process of squeezing toothpaste...Ch. 1 - It has been said that low-cost products are more...Ch. 1 - Prob. 24RQCh. 1 - If the rolls for the cold-rolling mill that...Ch. 1 - Make a list of service systems, giving an example...Ch. 1 - What is the fundamental difference between a...Ch. 1 - Prob. 28RQCh. 1 - What kind of process is powder metallurgy: casting...Ch. 1 - In view of Figure 1.2, who really determines the...Ch. 1 - What costs make up manufacturing cost (sometimes...Ch. 1 - What are major phases of a product life cycle?Ch. 1 - How many different manufacturing systems might be...Ch. 1 - In general, as the annual volume for a product...Ch. 1 - The Toyota truck plant in Indiana produces 150,000...Ch. 1 - A company is considering making automobile bumpers...Ch. 1 - Many companies are critically examining the...Ch. 1 - We can analogize your university to a...Ch. 1 - What kind of manufacturing system (design) is your...Ch. 1 - What are the major process steps in the assembly...Ch. 1 - What is the relationship between Figures 1.2Â...
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