EBK MANUFACTURING ENGINEERING & TECHNOL
7th Edition
ISBN: 9780100793439
Author: KALPAKJIAN
Publisher: YUZU
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Chapter 7, Problem 8RQ
What is crazing?
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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 7 Solutions
EBK MANUFACTURING ENGINEERING & TECHNOL
Ch. 7 - Summarize the important mechanical and physical...Ch. 7 - What are the major differences between the (a)...Ch. 7 - List properties that are influenced by the degree...Ch. 7 - What is the difference between condensation...Ch. 7 - Explain the differences between linear, branched,...Ch. 7 - What is the glass-transition temperature?Ch. 7 - List and explain the additives commonly used in...Ch. 7 - What is crazing?Ch. 7 - What are polyblends?Ch. 7 - List the major differences between thermoplastics...
Ch. 7 - What is an elastomer?Ch. 7 - What effects does a plasticizing agent have on a...Ch. 7 - Define the following abbreviations: PMMA, PVC,...Ch. 7 - Explain why it would be advantageous to produce a...Ch. 7 - What are the differences and similarities of...Ch. 7 - Are molecular weight and degree of polymerization...Ch. 7 - Why do polymers need to be dried before...Ch. 7 - What characteristics of polymers make them...Ch. 7 - Do polymers strain harden more than metals or vice...Ch. 7 - Inspect various plastic components in an...Ch. 7 - Give applications for which flammability of...Ch. 7 - What characteristics make polymers advantageous...Ch. 7 - What properties do elastomers have that...Ch. 7 - Do you think that the substitution of plastics for...Ch. 7 - Is it possible for a material to have a hysteresis...Ch. 7 - Observe the behavior of the specimen shown in Fig....Ch. 7 - Add more to the applications column in Table 7.3.Ch. 7 - Discuss the significance of the glass-transition...Ch. 7 - Prob. 29QLPCh. 7 - Explain how cross-linking improves the strength of...Ch. 7 - Describe the methods by which the optical...Ch. 7 - How can polymers be made to conduct electricity?...Ch. 7 - Explain the reasons for which elastomers were...Ch. 7 - Give several examples of plastic products or...Ch. 7 - Describe your opinions regarding the recycling of...Ch. 7 - Explain how you would go about determining the...Ch. 7 - Compare the values of the elastic modulus, given...Ch. 7 - Why is there so much variation in the stiffness of...Ch. 7 - Explain why thermoplastics are easier to recycle...Ch. 7 - Give an example where crazing is desirable.Ch. 7 - Describe the principle behind shrink wrapping.Ch. 7 - List and explain some environmental pros and cons...Ch. 7 - List the characteristics required of a polymer for...Ch. 7 - How can you tell whether a part is made of a...Ch. 7 - As you know, there are plastic paper clips...Ch. 7 - By incorporating small amounts of a blowing agent,...Ch. 7 - In injection-molding operations (Section 19.3), it...Ch. 7 - From an environmental standpoint, do you feel it...Ch. 7 - Calculate the areas under the stressstrain curve...Ch. 7 - Prob. 50QTPCh. 7 - Prob. 51QTPCh. 7 - Estimate the number of molecules in a typical...Ch. 7 - Using strength and density data, determine the...Ch. 7 - Prob. 54QTPCh. 7 - Prob. 55SDPCh. 7 - Describe the design considerations involved in...Ch. 7 - Assume that you are manufacturing a product in...Ch. 7 - Assume you work for a company that produces...Ch. 7 - Prob. 59SDPCh. 7 - Make a list of products or parts that currently...Ch. 7 - Prob. 61SDPCh. 7 - Prob. 62SDPCh. 7 - Prob. 63SDPCh. 7 - Prob. 64SDPCh. 7 - With Table 7.3 as a guide, inspect various...
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