Manufacturing Engineering & Technology
7th Edition
ISBN: 9780133128741
Author: Serope Kalpakjian, Steven Schmid
Publisher: Prentice Hall
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Textbook Question
Chapter 10, Problem 62SDP
Design an experiment to measure the constants C and n in Chvorinov’s rule, Eq. (10.7). Describe the features of your design, and comment on any difficulties that might be encountered in running such an experiment.
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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 10 Solutions
Manufacturing Engineering & Technology
Ch. 10 - Explain why casting is an important manufacturing...Ch. 10 - Why do most metals shrink when they are cast?Ch. 10 - What are the differences between the...Ch. 10 - What are dendrites? Why are they called so?Ch. 10 - Describe the difference between short and long...Ch. 10 - What is superheat? Is it important? What are the...Ch. 10 - Define shrinkage and porosity. How can you tell...Ch. 10 - What is the function of chills? What are they made...Ch. 10 - Why is the Reynolds number important in casting?Ch. 10 - What is a sprue? What shape should a sprue have if...
Ch. 10 - How is fluidity defined? Why is it important?Ch. 10 - Explain the reasons for hot tearing in castings.Ch. 10 - Why is it important to remove dross or slag during...Ch. 10 - Why is Bernoullis equation important in casting?Ch. 10 - Describe thixocasting and rheocasting.Ch. 10 - What is Chvorinovs Rule?Ch. 10 - How is a blister related to a scab?Ch. 10 - Is there porosity in a chocolate bar? In an ice...Ch. 10 - Describe the stages involved in the contraction of...Ch. 10 - Explain the effects of mold materials on fluid...Ch. 10 - It is known that pouring metal at a high rate into...Ch. 10 - Describe the events depicted in Fig. 10.5.Ch. 10 - Would you be concerned about the fact that...Ch. 10 - Review Fig. 10.8 and make a summary, explaining...Ch. 10 - Make a sketch of volume vs. temperature for a...Ch. 10 - What practical demonstrations can you suggest to...Ch. 10 - Explain why a casting may have to be subjected to...Ch. 10 - List and explain the reasons why porosity can...Ch. 10 - Why does porosity have detrimental effects on the...Ch. 10 - A spoked handwheel is to be cast in gray iron. In...Ch. 10 - Which of the following considerations are...Ch. 10 - Explain why the constant C in Eq. (10.7) depends...Ch. 10 - Are external chills as effective as internal...Ch. 10 - Explain why, as shown in Table 10.1, gray cast...Ch. 10 - Referring to Fig. 10.11, explain why internal...Ch. 10 - Note the shape of the two risers shown in Fig....Ch. 10 - Is there any difference in the tendency for...Ch. 10 - What is the influence of the cross-sectional area...Ch. 10 - It has long been observed that (a) low pouring...Ch. 10 - In casting metal alloys, what would you expect to...Ch. 10 - If you inspect a typical cube of ice, you are...Ch. 10 - How can you tell whether cavities in a casting are...Ch. 10 - Describe the drawbacks to having a riser that is...Ch. 10 - Reproduce Fig. 10.2 for a casting that is...Ch. 10 - List the process variables that affect the...Ch. 10 - Assume that you have a method of measuring...Ch. 10 - A round casting is 0.2 m (7.9 in.) in diameter and...Ch. 10 - A cylinder with a diameter of 2.0 in. and a height...Ch. 10 - The constant C in Chvorinovs rule is given as 2.5...Ch. 10 - Pure copper is poured into a sand mold. The metal...Ch. 10 - For the sprue described in Problem 10.58, what...Ch. 10 - When designing patterns for casting, pattern...Ch. 10 - Can you devise fluidity tests other than that...Ch. 10 - Figure P10.55 indicates various defects and...Ch. 10 - The fluidity test shown in Fig. 10.9 illustrates...Ch. 10 - Utilizing the equipment and materials available in...Ch. 10 - One method of relieving stress concentrations in a...Ch. 10 - Describe the effects on mold design, including the...Ch. 10 - Small amounts of slag often persist after skimming...Ch. 10 - Design an experiment to measure the constants C...
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