Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 7.10, Problem 11KCP
Describe a metal fatigue failure.
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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
B
y(t)
100 L
y(0) = 20 kg
2 L/min
1 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t > 0:
Analytically (hand calculations)
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.
www.m
k₁ = 3
(y₁ = 0).
m₁ = 1
k2=2
(y₂ = 0)
|m₂ = 1
Y2
y 2
System in
static
equilibrium
(Net change in
spring length
=32-31)
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)
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)
Chapter 7 Solutions
Foundations of Materials Science and Engineering
Ch. 7.10 - What are the characteristics of the surface of a...Ch. 7.10 - Prob. 2KCPCh. 7.10 - Prob. 3KCPCh. 7.10 - Prob. 4KCPCh. 7.10 - Prob. 5KCPCh. 7.10 - Prob. 6KCPCh. 7.10 - Prob. 7KCPCh. 7.10 - Prob. 8KCPCh. 7.10 - Prob. 9KCPCh. 7.10 - How does the carbon content of a plain-carbon...
Ch. 7.10 - Describe a metal fatigue failure.Ch. 7.10 - What two distinct types of surface areas are...Ch. 7.10 - Prob. 13KCPCh. 7.10 - Prob. 14KCPCh. 7.10 - Prob. 15KCPCh. 7.10 - Describe the four basic structural changes that...Ch. 7.10 - Describe the four major factors that affect the...Ch. 7.10 - Prob. 18KCPCh. 7.10 - Prob. 19KCPCh. 7.10 - Prob. 20KCPCh. 7.10 - Prob. 21KCPCh. 7.10 - Determine the critical crack length for a through...Ch. 7.10 - Determine the critical crack length for a through...Ch. 7.10 - The critical stress intensity (KIC) for a material...Ch. 7.10 - What is the largest size (in mm) of internal...Ch. 7.10 - A Ti-6Al-4V alloy plate contains an internal...Ch. 7.10 - Using the equation KIC=fa, plot the fracture...Ch. 7.10 - (a) Determine the critical crack length (mm) for a...Ch. 7.10 - A fatigue test is made with a maximum stress of 25...Ch. 7.10 - A fatigue test is made with a mean stress of...Ch. 7.10 - A large, flat plate is subjected to...Ch. 7.10 - Prob. 32AAPCh. 7.10 - Refer to Problem 7.31: Compute the final critical...Ch. 7.10 - Prob. 34AAPCh. 7.10 - Prob. 35AAPCh. 7.10 - Equiaxed MAR-M 247 alloy (Fig. 7.31) is used to...Ch. 7.10 - Prob. 37AAPCh. 7.10 - If DS CM 247 LC alloy (middle graph of Fig. 7.31)...Ch. 7.10 - Prob. 39AAPCh. 7.10 - Prob. 40AAPCh. 7.10 - Prob. 41SEPCh. 7.10 - Prob. 42SEPCh. 7.10 - A Charpy V-notch specimen is tested by the...Ch. 7.10 - Prob. 44SEPCh. 7.10 - Prob. 45SEPCh. 7.10 - Prob. 46SEPCh. 7.10 - Prob. 47SEPCh. 7.10 - Prob. 48SEPCh. 7.10 - Prob. 49SEPCh. 7.10 - Prob. 50SEPCh. 7.10 - While driving your car, a small pebble hits your...Ch. 7.10 - Prob. 52SEPCh. 7.10 - Prob. 53SEPCh. 7.10 - Prob. 54SEPCh. 7.10 - Prob. 56SEPCh. 7.10 - Prob. 57SEPCh. 7.10 - Prob. 58SEPCh. 7.10 - Prob. 59SEPCh. 7.10 - The components in Figure P7.60 are high-strength...
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