Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137503520
Author: Serope Kalpakjian, Steven Schmid
Publisher: PEARSON+
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Chapter 3, Problem 3.9Q
To determine
The different crystal structures exhibit different strengths and ductilities.
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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)
Chapter 3 Solutions
Pearson eText for Manufacturing Processes for Engineering Materials -- Instant Access (Pearson+)
Ch. 3 - Prob. 3.1QCh. 3 - Prob. 3.2QCh. 3 - Prob. 3.3QCh. 3 - Prob. 3.4QCh. 3 - Prob. 3.5QCh. 3 - Prob. 3.6QCh. 3 - Prob. 3.7QCh. 3 - Prob. 3.8QCh. 3 - Prob. 3.9QCh. 3 - Prob. 3.10Q
Ch. 3 - Prob. 3.11QCh. 3 - Prob. 3.12QCh. 3 - Prob. 3.13QCh. 3 - Prob. 3.14QCh. 3 - Prob. 3.15QCh. 3 - Prob. 3.16QCh. 3 - Prob. 3.17QCh. 3 - Prob. 3.18QCh. 3 - Prob. 3.19QCh. 3 - Prob. 3.20QCh. 3 - Prob. 3.21QCh. 3 - Prob. 3.22QCh. 3 - Prob. 3.23QCh. 3 - Prob. 3.24QCh. 3 - Prob. 3.25QCh. 3 - Prob. 3.26QCh. 3 - Prob. 3.27QCh. 3 - Prob. 3.28QCh. 3 - Prob. 3.29QCh. 3 - Prob. 3.30QCh. 3 - Prob. 3.31QCh. 3 - Prob. 3.32QCh. 3 - Prob. 3.33QCh. 3 - Prob. 3.34QCh. 3 - Prob. 3.35QCh. 3 - Prob. 3.36QCh. 3 - Prob. 3.37QCh. 3 - Prob. 3.38QCh. 3 - Prob. 3.39QCh. 3 - Prob. 3.40QCh. 3 - Prob. 3.41QCh. 3 - Prob. 3.42QCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48PCh. 3 - Prob. 3.49PCh. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54P
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