Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 2.9, Problem 21KCP
To determine
To describe the five stages that lead to the formation of an ionic solid and to state which of the stages produces energy and which requires energy.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Spur gears
Note : Exam is open notes &tables / Answer all questions.
Q.1. The press shown for Figure.1 has a rated load
of 22 kN. The twin screws have double start Acme
threads, a diameter of 50 mm, and a pitch of 6 mm.
Coefficients of friction are 0.05 for the threads and
0.08 for the collar bearings. Collar diameters are 90
mm. The gears have an efficiency of 95 percent and a
speed ratio of 60:1. A slip clutch, on the motor shaft,
prevents overloading. The full-load motor speed is
1720 rev/min.
(a) When the motor is turned on, how fast will the
press head move? (Vm= , Vser. =
)
(5M)
(b) What should be the horsepower rating of the
motor? (TR=, Tc= Pser. =
"
Bronze
bushings
Foot
Motor
Bearings
watt, Pm= watt, Pm= h.p.) (20M)
2['s
Fig.1
Worm
Collar
bearing
Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 2 Solutions
Foundations of Materials Science and Engineering
Ch. 2.9 - Prob. 1KCPCh. 2.9 - Prob. 2KCPCh. 2.9 - How was the existence of electrons first verified?...Ch. 2.9 - How was the existence of protons first verified?...Ch. 2.9 - What are the similarities and differences among...Ch. 2.9 - Prob. 6KCPCh. 2.9 - Prob. 7KCPCh. 2.9 - Prob. 8KCPCh. 2.9 - Explain the law of chemical periodicity.Ch. 2.9 - Prob. 10KCP
Ch. 2.9 - Prob. 11KCPCh. 2.9 - Prob. 12KCPCh. 2.9 - Prob. 13KCPCh. 2.9 - Prob. 14KCPCh. 2.9 - Prob. 15KCPCh. 2.9 - Prob. 16KCPCh. 2.9 - Prob. 17KCPCh. 2.9 - Describe the terms (a) metallic radius. (b)...Ch. 2.9 - Prob. 19KCPCh. 2.9 - Prob. 20KCPCh. 2.9 - Prob. 21KCPCh. 2.9 - Prob. 22KCPCh. 2.9 - Prob. 23KCPCh. 2.9 - Prob. 24KCPCh. 2.9 - Describe the properties (electrical, mechanical,...Ch. 2.9 - Prob. 26KCPCh. 2.9 - Prob. 27KCPCh. 2.9 - Prob. 28KCPCh. 2.9 - The diameter of a soccer ball is approximately...Ch. 2.9 - Each quarter produced by the U.S. mint is made up...Ch. 2.9 - Sterling silver contains 92.5 wt% silver and 7.5...Ch. 2.9 - Prob. 32AAPCh. 2.9 - Prob. 33AAPCh. 2.9 - Prob. 34AAPCh. 2.9 - Prob. 35AAPCh. 2.9 - Prob. 36AAPCh. 2.9 - Prob. 37AAPCh. 2.9 - Prob. 38AAPCh. 2.9 - Prob. 39AAPCh. 2.9 - Prob. 40AAPCh. 2.9 - Prob. 41AAPCh. 2.9 - Prob. 42AAPCh. 2.9 - Prob. 43AAPCh. 2.9 - Prob. 44AAPCh. 2.9 - Prob. 45AAPCh. 2.9 - Prob. 46AAPCh. 2.9 - Prob. 47AAPCh. 2.9 - Prob. 48AAPCh. 2.9 - Prob. 49AAPCh. 2.9 - Prob. 50AAPCh. 2.9 - Write the electron configurations of the following...Ch. 2.9 - Prob. 52AAPCh. 2.9 - Prob. 53AAPCh. 2.9 - Prob. 54AAPCh. 2.9 - Prob. 55AAPCh. 2.9 - Prob. 56AAPCh. 2.9 - Prob. 57AAPCh. 2.9 - Prob. 58AAPCh. 2.9 - Prob. 59AAPCh. 2.9 - Prob. 60AAPCh. 2.9 - Prob. 61AAPCh. 2.9 - Prob. 62AAPCh. 2.9 - Prob. 63AAPCh. 2.9 - For each bond in the following series of bonds,...Ch. 2.9 - Prob. 65AAPCh. 2.9 - Prob. 66AAPCh. 2.9 - Prob. 67AAPCh. 2.9 - Prob. 68AAPCh. 2.9 - Prob. 69SEPCh. 2.9 - Most modern scanning electron microscopes (SEMs)...Ch. 2.9 - Prob. 71SEPCh. 2.9 - Of the noble gases Ne, Ar, Kr, and Xe, which...Ch. 2.9 - Prob. 73SEPCh. 2.9 - Prob. 74SEPCh. 2.9 - Prob. 75SEPCh. 2.9 - Prob. 76SEPCh. 2.9 - Prob. 77SEPCh. 2.9 - Prob. 78SEPCh. 2.9 - Prob. 79SEPCh. 2.9 - Prob. 80SEPCh. 2.9 - Silicon is extensively used in the manufacture of...Ch. 2.9 - Prob. 82SEPCh. 2.9 - Prob. 83SEPCh. 2.9 - Prob. 84SEPCh. 2.9 - Prob. 85SEPCh. 2.9 - Prob. 86SEPCh. 2.9 - Prob. 87SEPCh. 2.9 - Prob. 88SEPCh. 2.9 - Prob. 89SEPCh. 2.9 - Prob. 90SEPCh. 2.9 - Prob. 91SEPCh. 2.9 - Prob. 92SEP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Understanding Motor ControlsMechanical EngineeringISBN:9781337798686Author:Stephen L. HermanPublisher:Delmar Cengage Learning
Understanding Motor Controls
Mechanical Engineering
ISBN:9781337798686
Author:Stephen L. Herman
Publisher:Delmar Cengage Learning