I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.


 Philomena Reynolds
 3 years ago
 Views:
Transcription
1 ME 270 Fall 2012 Fnal Exam Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded on the examnaton sheets. If addtonal space s requred, use the whte lned paper provded to you. Work on one sde of each sheet only, wth only one problem on a sheet. Each problem s worth 20 ponts. Please remember that for you to obtan maxmum credt for a problem, t must be clearly presented,.e. The coordnate system must be clearly dentfed. Where approprate, free body dagrams must be drawn. These should be drawn separately from the gven fgures. Unts must be clearly stated as part of the answer. You must carefully delneate vector and scalar quanttes. If the soluton does not follow a logcal thought process, t wll be assumed n error. When handng n the test, please make sure that all sheets are n the correct sequental order and make sure that your name s at the top of every page that you wsh to have graded. Instructor s Name and Secton: Sectons: J. Slvers 11:30am12:20pm E. Nauman 8:309:20am J. Jones 9:3010:20am M. Murphy 9:0010:15am K.M. L 2:303:20pm K.M. L 4:305:20pm Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Total
2 ME 270 Fall 2012 PROBLEM 1 (20 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: In your own words, state each of Newton s three laws of moton. Be sure to wrte legbly. Unreadable defntons wll be marked wrong. 1 st Law = 2 nd Law = 3 rd Law = PROBLEM 1B. (5 ponts) FIND: Two force vectors are shown to the rght. γ defnes the angle between F 1 and the xy plane; φ les n the xy plane; and F 2 les n the xz plane. Wrte F 1 and F 2 n vector form. Values for F 1, F 2 and the angles are gven to the rght. F 1 F N 300 N F 1 (3 pts) F 2 (2 pts)
3 ME 270 Fall 2012 PROBLEM 1C. (5 ponts) FIND: The force P = 120 lb s appled to the Lshaped bar ABC and acts n the drecton of the lne from C to D. Wrte P n vector form. Determne the moment about pont A due to the force P; express your answer n vector form. P M A (2 pts) (3 pts) PROBLEM 1D. (5 ponts) FIND: A cantlevered beam s subjected to the dstrbuted load shown. Determne the equvalent force and ts locaton, measured from the wall. Gve your answers n terms of A and/or L. F eq (2 pts) x (measured from wall on left) (3 pts)
4 ME 270 Fall 2012 PROBLEM 2. (20 ponts) A massless boom s used to support a 180lb load appled at pont D. The boom s attached to the wall at pont O wth a ball and socket and supported by cables at pont A. Please place your answers to the followng questons n the boxes provded. You wll be asked to: a) Complete the freebody for the boom on the fgure provded. (4 ponts) b) Express the tenson n cables n terms of ther known unt vectors and unknown magntudes. (4 ponts) c) Determne the magntude of the tenson n cables. (6 ponts) d) Determne the reactons at pont O. (6 ponts)
5 PROBLEM 2B. Express the tenson n cables T AB and TAC n terms of ther unt vectors and unknown magntudes. (4 ponts) Problem 2C. Determne the magntude of the tenson n cables. (6 ponts)
6 PROBLEM 2D. Determne the reactons at pont O. (6 ponts)
7 ME 270 Fall 2012 PROBLEM 3. (20 ponts) The frame s loaded wth a 1000 lb load as shown. Assume the mass of the members are neglgble compared to the load and that member DF can be treated as a twoforce member. DF has a crosssectonal area of 10 n2. Please place all answers n the box provded. All steps of your work must be shown to earn credt. a) The overall freebody dagram s provded. Complete the ndvdual freebody dagrams on the sketches provded. (4 pts) b) Determne the reacton forces at A and B. (4 pts) c) Determne the load n DF and whether t s n tenson or compresson. (4 pts) d) Determne the axal stress n DF. (4 pts) e) Assumng a sngleshear desgn (see nset pcture) and pn crosssecton of 0.1 n2, determne the shearstress at pn A. (4 pts) a) sngleshear Bx 1,000 lbs Ax Ay B E E C D F D A F b) Ax = Ay = Bx = c) FDF = Tenson or Compresson (Crcle One) d) σdf = e) 1,000 lbs τa =
8 NAME:
9 ME 270 Fall 2012 Problem 4A (10 ponts) A secton has a trapezum shape wth a crcular openng as shown n the followng dagram. The dagram has a scale of 0.2 m correspondng to 1 unt. Take the bottom left corner as the orgn. Calculate the centrod ( XY, ) of the shaded secton. Gve your answers n correct unts. y x (Note: Take the bottom left corner of the secton as the orgn n your calculaton.) X Y
10 Problem 4B (10 ponts) By symmetry, the centrod of the followng shaded secton passes through the axs Z. (a) Determne the second moment of area of the shaded secton passng through the centrod, I C (b) Determne the second moment of area of the shaded secton passng through the axs Z Z, I B You are requred to gve correct unts for the answers. Z Z Z Z The scale of the dagram s 1 unt = 1 nch. I C = I B =
11 NAME:
12 ME 270 Fall 2012 Problem 5 For ths problem, you may use the beam shown below (ts rectangular crosssecton s shown below as well). You may use the followng parameters: L = 6 ft., P = 450 lbs., M B = 250 ft.*lbs., b=4 n., and h = 7 n. Problem 5a. Usng an approprate free body dagram, determne the reactons at ponts C and D. (5 ponts) Problem 5b. Draw a free body dagram correspondng to a secton cut through pont E and show that t s n a state of pure bendng. (3 ponts) Problem 5c. Calculate the maxmum tensle and compressve stresses and locate them on the secton at pont E. (3 ponts)
13 Problem 5d. Draw the shear force and bendng moment dagrams for the beam below. (9 ponts)
14 NAME:
15 ME 270 Fnal Exam Equatons Sprng 2013 Normal Stress and Stran σ F A σ y My I ε σ E L L ε ε ε ε y y ρ FS σ σ Shear Stress and Stran τ V A τ ρ Tρ J τ Gγ G E 2 1 γ δ L π 2 θ For a rectangular crosssecton, τ y 6V h Ah 4 y τ 3V 2A Second Area Moment I y da I 1 12 bh Rectangle I π 4 r I I Ad Crcle Polar Area Moment J π 2 r r Tube Shear Force and Bendng Moment V x V 0 p d M x M 0 V d Buoyancy F =ρgv B Flud Statcs p=ρgh ( ) F = p Lw eq avg Belt Frcton T T L S = e µβ Dstrbuted Loads F eq xf eq = L 0 = L ( ) w x dx 0 Centrods x x= = xda c da y ( ) x w x dx x A = c A y= In 3D, x= y da c da y A c A x V c V Centers of Mass xɶ = xɶ = x ρda cm ρda yɶ = x ρa cm ρa yɶ = y ρda cm ρda y ρa cm ρa
16 Fall 2012 Fnal Exam Answers 1A. Defntons 1B. F 1 = j +154k N F 2 = k N 1C. P = j +40k lbs M A = j +80k lbsft 1D. F = eq 1 AL 4 4 x = 4 5 L 2A. FBDs T = T m + n j +p k = T  j + k B. AB AB AB AB AB AB T AC = TAC mac + nac j +p ACk = TAC  j + k C. T AB = 175 lbs T AC = 175 lbs 2D. O = j +30.0k lbs 3A. FBDs 3B. A x = 857 lbs A y = 1000 lbs B x = 857 lbs 3C. FDF 2500 lbs Compresson 3D. σ DF = 250 ps 3E. A = 13.2 ks 4A. X = m Y = m 4B. I = 178 n c 4 I = 400 n B 4
17 5A. C x = 0 C y = 142 lbs D y = 308 lbs 5B. FBD VE 5C. x 0 & snce the shear stress at pont E equals zero, the beam s n statc equlbrum of pure bendng σ = ps
18 5D.
I have not received unauthorized aid in the completion of this exam.
ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem
More informationIf the solution does not follow a logical thought process, it will be assumed in error.
Group # Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
ME 270 Sprng 2017 Exam 1 NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:
More informationIncrease Decrease Remain the Same (Circle one) (2 pts)
ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne
More informationI certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Examination No. 2 Please review the following statement: Group Number: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Group Number: Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem
More informationIf the solution does not follow a logical thought process, it will be assumed in error.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. If I detect cheating I will write a note on my exam and raise
More informationModule 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur
Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur Instructonal Objectves: At the end o ths lesson, the
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, MskolcEgyetemváros,
More informationI certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
NAME: ME 270 Fall 2012 Examination No. 3  Makeup Please review the following statement: Group No.: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
More informationChapter Eight. Review and Summary. Two methods in solid mechanics  vectorial methods and energy methods or variational methods
Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom  Castglano s frst theorem  Examples 8.4 Prncpal of statonary
More informationDUE: WEDS FEB 21ST 2018
HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant
More informationWeek 9 Chapter 10 Section 15
Week 9 Chapter 10 Secton 15 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationPlease initial the statement below to show that you have read it
EN0: Structural nalyss Exam I Wednesday, March 2, 2005 Dvson of Engneerng rown Unversty NME: General Instructons No collaboraton of any nd s permtted on ths examnaton. You may consult your own wrtten lecture
More informationAP Physics 1 & 2 Summer Assignment
AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: Instructor s Name and Section: (Circle Your Section)
More informationLast Name, First Name. I have not received unauthorized aid in the completion of this exam.
ME 270 Spring 2013 Examination No. 2 Please read and respond to the following statement, I have not received unauthorized aid in the completion of this exam. Agree Disagree Signature INSTRUCTIONS Begin
More informationσ τ τ τ σ τ τ τ σ Review Chapter Four States of Stress Part Three Review Review
Chapter Four States of Stress Part Three When makng your choce n lfe, do not neglect to lve. Samuel Johnson Revew When we use matrx notaton to show the stresses on an element The rows represent the axs
More informationIndeterminate pinjointed frames (trusses)
Indetermnate pnjonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all
More informationSpring 2002 Lecture #13
4450 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallelas Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the mdterm
More informationIf the solution does not follow a logical thought process, it will be assumed in error.
Please indicate your group number (If applicable) Circle Your Instructor s Name and Section: MWF 8:309:20 AM Prof. Kai Ming Li MWF 2:303:20 PM Prof. Fabio Semperlotti MWF 9:3010:20 AM Prof. Jim Jones
More informationORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.
Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams 
More informationSecond Order Analysis
Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to
More informationUNIVERSITY OF BOLTON RAK ACADEMIC CENTRE BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 2017/2018 FINITE ELEMENT AND DIFFERENCE SOLUTIONS
OCD0 UNIVERSITY OF BOLTON RAK ACADEMIC CENTRE BENG(HONS) MECHANICAL ENGINEERING SEMESTER TWO EXAMINATION 07/08 FINITE ELEMENT AND DIFFERENCE SOLUTIONS MODULE NO. AME6006 Date: Wednesda 0 Ma 08 Tme: 0:00
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided
More informationSo far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
More informationChapter 12 Equilibrium & Elasticity
Chapter 12 Equlbrum & Elastcty If there s a net force, an object wll experence a lnear acceleraton. (perod, end of story!) If there s a net torque, an object wll experence an angular acceleraton. (perod,
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationEN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st
EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to
More informationPhysics 207: Lecture 27. Announcements
Physcs 07: ecture 7 Announcements akeup labs are ths week Fnal hwk assgned ths week, fnal quz next week Revew sesson on Thursday ay 9, :30 4:00pm, Here Today s Agenda Statcs recap Beam & Strngs» What
More informationFUZZY FINITE ELEMENT METHOD
FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1s tme nterval. The velocty of the partcle
More informationCOMPLEX NUMBERS AND QUADRATIC EQUATIONS
COMPLEX NUMBERS AND QUADRATIC EQUATIONS INTRODUCTION We know that x 0 for all x R e the square of a real number (whether postve, negatve or ero) s nonnegatve Hence the equatons x, x, x + 7 0 etc are not
More informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationPlease initial the statement below to show that you have read it
EN40: Dynamcs and Vbratons Mdterm Examnaton Thursday March 5 009 Dvson of Engneerng rown Unversty NME: Isaac Newton General Instructons No collaboraton of any knd s permtted on ths examnaton. You may brng
More informationOne Dimensional Axial Deformations
One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The as s taken as the
More informationSTATIC ANALYSIS OF TWOLAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWOLERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc MskolcEgyetemváros
More informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and nonconservatve forces Mechancal Energy Conservaton of Mechancal
More informationGravitational Acceleration: A case of constant acceleration (approx. 2 hr.) (6/7/11)
Gravtatonal Acceleraton: A case of constant acceleraton (approx. hr.) (6/7/11) Introducton The gravtatonal force s one of the fundamental forces of nature. Under the nfluence of ths force all objects havng
More informationSTAT 511 FINAL EXAM NAME Spring 2001
STAT 5 FINAL EXAM NAME Sprng Instructons: Ths s a closed book exam. No notes or books are allowed. ou may use a calculator but you are not allowed to store notes or formulas n the calculator. Please wrte
More informationPhysics 114 Exam 3 Spring Name:
Physcs 114 Exam 3 Sprng 015 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem 4. Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse
More informationPhysics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.
Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays
More informationMath1110 (Spring 2009) Prelim 3  Solutions
Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3  Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.
More informationSCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 2 EXAMINATIONS 2011/2012 DYNAMICS ME247 DR. N.D.D. MICHÉ
s SCHOOL OF COMPUTING, ENGINEERING ND MTHEMTICS SEMESTER EXMINTIONS 011/01 DYNMICS ME47 DR. N.D.D. MICHÉ Tme allowed: THREE hours nswer: ny FOUR from SIX questons Each queston carres 5 marks Ths s a CLOSEDBOOK
More informationEN40: Dynamics and Vibrations. Homework 7: Rigid Body Kinematics
N40: ynamcs and Vbratons Homewor 7: Rgd Body Knematcs School of ngneerng Brown Unversty 1. In the fgure below, bar AB rotates counterclocwse at 4 rad/s. What are the angular veloctes of bars BC and C?.
More informationWeek 11: Chapter 11. The Vector Product. The Vector Product Defined. The Vector Product and Torque. More About the Vector Product
The Vector Product Week 11: Chapter 11 Angular Momentum There are nstances where the product of two vectors s another vector Earler we saw where the product of two vectors was a scalar Ths was called the
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationENGI 1313 Mechanics I
ENGI 11 Mechancs I Lecture 40: Center of Gravty, Center of Mass and Geometrc Centrod Shan Kenny, Ph.D., P.Eng. ssstant Professor Faculty of Engneerng and ppled Scence Memoral Unversty of Nefoundland spkenny@engr.mun.ca
More informationTHERMAL DISTRIBUTION IN THE HCL SPECTRUM OBJECTIVE
ame: THERMAL DISTRIBUTIO I THE HCL SPECTRUM OBJECTIVE To nvestgate a system s thermal dstrbuton n dscrete states; specfcally, determne HCl gas temperature from the relatve occupatons of ts rotatonal states.
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the followg statement: I certify that I have not given unauthorized aid nor have I received aid the completion of this eam. Signature: INSTRUCTIONS Beg each problem the space provided on
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
More informationACTM State Calculus Competition Saturday April 30, 2011
ACTM State Calculus Competton Saturday Aprl 30, 2011 ACTM State Calculus Competton Sprng 2011 Page 1 Instructons: For questons 1 through 25, mark the best answer choce on the answer sheet provde Afterward
More informationFirst Year Examination Department of Statistics, University of Florida
Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am  1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationStrain Energy in Linear Elastic Solids
Duke Unverst Department of Cv and Envronmenta Engneerng CEE 41L. Matr Structura Anass Fa, Henr P. Gavn Stran Energ n Lnear Eastc Sods Consder a force, F, apped gradua to a structure. Let D be the resutng
More informationFirst Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.
Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act
More informationNovember 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project
SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω
More informationMath 217 Fall 2013 Homework 2 Solutions
Math 17 Fall 013 Homework Solutons Due Thursday Sept. 6, 013 5pm Ths homework conssts of 6 problems of 5 ponts each. The total s 30. You need to fully justfy your answer prove that your functon ndeed has
More informationMECHANICS OF MATERIALS
Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng
More informationMEASUREMENT OF MOMENT OF INERTIA
1. measurement MESUREMENT OF MOMENT OF INERTI The am of ths measurement s to determne the moment of nerta of the rotor of an electrc motor. 1. General relatons Rotatng moton and moment of nerta Let us
More informationˆ (0.10 m) E ( N m /C ) 36 ˆj ( j C m)
7.. = = 3 = 4 = 5. The electrc feld s constant everywhere between the plates. Ths s ndcated by the electrc feld vectors, whch are all the same length and n the same drecton. 7.5. Model: The dstances to
More informationand F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points)
ME 270 3 rd Sample inal Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) IND: In your own words, please state Newton s Laws: 1 st Law = 2 nd Law = 3 rd Law = PROBLEM
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: Instructor s Name and Section: (Circle Your Section)
More information8.1 Arc Length. What is the length of a curve? How can we approximate it? We could do it following the pattern we ve used before
.1 Arc Length hat s the length of a curve? How can we approxmate t? e could do t followng the pattern we ve used before Use a sequence of ncreasngly short segments to approxmate the curve: As the segments
More information/ n ) are compared. The logic is: if the two
STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence
More informationPhysics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2
Physcs 607 Exam 1 Please be wellorganzed, and show all sgnfcant steps clearly n all problems. You are graded on your wor, so please do not just wrte down answers wth no explanaton! Do all your wor on
More informationCHAPTER 6. LAGRANGE S EQUATIONS (Analytical Mechanics)
CHAPTER 6 LAGRANGE S EQUATIONS (Analytcal Mechancs) 1 Ex. 1: Consder a partcle movng on a fxed horzontal surface. r P Let, be the poston and F be the total force on the partcle. The FBD s: mgk F 1 x O
More information. You need to do this for each force. Let s suppose that there are N forces, with components ( N) ( N) ( N) = i j k
EN3: Introducton to Engneerng and Statcs Dvson of Engneerng Brown Unversty 3. Resultant of systems of forces Machnes and structures are usually subected to lots of forces. When we analyze force systems
More informationME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH8 LEC 35 Slde 2 Dr.. zz Bazoune Chapter
More informationStrength Requirements for Fore Deck Fittings and Equipment
(Nov 2002) (Rev.1 March 2003) (Corr.1 July 2003) (Rev.2 Nov 2003) (Rev.3 July 2004) (Rev.4 Nov 2004) (Rev.5 May 2010) Strength Requrements for Fore Deck Fttngs and Equpment 1. General 1.1 Ths UR S 27 provdes
More informationRotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa
Rotatonal Dynamcs Physcs 1425 Lecture 19 Mchael Fowler, UVa Rotatonal Dynamcs Newton s Frst Law: a rotatng body wll contnue to rotate at constant angular velocty as long as there s no torque actng on t.
More information1 Matrix representations of canonical matrices
1 Matrx representatons of canoncal matrces 2d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3d rotaton around the xaxs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3d rotaton around the yaxs:
More informationAPPENDIX F A DISPLACEMENTBASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a NonPrismatic Beam
APPENDIX F A DISPACEMENTBASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a NonPrsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development
More informationIn this section is given an overview of the common elasticity models.
Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp
More informationAn influence line shows how the force in a particular member changes as a concentrated load is moved along the structure.
CE 331, Fall 2010 Influence Les for Trusses 1 / 7 An fluence le shows how the force a partcular member changes as a concentrated load s moved along the structure. For eample, say we are desgng the seven
More informationImportant Instructions to the Examiners:
Summer 0 Examnaton Subject & Code: asc Maths (70) Model Answer Page No: / Important Instructons to the Examners: ) The Answers should be examned by key words and not as wordtoword as gven n the model
More information10/23/2003 PHY Lecture 14R 1
Announcements. Remember  Tuesday, Oct. 8 th, 9:30 AM Second exam (coverng Chapters 94 of HRW) Brng the followng: a) equaton sheet b) Calculator c) Pencl d) Clear head e) Note: If you have kept up wth
More informationPHYSICS  CLUTCH CH 28: INDUCTION AND INDUCTANCE.
!! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t  Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways
More informationName (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM
Name (Print) (Last) (First) Instructions: ME 323  Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Circle your lecturer s name and your class meeting time. Gonzalez Krousgrill
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationPhysics 1202: Lecture 11 Today s Agenda
Physcs 122: Lecture 11 Today s Agenda Announcements: Team problems start ths Thursday Team 1: Hend Ouda, Mke Glnsk, Stephane Auger Team 2: Analese Bruder, Krsten Dean, Alson Smth Offce hours: Monday 2:33:3
More informationSection 8.1 Exercises
Secton 8.1 Nonrght Trangles: Law of Snes and Cosnes 519 Secton 8.1 Exercses Solve for the unknown sdes and angles of the trangles shown. 10 70 50 1.. 18 40 110 45 5 6 3. 10 4. 75 15 5 6 90 70 65 5. 6.
More informationPhysics 111: Mechanics Lecture 11
Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 RgdBody Rotaton
More informationSpinrotation coupling of the angularly accelerated rigid body
Spnrotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 Emal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s
More informationAngular Momentum and Fixed Axis Rotation. 8.01t Nov 10, 2004
Angular Momentum and Fxed Axs Rotaton 8.01t Nov 10, 2004 Dynamcs: Translatonal and Rotatonal Moton Translatonal Dynamcs Total Force Torque Angular Momentum about Dynamcs of Rotaton F ext Momentum of a
More informationΔ x. u(x,t) Fig. Schematic view of elastic bar undergoing axial motions
ME67  Handout 4 Vbratons of Contnuous Systems Axal vbratons of elastc bars The fgure shows a unform elastc bar of length and cross secton A. The bar materal propertes are ts densty ρ and elastc modulus
More informationAxial Turbine Analysis
Axal Turbne Analyss From Euler turbomachnery (conservaton) equatons need to Nole understand change n tangental velocty to relate to forces on blades and power m W m rc e rc uc uc e Analye flow n a plane
More informationImportant Dates: Post Test: Dec during recitations. If you have taken the post test, don t come to recitation!
Important Dates: Post Test: Dec. 8 0 durng rectatons. If you have taken the post test, don t come to rectaton! Post Test MakeUp Sessons n ARC 03: Sat Dec. 6, 0 AM noon, and Sun Dec. 7, 8 PM 0 PM. Post
More informationINDETERMINATE STRUCTURES METHOD OF CONSISTENT DEFORMATIONS (FORCE METHOD)
INETNTE STUTUES ETHO OF ONSISTENT EFOTIONS (FOE ETHO) If all the support reactons and nternal forces (, Q, and N) can not be determned by usng equlbrum equatons only, the structure wll be referred as STTIY
More informationΔ x. u(x,t) Fig. Schematic view of elastic bar undergoing axial motions
ME67  Handout 4 Vbratons of Contnuous Systems Axal vbratons of elastc bars The fgure shows a unform elastc bar of length and cross secton A. The bar materal propertes are ts densty ρ and elastc modulus
More information