F R. + F 3x. + F 2y. = (F 1x. j + F 3x. i + F 2y. i F 3y. i + F 1y. j F 2x. ) i + (F 1y. ) j. F 2x. F 3y. = (F ) i + (F ) j. ) j

Size: px
Start display at page:

Download "F R. + F 3x. + F 2y. = (F 1x. j + F 3x. i + F 2y. i F 3y. i + F 1y. j F 2x. ) i + (F 1y. ) j. F 2x. F 3y. = (F ) i + (F ) j. ) j"

Transcription

1 General comments: closed book and notes but optional one page crib sheet allowed. STUDY: old exams, homework and power point lectures! Key: make sure you can solve your homework problems and exam problems. There will be approx. 6 8 problems and possibly some multiple choices. Good luck! 1. Chapter 2: Finding resultants of vectors (i.e. addition of vectors), resolving vectors into rectangular components (i.e. Cartesian vector notation). a. Graphical approaches (2D, recommend for 2 forces): triangle method, polygon method, parallelogram method. b. Multiple forces find resultant by resolving forces into their rectangular components c. You should be able to express resultants by magnitude and direction OR by rectangular components, I, j and k (Cartesian vector notation). Example 1 (example 2 1) : Find resultant force using triangle method. Specify resultant by magnitude and direction. Also, specify resultant in Cartesian vector notation (i.e. i, j rectangular components): Answer: Example 2: Find the resultant of the 3 force system by breaking forces into rectangular components and adding. Express resultant in Cartesian vector notation and by magnitude and direction (angle it makes with the x axis: 1

2 Step 1 is to resolve each force into its components. Step 2 is to add all the x components together, followed by adding all the y components together. These two totals are the x and y components of the resultant vector. F R = F 1 + F 2 + F 3 = F 1x i + F 1y j F 2x i + F 2y j + F 3x i F 3y j = (F 1x F 2x + F 3x ) i + (F 1y + F 2y F 3y ) j = (F Rx ) i + (F Ry ) j Step 3 is to specify resultant by magnitude and direction: Or Cartesian vector notation: F R = (F ) i + (F ) j Rx Ry Example 3: What if 3D?? Same approach as example 2 except need to break a 3D force up into components. How do you break a 3D force up into components??? Option 1 if given coordinate (directional) angles: F = Fcos(θ ) F = Fcos(θ ) F = Fcos(θ ) x x y y z z 2

3 Option 2 If know line of action: F x = F(d x /d) F y = F(d y /d) F z = F(d z /d) Where d = total displacement = d d 2 x d 2 y d 2 z Option 2a Same as 2 except use position vectors (books method): a) Find the position vector, r, along two points on that line. AB b) Find the unit vector describing the line s direction, u AB = (r /r ). AB AB c) Multiply the unit vector by the magnitude of the force, F = F u AB. Then add up I, j and k components and express resultant vector: F R = (F Rx ) i + (F Ry ) j + (F Rz ) k what if want to specify resultant as magnitude and direction? Example 3: Find the resultant of the two 3D forces shown below: 3

4 2. Chapter 3: springs, coplanar force systems, 2D static particle equilibrium, intro to FBDs and reaction forces. Example 1: Find tension in each cable CA and CB for an angle theta = 40 degrees and a 10 kg cylinder. Note, can also give you tension forces and ask you to calculate mass or give you tension forces, mass and ask you to calculate angle, etc Step 1: Draw FBD joint C Step 2: break each force up into components as detailed above. Step 3: Apply scalar equations of static equilibrium and solve for unknowns: ΣF x = 0 ΣF y = 0 ΣF z = 0 (if 3D) Other 2D static equilibrium problems we ve solved in class: Example 2: For the 3D system shown, determine cable forces necessary to support the 40 lb crate. Solve this problem on board!! End of Exam 1 Material!! 4

5 3. Chapter 4: principle of moments, moment of a force, force couples, equivalent force systems (recall a general system of forces and moments acting on a rigid body can be reduced to a single equivalent force and single equivalent moment) Example: 4. (simplification of a force and couple system). Given: A 2-D force system with geometry as shown. Find: The equivalent resultant force and couple moment acting at A and then the equivalent single force location measured from A. 4. Chapter 5: 2D rigid body equilibrium, reaction forces, stability, FBD s, 2 Force members: Example: Find reactions at A, C and D. Draw FBD s for beam A C B and 2 Force member D C. Other 2D Rigid Body Equilibrium examples we did in class find reactions for the following: 5

6 More 2D Equilibrium: Recall, this problem was a stability problem. What counterweight is necessary to prevent tipping? Key: at point of tipping, Nc = 0. Chapter 5, Part 2 3D Rigid Body Equilibruim (study powerpoint, know 3D reactions, how to draw FBDs and simple 3D rigid body equilibrium problems): Recall for 3D there are six scalar equations of equilibrium (EofE). These are: F X = F Y = F Z = 0 M X = M Y = M Z = 0 End of Exam 2 Material!! 6

7 Chapter 6: Structural analysis for trusses, zero force members, assumptions for truss analysis, method of joints. Example: Determine the force in each member of the truss and state if the members are in tension or compression: Structural analysis for frames and machines, pulleys, mechanical advantage, etc. Examples we did in class: 7

8 End of Exam 3!! 5. Chapter 8 Friction: Just sections 8.1, 8.2, 8.3. Dry friction, inclined planes, sliding vs. static equilibrium (i.e. friction high enough to prevent sliding), tipping, wedges, etc. Determine the minimum horizontal force, P, required to hold the crate from sliding down the plane. The crate has a mass of 50 kg and the coefficient of static friction between the create and plane is 0.25) 8

9 What angle can the ladder be before it slips if the coef of friction at A between the friction pad and ground is 0.4. The man weighs 180 lb. Neglect friction at B. 6. Chapter 9: centroids and moment of inertia. Know how to calculate centroids for composite shapes. Know how to calculate moment of inertia for composite shapes using parallel axis theorem. The moment of inertia calculated w.r.t. centroid (note for the inertia problem I may give you the centroid location. Example: Find centroid location, then find moment of inertia, Ix thru centroid: Note, due to symmetry, centroid is located at x = 0 so you only need to find y bar. 9

STATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.

STATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved. STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle

More information

TABLE OF CONTENTS. Preface...

TABLE OF CONTENTS. Preface... TABLE OF CONTENTS Preface...................................... xiv 1 Introduction........................................ 1 1.1 Engineering and Statics.............................. 1 1.2 A Brief History

More information

REVIEW. Final Exam. Final Exam Information. Final Exam Information. Strategy for Studying. Test taking strategy. Sign Convention Rules

REVIEW. Final Exam. Final Exam Information. Final Exam Information. Strategy for Studying. Test taking strategy. Sign Convention Rules Final Exam Information REVIEW Final Exam (Print notes) DATE: WEDNESDAY, MAY 12 TIME: 1:30 PM - 3:30 PM ROOM ASSIGNMENT: Toomey Hall Room 199 1 2 Final Exam Information Comprehensive exam covers all topics

More information

STATICS SECOND EDITION

STATICS SECOND EDITION Engineering Mechanics STATICS SECOND EDITION Michael E. Plesha Department of Engineering Physics University of Wisconsin-Madison Gary L. Gray Department of Engineering Science and Mechanics Penn State

More information

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. In-Class

More information

MEE224: Engineering Mechanics Lecture 4

MEE224: Engineering Mechanics Lecture 4 Lecture 4: Structural Analysis Part 1: Trusses So far we have only analysed forces and moments on a single rigid body, i.e. bars. Remember that a structure is a formed by and this lecture will investigate

More information

MECHANICS. Prepared by Engr. John Paul Timola

MECHANICS. Prepared by Engr. John Paul Timola MECHANICS Prepared by Engr. John Paul Timola MECHANICS a branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces. subdivided

More information

2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system.

2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system. Code No: R21031 R10 SET - 1 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions

More information

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3

Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 2 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the

More information

Announcements. Equilibrium of a Particle in 2-D

Announcements. Equilibrium of a Particle in 2-D nnouncements Equilibrium of a Particle in 2-D Today s Objectives Draw a free body diagram (FBD) pply equations of equilibrium to solve a 2-D problem Class ctivities pplications What, why, and how of a

More information

EQUATIONS OF MOTION: RECTANGULAR COORDINATES

EQUATIONS OF MOTION: RECTANGULAR COORDINATES EQUATIONS OF MOTION: RECTANGULAR COORDINATES Today s Objectives: Students will be able to: 1. Apply Newton s second law to determine forces and accelerations for particles in rectilinear motion. In-Class

More information

Questions from all units

Questions from all units Questions from all units S.NO 1. 1 UNT NO QUESTON Explain the concept of force and its characteristics. BLOOMS LEVEL LEVEL 2. 2 Explain different types of force systems with examples. Determine the magnitude

More information

E 490 FE Exam Prep. Engineering Mechanics

E 490 FE Exam Prep. Engineering Mechanics E 490 FE Exam Prep Engineering Mechanics 2008 E 490 Course Topics Statics Newton s Laws of Motion Resultant Force Systems Moment of Forces and Couples Equilibrium Pulley Systems Trusses Centroid of an

More information

Name. ME 270 Fall 2005 Final Exam PROBLEM NO. 1. Given: A distributed load is applied to the top link which is, in turn, supported by link AC.

Name. ME 270 Fall 2005 Final Exam PROBLEM NO. 1. Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Name ME 270 Fall 2005 Final Exam PROBLEM NO. 1 Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Find: a) Draw a free body diagram of link BCDE and one of link

More information

The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by

The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by Unit 12 Centroids Page 12-1 The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by (12-5) For the area shown

More information

FE Statics Review. Sanford Meek Department of Mechanical Engineering Kenn 226 (801)

FE Statics Review. Sanford Meek Department of Mechanical Engineering Kenn 226 (801) FE Statics Review Sanford Meek Department of Mechanical Engineering Kenn 226 (801)581-8562 meek@mech.utah.edu Statics! forces = 0!moments = 0 2 Vectors Scalars have magnitude only Vectors have magnitude

More information

ENGINEERING MECHANICS - Question Bank

ENGINEERING MECHANICS - Question Bank E Semester-_IST YEAR (CIVIL, MECH, AUTO, CHEM, RUER, PLASTIC, ENV,TT,AERO) ENGINEERING MECHANICS - Question ank All questions carry equal marks(10 marks) Q.1 Define space,time matter and force, scalar

More information

Announcements. Equilibrium of a Rigid Body

Announcements. Equilibrium of a Rigid Body Announcements Equilibrium of a Rigid Body Today s Objectives Identify support reactions Draw a free body diagram Class Activities Applications Support reactions Free body diagrams Examples Engr221 Chapter

More information

STATICS & DYNAMICS. Engineering Mechanics. Gary L. Gray. Francesco Costanzo. Michael E. Plesha. University of Wisconsin-Madison

STATICS & DYNAMICS. Engineering Mechanics. Gary L. Gray. Francesco Costanzo. Michael E. Plesha. University of Wisconsin-Madison Engineering Mechanics STATICS & DYNAMICS SECOND EDITION Francesco Costanzo Department of Engineering Science and Mechanics Penn State University Michael E. Plesha Department of Engineering Physics University

More information

1. Replace the given system of forces acting on a body as shown in figure 1 by a single force and couple acting at the point A.

1. Replace the given system of forces acting on a body as shown in figure 1 by a single force and couple acting at the point A. Code No: Z0321 / R07 Set No. 1 I B.Tech - Regular Examinations, June 2009 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile

More information

Equilibrium of a Particle

Equilibrium of a Particle ME 108 - Statics Equilibrium of a Particle Chapter 3 Applications For a spool of given weight, what are the forces in cables AB and AC? Applications For a given weight of the lights, what are the forces

More information

Eng Sample Test 4

Eng Sample Test 4 1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by

More information

ENGR-1100 Introduction to Engineering Analysis. Lecture 13

ENGR-1100 Introduction to Engineering Analysis. Lecture 13 ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body

More information

Engineering Mechanics: Statics in SI Units, 12e

Engineering Mechanics: Statics in SI Units, 12e Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle Chapter Objectives To introduce the concept of the free-body diagram for a particle To show how to solve particle equilibrium

More information

CHAPTER 2: EQUILIBRIUM OF RIGID BODIES

CHAPTER 2: EQUILIBRIUM OF RIGID BODIES For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be zero Summation of all external forces. Equilibrium: Sum of moments of all external forces.

More information

Course Overview. Statics (Freshman Fall) Dynamics: x(t)= f(f(t)) displacement as a function of time and applied force

Course Overview. Statics (Freshman Fall) Dynamics: x(t)= f(f(t)) displacement as a function of time and applied force Course Overview Statics (Freshman Fall) Engineering Mechanics Dynamics (Freshman Spring) Strength of Materials (Sophomore Fall) Mechanism Kinematics and Dynamics (Sophomore Spring ) Aircraft structures

More information

Vector Mechanics: Statics

Vector Mechanics: Statics PDHOnline Course G492 (4 PDH) Vector Mechanics: Statics Mark A. Strain, P.E. 2014 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org www.pdhcenter.com

More information

Name ME 270 Summer 2006 Examination No. 1 PROBLEM NO. 3 Given: Below is a Warren Bridge Truss. The total vertical height of the bridge is 10 feet and each triangle has a base of length, L = 8ft. Find:

More information

KINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK UNIT I - PART-A

KINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK UNIT I - PART-A KINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK Sub. Code: CE1151 Sub. Name: Engg. Mechanics UNIT I - PART-A Sem / Year II / I 1.Distinguish the following system of forces with a suitable

More information

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.

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. 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 information

Final Exam - Spring

Final Exam - Spring EM121 Final Exam - Spring 2011-2012 Name : Section Number : Record all your answers to the multiple choice problems (1-15) by filling in the appropriate circle. All multiple choice answers will be graded

More information

Last Name, First Name. I have not received unauthorized aid in the completion of this exam.

Last 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 information

Final Examination Study Set 1. (Solutions will be in the Solutions Manual of Textbook)

Final Examination Study Set 1. (Solutions will be in the Solutions Manual of Textbook) Final Examination Study Set 1 (Solutions will be in the Solutions Manual of Textbook) Final Examination Study Set 2 (Solutions will be in the Solutions Manual of Textbook) 3/86 The shaft, lever,

More information

SKAA 1213 Engineering Mechanics

SKAA 1213 Engineering Mechanics SKAA 1213 Engineering Mechanics TOPIC 6 FRICTION Lecturers: Rosli Anang Dr. Mohd Yunus Ishak Dr. Tan Cher Siang Lesson 7 Outline Introduction Equilibrium on a horizontal plane Equilibrium i on an inclined

More information

Announcements. Trusses Method of Joints

Announcements. Trusses Method of Joints Announcements Mountain Dew is an herbal supplement Today s Objectives Define a simple truss Trusses Method of Joints Determine the forces in members of a simple truss Identify zero-force members Class

More information

Engineering Mechanics: Statics in SI Units, 12e

Engineering Mechanics: Statics in SI Units, 12e Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle 1 Chapter Objectives Concept of the free-body diagram for a particle Solve particle equilibrium problems using the equations

More information

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.

More information

ENG202 Statics Lecture 16, Section 7.1

ENG202 Statics Lecture 16, Section 7.1 ENG202 Statics Lecture 16, Section 7.1 Internal Forces Developed in Structural Members - Design of any structural member requires an investigation of the loading acting within the member in order to be

More information

Unit 21 Couples and Resultants with Couples

Unit 21 Couples and Resultants with Couples Unit 21 Couples and Resultants with Couples Page 21-1 Couples A couple is defined as (21-5) Moment of Couple The coplanar forces F 1 and F 2 make up a couple and the coordinate axes are chosen so that

More information

e14 - applied mechanics: statics e14 - applied mechanics: statics mon/wed/fri, 12:50-2:05pm, syllabus e14 - applied mechanics: statics

e14 - applied mechanics: statics e14 - applied mechanics: statics mon/wed/fri, 12:50-2:05pm, syllabus e14 - applied mechanics: statics e14 - applied mechanics: statics e14 - applied mechanics: statics mon/wed/fri, 12:50-2:05pm, 370-3701 e14 - applied mechanics: statics regular final mon, 06/06/11, 8:30-10:30am, 120 min, cubaud regular

More information

Static Equilibrium; Torque

Static Equilibrium; Torque Static Equilibrium; Torque The Conditions for Equilibrium An object with forces acting on it, but that is not moving, is said to be in equilibrium. The first condition for equilibrium is that the net force

More information

Set No - 1 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS

Set No - 1 I B. Tech I Semester Regular Examinations Jan./Feb ENGINEERING MECHANICS 3 Set No - 1 I B. Tech I Semester Regular Examinations Jan./Feb. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Question Paper Consists

More information

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.

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. 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 information

6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads.

6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads. 6.6 FRAMES AND MACHINES APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a

More information

Appendix. Vectors, Systems of Equations

Appendix. Vectors, Systems of Equations ppendix Vectors, Systems of Equations Vectors, Systems of Equations.1.1 Vectors Scalar physical quantities (e.g., time, mass, density) possess only magnitude. Vectors are physical quantities (e.g., force,

More information

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

I 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 information

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns b) Identify support reactions c) Recognize

More information

EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS

EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. READING

More information

ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division

ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division ES226 (01) Engineering Mechanics: Statics Spring 2018 Lafayette College Engineering Division Exam 1 Study Guide Exam 1: Tuesday, February 6, 2018 7:30 to 8:30pm Kirby Room 104 Exam Format: 50 minute time

More information

READING QUIZ. 2. When using the method of joints, typically equations of equilibrium are applied at every joint. A) Two B) Three C) Four D) Six

READING QUIZ. 2. When using the method of joints, typically equations of equilibrium are applied at every joint. A) Two B) Three C) Four D) Six READING QUIZ 1. One of the assumptions used when analyzing a simple truss is that the members are joined together by. A) Welding B) Bolting C) Riveting D) Smooth pins E) Super glue 2. When using the method

More information

ME 230 Kinematics and Dynamics

ME 230 Kinematics and Dynamics ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 6: Particle Kinetics Kinetics of a particle (Chapter 13) - 13.4-13.6 Chapter 13: Objectives

More information

FE Sta'cs Review. Torch Ellio0 (801) MCE room 2016 (through 2000B door)

FE Sta'cs Review. Torch Ellio0 (801) MCE room 2016 (through 2000B door) FE Sta'cs Review h0p://www.coe.utah.edu/current- undergrad/fee.php Scroll down to: Sta'cs Review - Slides Torch Ellio0 ellio0@eng.utah.edu (801) 587-9016 MCE room 2016 (through 2000B door) Posi'on and

More information

Spring 2018 Lecture 28 Exam Review

Spring 2018 Lecture 28 Exam Review Statics - TAM 210 & TAM 211 Spring 2018 Lecture 28 Exam Review Announcements Concept Inventory: Ungraded assessment of course knowledge Extra credit: Complete #1 or #2 for 0.5 out of 100 pt of final grade

More information

ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER /13

ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER /13 ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER 2 2012/13 COURSE NAME: ENGINEERING MECHANICS - STATICS CODE: ENG 2008 GROUP: AD ENG II DATE: May 2013 TIME: DURATION: 2 HOURS INSTRUCTIONS: 1. This

More information

Chapter 4: Newton s Second Law F = m a. F = m a (4.2)

Chapter 4: Newton s Second Law F = m a. F = m a (4.2) Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.

More information

C7047. PART A Answer all questions, each carries 5 marks.

C7047. PART A Answer all questions, each carries 5 marks. 7047 Reg No.: Total Pages: 3 Name: Max. Marks: 100 PJ DUL KLM TEHNOLOGIL UNIVERSITY FIRST SEMESTER.TEH DEGREE EXMINTION, DEEMER 2017 ourse ode: E100 ourse Name: ENGINEERING MEHNIS PRT nswer all questions,

More information

ENGINEERING MECHANICS SOLUTIONS UNIT-I

ENGINEERING MECHANICS SOLUTIONS UNIT-I LONG QUESTIONS ENGINEERING MECHANICS SOLUTIONS UNIT-I 1. A roller shown in Figure 1 is mass 150 Kg. What force P is necessary to start the roller over the block A? =90+25 =115 = 90+25.377 = 115.377 = 360-(115+115.377)

More information

Hong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 1 PRINCIPLES OF STATICS

Hong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 1 PRINCIPLES OF STATICS PRINCIPLES OF STTICS Statics is the study of how forces act and react on rigid bodies which are at rest or not in motion. This study is the basis for the engineering principles, which guide the design

More information

if the initial displacement and velocities are zero each. [ ] PART-B

if the initial displacement and velocities are zero each. [ ] PART-B Set No - 1 I. Tech II Semester Regular Examinations ugust - 2014 ENGINEERING MECHNICS (Common to ECE, EEE, EIE, io-tech, E Com.E, gri. E) Time: 3 hours Max. Marks: 70 Question Paper Consists of Part- and

More information

EQUILIBRIUM OF A RIGID BODY

EQUILIBRIUM OF A RIGID BODY EQUILIBRIUM OF A RIGID BODY Today s Objectives: Students will be able to a) Identify support reactions, and, b) Draw a free diagram. APPLICATIONS A 200 kg platform is suspended off an oil rig. How do we

More information

LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action

LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC 107 1. Concurrent forces are those forces whose lines of action 1. Meet on the same plane 2. Meet at one point 3. Lie

More information

Physics 101 Lecture 5 Newton`s Laws

Physics 101 Lecture 5 Newton`s Laws Physics 101 Lecture 5 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department The Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law qfrictional forces q Examples

More information

Chapter 2: Statics of Particles

Chapter 2: Statics of Particles CE297-A09-Ch2 Page 1 Wednesday, August 26, 2009 4:18 AM Chapter 2: Statics of Particles 2.1-2.3 orces as Vectors & Resultants orces are drawn as directed arrows. The length of the arrow represents the

More information

M D P L sin x FN L sin C W L sin C fl cos D 0.

M D P L sin x FN L sin C W L sin C fl cos D 0. 789 roblem 9.26 he masses of the ladder and person are 18 kg and 90 kg, respectively. he center of mass of the 4-m ladder is at its midpoint. If D 30, what is the minimum coefficient of static friction

More information

CIV100: Mechanics. Lecture Notes. Module 1: Force & Moment in 2D. You Know What to Do!

CIV100: Mechanics. Lecture Notes. Module 1: Force & Moment in 2D. You Know What to Do! CIV100: Mechanics Lecture Notes Module 1: Force & Moment in 2D By: Tamer El-Diraby, PhD, PEng. Associate Prof. & Director, I2C University of Toronto Acknowledgment: Hesham Osman, PhD and Jinyue Zhang,

More information

PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION

PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION Today s Objectives: Students will be able to: 1. Apply the three equations of motion for a rigid body in planar motion. 2. Analyze problems involving translational

More information

Course Review. Physics 2210 Fall Semester 2014

Course Review. Physics 2210 Fall Semester 2014 Course Review Physics 2210 Fall Semester 2014 Announcements Unit 21 Simple and Physical Pendula (Nov 24th) HW Due 11/25th as usual No new material Wednesday November 26th. In-class discussion of problems

More information

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd

Chapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of the free-body diagram for a rigid body. To show how to solve rigid-body equilibrium problems using

More information

Engineering Mechanics: Statics in SI Units, 12e

Engineering Mechanics: Statics in SI Units, 12e Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If 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 8:30-9:20 AM Prof. Kai Ming Li MWF 2:30-3:20 PM Prof. Fabio Semperlotti MWF 9:30-10:20 AM Prof. Jim Jones

More information

SOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. + c F y = 0; N B = 0

SOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. + c F y = 0; N B = 0 8 1. The mine car and its contents have a total mass of 6 Mg and a center of gravity at G. If the coefficient of static friction between the wheels and the tracks is m s = 0.4 when the wheels are locked,

More information

If the solution does not follow a logical thought process, it will be assumed in error.

If 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 information

Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions.

Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions. Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions 1. Find the resultant force and its direction for the given figure 2. Two forces are acting at a point O as shown in

More information

CHAPTER 4 NEWTON S LAWS OF MOTION

CHAPTER 4 NEWTON S LAWS OF MOTION 62 CHAPTER 4 NEWTON S LAWS O MOTION CHAPTER 4 NEWTON S LAWS O MOTION 63 Up to now we have described the motion of particles using quantities like displacement, velocity and acceleration. These quantities

More information

Vectors. Example: Example: 2 cm. Parts of a vector: 3 cm. Body / Line Segment. Tail / Toe. Tip / Head

Vectors. Example: Example: 2 cm. Parts of a vector: 3 cm. Body / Line Segment. Tail / Toe. Tip / Head Vectors The study of motion involves the introduction of a variety of quantities which are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity,

More information

NEWTON S LAWS OF MOTION (EQUATION OF MOTION) (Sections )

NEWTON S LAWS OF MOTION (EQUATION OF MOTION) (Sections ) NEWTON S LAWS OF MOTION (EQUATION OF MOTION) (Sections 13.1-13.3) Today s Objectives: Students will be able to: a) Write the equation of motion for an accelerating body. b) Draw the free-body and kinetic

More information

Outline: Frames Machines Trusses

Outline: Frames Machines Trusses Outline: Frames Machines Trusses Properties and Types Zero Force Members Method of Joints Method of Sections Space Trusses 1 structures are made up of several connected parts we consider forces holding

More information

STATICS. Bodies. Vector Mechanics for Engineers: Statics VECTOR MECHANICS FOR ENGINEERS: Design of a support

STATICS. Bodies. Vector Mechanics for Engineers: Statics VECTOR MECHANICS FOR ENGINEERS: Design of a support 4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies 2010 The McGraw-Hill Companies,

More information

Hours / 100 Marks Seat No.

Hours / 100 Marks Seat No. 17204 15162 3 Hours / 100 Marks Seat No. Instructions : (1) All Questions are compulsory. (2) Answer each next main Question on a new page. (3) Illustrate your answers with neat sketches wherever necessary.

More information

Introduction to Engineering Analysis - ENGR1100 Course Description and Syllabus Tuesday / Friday Sections. Spring '13.

Introduction to Engineering Analysis - ENGR1100 Course Description and Syllabus Tuesday / Friday Sections. Spring '13. Introduction to Engineering Analysis - ENGR1100 Course Description and Syllabus Tuesday / Friday Sections Spring 2013 Back exams, HW solutions, and other useful links can be found at the following website:

More information

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.

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. 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 information

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE ENGS STATICS

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE ENGS STATICS STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE PREPARED BY: ARTHUR HURLBUT, Ph.D. P.E.(October 2006) UPDATED BY: MICHAEL J. NEWTOWN, P.E. (October 2006) REVISED BY:

More information

EGN 3310 Practice Final Spring 2017

EGN 3310 Practice Final Spring 2017 EGN 3310 Practice Final Spring 2017 *Try finishing each problem in 15 minutes or less to practice test-like time contraints. The topics on the practice exam are what I feel have been stressed in class,

More information

Faculty of Engineering and Department of Physics Engineering Physics 131 Final Examination Saturday April 21, 2018; 14:00 pm 16:30 pm

Faculty of Engineering and Department of Physics Engineering Physics 131 Final Examination Saturday April 21, 2018; 14:00 pm 16:30 pm Faculty of Engineering and Department of Physics Engineering Physics 131 Final Examination Saturday April 21, 2018; 14:00 pm 16:30 pm 1. Closed book exam. No notes or textbooks allowed. 2. Formula sheets

More information

NAME: Section: RIN: Tuesday, May 19, :00 11:00. Problem Points Score Total 100

NAME: Section: RIN: Tuesday, May 19, :00 11:00. Problem Points Score Total 100 RENSSELAER POLYTECHNIC INSTITUTE TROY, NY FINAL EXAM INTRODUCTION TO ENGINEERING ANALYSIS (ENGR-1100) NAME: Section: RIN: Tuesday, May 19, 2015 8:00 11:00 Problem Points Score 1 20 2 20 3 20 4 20 5 20

More information

CHARACTERISTICS OF DRY FRICTION & PROBLEMS INVOLVING DRY FRICTION

CHARACTERISTICS OF DRY FRICTION & PROBLEMS INVOLVING DRY FRICTION CHARACTERISTICS OF DRY FRICTION & PROBLEMS INVOLVING DRY FRICTION Today s Objective: Students will be able to: a) Understand the characteristics of dry friction. b) Draw a FBD including friction. c) Solve

More information

CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5

CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5 1 / 40 CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa 2 / 40 EQUATIONS OF MOTION:RECTANGULAR COORDINATES

More information

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS

EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and b) Recognize two-force members. In-Class

More information

b) Fluid friction: occurs when adjacent layers in a fluid are moving at different velocities.

b) Fluid friction: occurs when adjacent layers in a fluid are moving at different velocities. Ch.6 Friction Types of friction a) Dry friction: occurs when non smooth (non ideal) surfaces of two solids are in contact under a condition of sliding or a tendency to slide. (also called Coulomb friction)

More information

1. The horizontal beam represented in Examination Figure 6 carries three loads P 1. and R 2

1. The horizontal beam represented in Examination Figure 6 carries three loads P 1. and R 2 Student ID: 52573847 Exam: 286037RR - Engineering Mechanics, Part 2 When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you hit Submit Exam.

More information

three Equilibrium 1 and planar trusses ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture ARCH 614

three Equilibrium 1 and planar trusses ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture ARCH 614 ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture three equilibrium and planar trusses Equilibrium 1 Equilibrium balanced steady resultant of forces

More information

A. Objective of the Course: Objectives of introducing this subject at second year level in civil branches are: 1. Introduction 02

A. Objective of the Course: Objectives of introducing this subject at second year level in civil branches are: 1. Introduction 02 Subject Code: 0CL030 Subject Name: Mechanics of Solids B.Tech. II Year (Sem-3) Mechanical & Automobile Engineering Teaching Credits Examination Marks Scheme Theory Marks Practical Marks Total L 4 T 0 P

More information

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)

More information

FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a

FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations

More information

MARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.

MARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment. Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL

More information

LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action

LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC 107 1. Concurrent forces are those forces whose lines of action 1. Meet on the same plane 2. Meet at one point 3. Lie

More information

ME 201 Engineering Mechanics: Statics. Final Exam Review

ME 201 Engineering Mechanics: Statics. Final Exam Review ME 201 Engineering Mechanics: Statics inal Exam Review inal Exam Testing Center (Proctored, 1 attempt) Opens: Monday, April 9 th Closes : riday, April 13 th Test ormat 15 Problems 10 Multiple Choice (75%)

More information

Engineering Mechanics: Statics STRUCTURAL ANALYSIS. by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics

Engineering Mechanics: Statics STRUCTURAL ANALYSIS. by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics CHAPTER Engineering Mechanics: Statics STRUCTURAL ANALYSIS College of Engineering Department of Mechanical Engineering Tenth Edition 6a by Dr. Ibrahim A. Assakkaf SPRING 2007 ENES 110 Statics Department

More information

Chapter 12 Static Equilibrium

Chapter 12 Static Equilibrium Chapter Static Equilibrium. Analysis Model: Rigid Body in Equilibrium. More on the Center of Gravity. Examples of Rigid Objects in Static Equilibrium CHAPTER : STATIC EQUILIBRIUM AND ELASTICITY.) The Conditions

More information

The case where there is no net effect of the forces acting on a rigid body

The case where there is no net effect of the forces acting on a rigid body The case where there is no net effect of the forces acting on a rigid body Outline: Introduction and Definition of Equilibrium Equilibrium in Two-Dimensions Special cases Equilibrium in Three-Dimensions

More information