Vector Mechanics -- Statics

Vector Mechanics -- Statics


Spring 2011
01/18/2011 - 05/15/2011

Course Information

Section 002
MW 9:10AM - 10:30AM
RGC1 331
Saad Eways
(512) 223.3219

Office Hours

No office hours have been entered for this term.


ENGR 2301

Vector Mechanics I: Statics

Spring 2011

Section # and Synonym: Section 002, Synonym 23478.

Meeting Times and Place: MW Lec: 9:10 - 10:30 A. M. Room 331.

Credit: 3 credit hours.

Instructor: Dr. Saad Eways

Office: RGC 309

Office Hours: MW 8:00 AM - 9:00 AM. All my office hours are posted on the bulletin board in front of my office. If you need help in any matter concerning this course and you can not make any of my office hours, you should get in touch with me and I will arrange some office hours which are suitable for you.

Phone: Office 223-3219.

email Address: Under normal circumstances, I answer emails within a 24-hr period.

Textbook: Vector Mechanics for Engineers: Statics, 9th edition, by F. P. Beer, E. R. John- ston Jr., D. F. Mazurek, and E. R. Eisenberg.

Prerequisites: Engineering Physics I (PHYS 2425) or equivalent and credit or registration in Calculus III (MATH 2415). Based on this, I will assume that the student has previous knowledge of vectors, vector addition, the scalar product and the vector product. The stu- dent who is well prepared for this class should know how to do all the problems given on the pretest which will be given on the first day of class. By the second day of class, all students must present documentation showing they have sat- isfied the prerequisites. Examples of documentation: 1) recent grade report, 2) transcript. If you do not have the prerequisites or you can not produce documentation, you should withdraw from the course or you will be withdrawn.

Course Description: Calculus-based study of the composition and resolution of forces. Vector algebra, force systems, free body diagrams; equilibrium of particles, rigid bodies and structures; centroids, distributed loads, friction and moment of inertia.

Methodology: I will introduce the basic ideas quickly and most of the class time will be spent in class discussions and problem solving sessions in which the student will be an active participant.


Twi Exams 50%
Final Exam 30%
Homework 10%
Quizzes and Class Activities 10%

The distribution of grades is as follows:

90 - 100 A
80 - 89 B
79 - 79 C
60 - 69 D
Less than 60 F

Homework quizzes will be given on the day the homework is due and the quiz problem will be one of the homework problems. Class activities will consist of problem solving done in class. If you finish the problem (s) in class you will be given full credit for it. If you do not finish, you will be given partial credit and given the option to finish the problem at home and turn it in the next class and you will be given full credit for it.

Homework: Homework is assigned on a weekly basis and is due at the beginning of the class on the due date. Late Homework Policy: Homework not turned in on the due date is considered late. Late homework is accepted until the next class after the due date and will receive a maximum of 80% of the credit.

Exams: The exams will consist of problem solving like the homework. The first exam will be over chapters 2, 3 and 4. The second exam will be over chapters 5, 6 and 7. The final exam is a cumulative exam and will be given on the last day of the semester.

Subject Matter: In this course we will cover chapters 2 through 9. We will omit some sections in these chapters and I will point them out as we go. Chapter 1 is an introduction and will be reviewed quickly.
Important Note: The time requirement for this class is about 12 hours a week. This much time is needed to study the material carefully, do the homework and prepare yourself for the exams. You need to make sure this much time is available in your schedule. If your other obligations do not allow you to spend the necessary time on this course, I strongly urge you to drop it and take it another semester when you are not so busy with other responsibilities. The time you spend studying and doing homework is the single most important factor in determining how well you do in this class.

Course Policies:

1. Attendance policy:
(a) Quizzes and class activities given in the classroom are 10%in the of the credit. Make-ups are given only in the case of documented absences due to sickness or other extraordinary circumstances. You must show documentation (doctor’s report as an example) which shows that you could not have attended class on that day.
(b) If you have a condition which may force you to miss class several times, I urge you to go to the OSD (Office of Students with Disabilities) and discuss the situation with them. See the note below concerning OSD.
2. Withdrawals: This is your responsibility. The last day to withdraw is Monday 4/25. 3.

3. Incomplete: See the incomplete rule in the college catalog. Generally I do not give incompletes.
4. Scholastic Dishonesty: Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to cheating on an exam, quiz, plagiarizing and unauthorized collaboration with another in prepar- ing outside work. Academic work submitted by students shall be the result of theirthought, research or self expression. Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations and homework.
5. Academic Freedom: Students are free to disagree with instructors on matters of opinion or personal philosophy, and will incur no penalty for doing so. However, instructors will judge work based upon its relation to the current state of mainstream scientific fact and theory. Students are allowed to voice opinions, concerns, com- plaints and suggestions to the instructor. However, it is up to the instructor to decide how to use the student’s comments to meet the class’s best interests.
6. Student Discipline: Matters of student discipline will be adjudicated by the instruc- tor on a case-by-case basis, in conjunction with the Department Head or the Dean. Students may consult with the Office of Students Services or the Assistant Dean on these matters.
7. Office for Students with Disabilities: Each ACC campus offers support services with documented physical or psychological disabilities. Students with disabilities must request reasonable accommodations through the Office for Students with Dis- abilities on the campus where they expect to take the majority of their classes. Stu- dents are encouraged to do this three weeks before the start of the semester.
8. Students Services and Instructional Services: The web address for student ser- vices is php. The web address for instructional services is http://www3.austincc. edu/evpcss/memos/reference.htm. The ACC student handbook can be found at

Important Note on Homework

1. Homework is due at the beginning of class on the due date.
2. Working problems is the single most important way to learn the basic ideas in this course and the best way to prepare yourself for the exams. The solution of engineer- ing problems should follow the standard method followed in the textbook examples and also used in the classroom. This is the engineering method of problem solving. In this method, a free-body-diagram is drawn showing all the forces acting on the object. There may be more than one of these required for the solution of a certain problem. Then the basic idea of the problem is expressed in an equation like the sum of the forces is zero or the sum of the moments is zero. Then an answer is found after some algebraic manipulation. I expect this standard method to be used in the solution of homework problems. I also expect your solution to be neat, organized and logically systematic.
3. Grading of the homework: I will look through your homework to get an idea of the effort you have given, then I will randomly choose two problems and grade them out of 10 points each. The grade you get on these two problems is your grade for the homework set.
4. Important note on homework: The solution of homework problems should be the result of your own work. If I feel that your homework solutions are copied from another student, from a solution manual you have in your possession or from some solutions available online, your homework will not be graded and you will get a zero for that homework set. I will point this out to you and will attempt to resolve the matter to the satisfaction of everyone. In short, copying homework (or anything else concerning this course) will not be tolerated and will be dealt with according to the rules of the College.

When I grade the homework, I look for the following items:
1. Diagram or diagrams showing axes, forces, moments, directions, components, resul- tants, etc.
2. FBD of the object under consideration. This diagram will show all the forces and moments acting on the object.
3. Equations expressing static equilibrium of the object under consideration.
4. Solutions must contain all steps leading to the final answer.
5. Intermediate and final answers must be accompanied by the appropriate units and rounded off to the appropriate number of significant figures. Please see chapter (1) for a discussion of systems of units, unit conversions, problem solution method and numerical accuracy.

6. If a problem has several parts such as (a), (b) and (c), your solution should have corresponding parts clearly labeled (a), (b) and (c).
7. Your homework should be clean, clear and easily readable and well organized such that I am able to read, understand and assign the proper grade. If I can’t read it, I can’t grade it.
Problems which do not follow the above method and do not contain the elements stated above will not be graded and will earn zero credit.


These problems are intended as extra practice. Generally the homework does not give you enough practice to master the concepts and become proficient at solving problems to the point where you can do very well on the exams. The student is encouraged to do as many of these problems as needed to master the concepts. These problems are not to be turned in.

Chapter 2: 3, 7, 11, 19, 25, 30, 38, 44,49, 60, 67, 72, 76, 87, 90, 100, 105, 121

Chapter 3: 1, 6, 9, 12, 14, 25, 50, 54, 71, 72, 75, 84, 89, 101, 102, 107, 115, 151

Chapter 4: 2, 3, 4, 18, 19, 23, 29, 43, 49, 62, 68, 75, 85, 91, 99, 108, 109, 127, 137

Chapter 5: 1, 5, 11, 30, 70, 71, 96, 97, 100, 117, 137, 138

chapter 6: 1, 5, 6, 13, 19, 28, 35, 43, 45, 53, 63, 76, 82, 90, 122, 129, 141

chapter 7: 2,7,9,15,21,24,30,34,36,76,79, 88

chapter 8: 2, 3, 7, 12, 16, 18, 21, 26, 39, 46, 51, 67, 101, 104, 105, 110, 141

Chapter 9: 22, 32, 35, 37, 39, 43, 53, 113

Course Requirements


ENGR 2301

Vector Mechanics I: Statics

Spring 2011

Course Description: Calculus-based study of the composition and resolution of forces. Vector algebra, force systems, freebody diagrams; equilibrium of particles, rigid bodies and structures; centroids, distributed loads, friction and
moment of inertia.
Two exams    50%. 1st exam is over chapters 2, 3 and 4. Exam 2 is over chapters 5, 6, and 7.
Final exam    30%. The final exam is a cumulative exam.
Homework    10%   Homework is assigned on a weekly basis. 8 problems per set two sets per chapter.
Quizzes        10%   Homework quizzes given in class and the quiz problem will be one of the homework problems.
The distribution of grades is as follows:
90 - 100     A
80 - 89    B
70 - 79   C
60 - 69   D
Less than 60   F.

ENGR 2301: Statics, Homework

Chapter Homework Problems Due Date
2 9, 36, 37, 41, 46, 48, 55,61, 63, 67 Wed 1/26
2 77, 83, 85, 99, 109, 111, 114, 137 Wed 2/2
3 3, 8, 10, 21, 22, 24, 49, 53, 55 Mon 2/7
3 70, 81, 82, 88, 106, 119, 120, 129 Mon 2/14
4 1, 22, 28, 31, 38, 46, 55, 66 Wed 2/16
4 94, 106, 114, 115, 121, 122, 133, 152 Mon 2/21
EXAM I Chapters 2, 3, 4 Mon 2/28
5 2, 9, 12, 18, 22, 28, 29, 31 Mon 3/7
5 34, 46, 66, 68, 99, 105, 108, 114 Wed 3/9
6 2, 4, 12, 17, 50, 51, 57, 61 Mon 3/21
6 75, 79, 92, 95, 124, 135, 152, 159 Mon 3/28
7 1, 5, 7, 9, 11, 15, 17, 25 Mon 4/4
7 29, 31, 34, 42, 53, 83, 87, 88 Mon 4/11
EXAM II chapters 5, 6, 7 Mon 4/18
8 1, 8, 9, 11, 17, 19, 27, 32 Mon 4/25
8 48, 54, 57, 69, 103, 107, 112, 126 Mon 5/2
9 3, 21, 31, 36, 50, 51, 55 Wed 5/4
9 112, 117, 129, 133, 141 Mon 5/9
Final Exam Cumulative Wed 5/11


Textbook: Vector Mechanics for Engineers: Statics, 9th edition, by F. P. Beer, E. R. John- ston Jr., D. F. Mazurek, and E. R. Eisenberg.

The subject matter is chapters 1 - 9.

Chapter 1:  Introduction.

Chapter 2: Statics of Particles.

Chapter 3: Rigid Bodies: Equivalent Systems of Forces.

Chapter 4: Equilibrium of Rigid Bodies.

Chapter 5: Distributed Forces: Centroids and Center of Gravity.

Chapter 6: Analysis of Structures.

Chapter 7: Forces in Beams and Cables.

Chapter 8: Friction.

Chapter 9: Distributed forces: Moment of Inertia.

Course Subjects

The course subjects are the materials of the 9 chapters listed above:

1. Force systems, resultants.

2. Equilibrium of particles in two and three dimensions.

3. Moment of force about a point and axis, moment resultants.

4. Equilibrium of rigid bodies.

5. Centroids of areas and volumes and distributed force systems.

6. Structures: Trusses, Frames and Machines.

7. Structures: Internal forces, shear and bending moment.

8. Friction: Static and kinetic friction. Wedges and screws, drive belts and bearing friction.

9. Moment of inertia of sections and areas and mass moment of inertia of plates and bodies.

Student Learning Outcomes/Learning Objectives

Upon successful completion of this course, students will be able to:

  1. State the fundamental principles used in the study of mechanics.
  2. Define magnitude and direction of forces and moments and identify associated scalar and vector products.
  3. Draw free body diagrams for two- and three-dimensional force systems.
  4. Solve problems using the equations of static equilibrium.
  5. Compute the moment of force about a specified point or line.
  6. Replace a system of forces by an equivalent simplified system.
  7. Analyze the forces and couples acting on a variety of objects.
  8. Determine unknown forces and couples acting on objects in equilibrium.
  9. Analyze simple trusses using the method of joints or the method of sections.
  10. Determine the location of the centroid and the center of mass for a system of discrete particles and for objects of arbitrary shape.
  11. Analyze structures with a distributed load.
  12. Calculate moments of inertia for lines, areas, and volumes.
  13. Apply the parallel axis theorem to compute moments of inertia for composite regions.
  14. Solve problems involving equilibrium of rigid bodies subjected to a system of forces and moments that include friction.
  15. Solve problems involving dry sliding friction, including problems with wedges and belts.