Vector Mechanics for Engineers: Dynamics MECN 3010

1. Vector Mechanics for Engineers: Dynamics MECN 3010 Department of Mechanical Engineering Inter American University of Puerto Rico Bayamon Campus Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://www.bc.inter.edu/facultad/omeza

2. Syllabus • Catalog Description: : Kinematic analysis of particles and rigid bodies in one, two and three dimensions. Emphasis in curvilinear motion. Application of the Newton ‘s second law, energy and work, impulse and momentum principles on particles and rigid bodies. • Prerequisites: MECN 3005 – Vector Mechanics for Engineers: Statics. • Course Text: Hibbeler, R.C., Engineering Mechanics - Static and Dynamics, 12th. Ed., Prentice Hall, 2009.

3. Syllabus • Absences: On those days when you will be absent, find a friend or an acquaintance to take notes for you or visit the web page. Do not call or send an e-mail the instructor and ask what went on in class, and what the homework assignment is. • Homework assignments: Homework problems will be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on any white paper with no more than one problem written on one sheet of paper. Homework will be collected when due, with your name written legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any reason) will not be accepted.

4. Syllabus • Problem-Solving Technique: • Known • Find • Assumptions • Schematic • Analysis, and • Results • Quiz : There are several partial quizzes during the semester. • Partial Exams and Final Exam: There are three partial exams during the semester, and a final exam at the end of the semester.

5. Course Grading • The total course grade is comprised of homework assignments, quiz, partial exams, and final exam as follows: • Homework 25% • Quiz 25% • Partial Exam (3) 25% • Final Exam 25% • 100% • Cheating: You are allowed to cooperate on homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from others will be considered academic misconduct and will get no points.

6. Course Materials • Most Course Material (Course Notes, Handouts, and Homework) on Web Page of the course MECN 3010: http://facultad.bayamon.inter.edu/omeza/ • Power Point Lectures will posted every week or two • Office Hours: G235 • Contact Email: mezacoe@gmail.com

7. Tentative Lecture Schedule

8. Reference • Bedford, Anthony. and Fowler Wallace., Engineering Mechanics - Statics and Dynamics, 5th Ed., Prentice Hall, 2008. • Beer, F.P. and Johnston, E.R., Vector Mechanics for Engineers - Statics and Dynamics, 8th Ed., McGraw-Hill, 2007. • Meriam J. L.,Kraige L. G., Engineering Mechanics: Statics and Dynamics, 6th Ed., John Wiley & Sons, 2006

9. "Lo peor es educar por métodos basados en el temor, la fuerza, la autoridad, porque se destruye la sinceridad y la confianza, y sólo se consigue una falsa sumisión” Einstein Albert Topic 1: Kinematics of a Particle Introduction and Basic Concepts

10. Chapter Objectives • To introduce the concepts of position, displacement, velocity, and acceleration. • To study particle motion along a straight line and represent this motion graphically. • To investigate particle motion along a curve path using different coordinate systems. • To present an analysis of dependent motion of two particles. • To examine the principles of relative motion of two particles using translating axes.

11. Dynamics Kinematics Kinetics Mass Acceleration Work Energy Analysis of the forces causing the motion Treats only the geometric aspects of the motion 12.1 Introduction. What is dynamics ??? • Study the accelerated motion of a body Impulse Moment

12. 12.1 Introduction. What may happen if dynamic’s is not applied properly ???

13. 12.2 Rectilinear Kinematics: Continuous Motion 1. Rectilinear Kinematics: It is characterized by specifying, at any given instant, the particle’s position, velocity and acceleration. a. Position: The straight-line path of a particle will be defined using a single coordinate axis s. The origin O on the path is a fixed point, and from this point the position coordinate s is used to specify the location of the particle at any time b. Displacement: It is defined as the change in its position and it is also a vector quantity

14. 12.2 Rectilinear Kinematics: Continuous Motion c. Velocity: If the particle moves through a displacement Δsduring the time interval Δt, the average velocity of the particle during this time interval is If we take smaller and smaller values of , the magnitude of becomes smaller and smaller. The instantaneous velocity is a vector defined as The velocity can be positive (+) or negative (-). The magnitude of the velocity is called speed, and it is generally expressed in units of m/s or ft/s.

15. 12.2 Rectilinear Kinematics: Continuous Motion d. Acceleration: Provided the velocity of the particle is known at two points, the average acceleration of the particle during the time interval Δt, is defined as The Δv = v’ - v represents the difference in the velocity during the time interval Δt The instantaneous acceleration is a vector defined as The acceleration can be either positive (+) or negative (-). The magnitude of the acceleration is generally expressed in units of m/s2 or ft/s2.

16. 12.2 Rectilinear Kinematics: Continuous Motion Relating the equations It is obtained an important differentia relation involving displacement, velocity and acceleration Constant Acceleration, a=ac Velocity as a Function of Time. Integrate ac=dv/dt, assuming that initially v=v0 when t=0 (1) Constant Acceleration

17. 12.2 Rectilinear Kinematics: Continuous Motion Position as a Function of Time. Integrate v=ds/dt=v0+act, assuming that initially s=s0 when t=0 (2) Constant Acceleration Velocity as a Function of Position. Substituting the previous equation (1) into the (2) equation or integrate vdv=acds, assuming that initially v=v0 at s=s0 Constant Acceleration

18. Application Problems

27. Homework1  WebPage Due, Thursday, February 01, 2012 Omar E. Meza Castillo Ph.D.