| Date post: | 02-Jan-2016 |
| Category: |
Documents |
| Upload: | valerie-arnold |
| View: | 220 times |
| Download: | 2 times |
LectureLecture
11Vector Mechanics for Engineers: Vector Mechanics for Engineers:
DynamicsDynamics MECN 3010 MECN 3010
Department of Mechanical EngineeringDepartment of Mechanical Engineering
Inter American University of Puerto RicoInter American University of Puerto Rico
Bayamon CampusBayamon Campus
Dr. Omar E. Meza CastilloDr. Omar E. Meza [email protected]
http://www.bc.inter.edu/facultad/omeza
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Catalog DescriptionCatalog Description: : : Kinematic analysis of : Kinematic analysis of particles and rigid bodies in one, two and three particles and rigid bodies in one, two and three dimensions. Emphasis in curvilinear motion. dimensions. Emphasis in curvilinear motion. Application of the Newton ‘s second law, energy Application of the Newton ‘s second law, energy and work, impulse and momentum principles on and work, impulse and momentum principles on particles and rigid bodies.particles and rigid bodies.
Prerequisites: Prerequisites: MECN 3005 – Vector Mechanics for MECN 3005 – Vector Mechanics for Engineers: Statics.Engineers: Statics.
Course Text: Course Text: Hibbeler, R.C., Hibbeler, R.C., Engineering Engineering Mechanics - Static and DynamicsMechanics - Static and Dynamics, 12, 12thth. Ed., . Ed., Prentice Hall, 2009.Prentice Hall, 2009.
22
SyllabusSyllabus
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Absences:Absences: On those days when you will be absent, On those days when you will be absent, find a friend or an acquaintance to take notes for find a friend or an acquaintance to take notes for you or visit the web page. you or visit the web page. Do not call or send an Do not call or send an e-mail the instructor and ask what went on in e-mail the instructor and ask what went on in class, and what the homework assignment is.class, and what the homework assignment is.
Homework assignments:Homework assignments: Homework problems will Homework problems will be assigned on a regular basis. Problems will be be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on solved using the Problem-Solving Technique on any white paper with no more than one problem any white paper with no more than one problem written on one sheet of paper. Homework will be written on one sheet of paper. Homework will be collected when due, with your name written collected when due, with your name written legibly on the front of the title page. It is graded legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any on a 0 to 100 points scale. Late homework (any reason) reason) will not be acceptedwill not be accepted..
33
SyllabusSyllabus
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Problem-Solving Technique:Problem-Solving Technique:
A.A. KnownKnown
B.B. FindFind
C.C. AssumptionsAssumptions
D.D. SchematicSchematic
E.E. Analysis, andAnalysis, and
F.F. ResultsResults
Quiz : Quiz : There are several partial quizzes during the There are several partial quizzes during the semester.semester.
Partial Exams and Final Exam: Partial Exams and Final Exam: There are three There are three partial exams during the semester, and a final partial exams during the semester, and a final exam at the end of the semester.exam at the end of the semester.
44
SyllabusSyllabus
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on Course GradingCourse Grading
The total course grade is comprised of homework The total course grade is comprised of homework assignments, quiz, partial exams, and final exam assignments, quiz, partial exams, and final exam as follows:as follows: HomeworkHomework 25%25% QuizQuiz 25%25% Partial Exam (3) Partial Exam (3) 25%25% Final ExamFinal Exam
25%25%
100%100% Cheating: Cheating: You are allowed to cooperate on You are allowed to cooperate on
homework by sharing ideas and methods. Copying homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from will not be tolerated. Submitted work copied from others will be considered academic misconduct others will be considered academic misconduct and and will get no pointswill get no points..
55
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Most Course Material (Course Notes, Handouts, Most Course Material (Course Notes, Handouts, and Homework) on Web Page of the course MECN and Homework) on Web Page of the course MECN 3010:3010:
http://facultad.bayamon.inter.edu/omeza/ Power Point Lectures will posted every week or Power Point Lectures will posted every week or
twotwo Office Hours: G235Office Hours: G235 Contact Email: Contact Email: [email protected]
66
Course MaterialsCourse Materials
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
77
Tentative Lecture ScheduleTentative Lecture Schedule
TopicTopic LectureLecture
Kinematics of a ParticleKinematics of a Particle 11
Kinetics of a Particle: Force and AccelerationKinetics of a Particle: Force and Acceleration
Kinetics of a Particle: Work and EnergyKinetics of a Particle: Work and Energy
Kinetics of a Particle: Impulse and MomentumKinetics of a Particle: Impulse and Momentum
Planar Kinematics of a Rigid BodyPlanar Kinematics of a Rigid Body
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
88
ReferenceReference
Bedford, Anthony. and Fowler WallaceBedford, Anthony. and Fowler Wallace., ., Engineering Engineering Mechanics - Statics and DynamicsMechanics - Statics and Dynamics, 5, 5thth Ed., Prentice Ed., Prentice Hall, 2008.Hall, 2008.
Beer, F.P. and Johnston, E.RBeer, F.P. and Johnston, E.R., ., Vector Mechanics for Vector Mechanics for Engineers - Statics and DynamicsEngineers - Statics and Dynamics, 8, 8thth Ed., McGraw-Hill, Ed., McGraw-Hill, 2007.2007.
Meriam J. L.,Kraige L. GMeriam J. L.,Kraige L. G., ., Engineering Mechanics: Statics Engineering Mechanics: Statics and Dynamicsand Dynamics, 6, 6thth Ed., John Wiley & Sons, 2006 Ed., John Wiley & Sons, 2006
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Introduction and Basic ConceptsIntroduction and Basic Concepts
Topic 1: Kinematics of a Topic 1: Kinematics of a ParticleParticle
99
"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 AlbertEinstein Albert
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Chapter ObjectivesChapter Objectives
To introduce the concepts of position, To introduce the concepts of position, displacement, velocity, and acceleration.displacement, velocity, and acceleration.
To study particle motion along a straight To study particle motion along a straight line and represent this motion graphically.line and represent this motion graphically.
To investigate particle motion along a To investigate particle motion along a curve path using different coordinate curve path using different coordinate systems.systems.
To present an analysis of dependent To present an analysis of dependent motion of two particles.motion of two particles.
To examine the principles of relative To examine the principles of relative motion of two particles using translating motion of two particles using translating axes.axes.
1010
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on 12.1 Introduction. 12.1 Introduction. What is dynamics ???What is dynamics ???
Study the accelerated motion of a body
DynamicsDynamics
KinematicsKinematics KineticsKinetics
Mass Acceleration
Mass Acceleration
WorkEnergyWork
Energy
Treats only the geometric aspects of the motion
ImpulseMoment
ImpulseMoment
Analysis of the forces causing the motion
11
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.1 Introduction. 12.1 Introduction. What may happen if dynamic’s is not applied properly ??? What may happen if dynamic’s is not applied properly ???
12
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.2 Rectilinear Kinematics: 12.2 Rectilinear Kinematics: Continuous MotionContinuous Motion
1. Rectilinear Kinematics: 1. Rectilinear Kinematics: It is characterized by It is characterized by specifying, at any given instant, the particle’s position, specifying, at any given instant, the particle’s position, velocity and acceleration.velocity and acceleration.
a. Position: a. Position: The straight-line The straight-line path of a particle will be path of a particle will be defined using a single defined using a single coordinate axis s. The origin coordinate axis s. The origin OO on the path is a fixed on the path is a fixed point, and from this point point, and from this point the position coordinate the position coordinate ss is is used to specify the location used to specify the location of the particle at any timeof the particle at any time
b. Displacement: b. Displacement: It is defined as It is defined as the change in its position and the change in its position and it is also it is also a vector quantitya vector quantity
sss '
13
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.2 Rectilinear Kinematics: 12.2 Rectilinear Kinematics: Continuous MotionContinuous Motion
c. Velocity: c. Velocity: If the particle If the particle moves through a moves through a
displacement displacement ΔΔss during the during the time interval time interval ΔΔtt, the , the average average velocity velocity of the particle of the particle during this time interval isduring this time interval is
If we take smaller and If we take smaller and smaller values of , the smaller values of , the magnitude of becomes magnitude of becomes smaller and smaller. The smaller and smaller. The instantaneous velocity instantaneous velocity is a is a vector defined as vector defined as tsv
t
/lim
0
t
svavg
dt
dsvor
The velocity can be The velocity can be positivepositive (+) or (+) or negativenegative (-).(-).
The magnitude of the The magnitude of the velocity is called velocity is called speed, speed, and it is generally and it is generally expressed in units of m/s expressed in units of m/s or ft/s.or ft/s.
14
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.2 Rectilinear Kinematics: 12.2 Rectilinear Kinematics: Continuous MotionContinuous Motion
d. Acceleration: d. Acceleration: Provided the Provided the velocity of the particle is velocity of the particle is known at two points, the known at two points, the average acceleration average acceleration of the of the particle during the time particle during the time interval interval ΔΔtt, is defined as, is defined as
The The ΔΔv = v’ - vv = v’ - v represents represents the difference in the velocity the difference in the velocity during the time interval during the time interval ΔΔtt
The The instantaneous instantaneous acceleration acceleration is a vector is a vector defined as defined as tva
t
/lim
0
t
vaavg
2
2
dt
sd
dt
dvaor
The acceleration can be The acceleration can be either either positivepositive (+) or (+) or negativenegative (-). (-).
The magnitude of the The magnitude of the acceleration is generally acceleration is generally expressed in units of expressed in units of m/sm/s22 or ft/s or ft/s22..
1515
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.2 Rectilinear Kinematics: 12.2 Rectilinear Kinematics: Continuous MotionContinuous Motion
Relating the equations Relating the equations
t
sv
dvvdsa t
va
It is obtained an important It is obtained an important differentia relation involving differentia relation involving displacement, velocity and displacement, velocity and accelerationacceleration
Constant Acceleration, a=aConstant Acceleration, a=acc
Velocity as a Function of Velocity as a Function of TimeTime. Integrate a. Integrate acc=dv/dt, =dv/dt, assuming that initially v=vassuming that initially v=v00 when t=0when t=0
t
c
v
v
dtadv00
tavv c 0
Constant AccelerationConstant Acceleration
(1)(1)
1616
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
12.2 Rectilinear Kinematics: 12.2 Rectilinear Kinematics: Continuous MotionContinuous Motion
Position as a Function of Position as a Function of TimeTime. Integrate . Integrate v=ds/dt=vv=ds/dt=v00+a+acct, assuming t, assuming that initially s=sthat initially s=s00 when t=0 when t=0
t
c
s
s
dtavds0
0
0
200 2
1tatvss c
Constant AccelerationConstant Acceleration
Velocity as a Function of Velocity as a Function of PositionPosition. Substituting the . Substituting the previous equation (1) into previous equation (1) into the (2) equation or integrate the (2) equation or integrate vdv=avdv=accds, assuming that ds, assuming that initially v=vinitially v=v00 at s=s at s=s00
s
s
c
v
v
dsavdv00
0022 2 ssavv c
Constant AccelerationConstant Acceleration
(2)(2)
1717
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
1818
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
1919
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2020
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2121
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2222
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2323
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2424
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2525
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
2626
Lecture 1Lecture 1MEC
N 4
600 I
nte
r -
Bayam
on
MEC
N 4
600 I
nte
r -
Bayam
on
Due, Due, Thursday, February 01, 2012Thursday, February 01, 2012
Omar E. Meza Castillo Ph.D.Omar E. Meza Castillo Ph.D.
Homework1 Homework1 WebPage WebPage
2727
