Lecture
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
Inter - Bayamon
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:
MECN 4600
Hibbeler,
R.C.,
Engineering
Mechanics - Static and Dynamics, 12th. Ed.,
Prentice Hall, 2009.
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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 email 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.
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Syllabus
 Problem-Solving Technique:
A. Known
B. Find
C. Assumptions
D. Schematic
E. Analysis, and
F. 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.
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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.
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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
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Tentative Lecture Schedule
Topic
Lecture
Kinematics of a Particle
1
Kinetics of a Particle: Force and Acceleration
Kinetics of a Particle: Work and Energy
Kinetics of a Particle: Impulse and Momentum
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Planar Kinematics of a Rigid Body
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Reference


MECN 4600

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
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"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
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Introduction and Basic Concepts
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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.
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12.1 Introduction. What is dynamics ???
Study the accelerated motion of a body
Dynamics
Kinematics
Kinetics
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Mass
Acceleration
Work
Energy
Impulse
Moment
Analysis of the forces causing the
motion
Treats only the geometric aspects of the
motion
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12.1 Introduction. What may happen if dynamic’s is not applied properly ???
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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
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b. Displacement: It is defined as
the change in its position and
it is also a vector quantity
s  s '  s
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12.2 Rectilinear Kinematics: Continuous Motion
c.
Velocity:
moves
If the particle
through
a
displacement Δs during the
time interval Δt, the average
velocity
of
the
particle
during this time interval is
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vavg 
s
t
If we take smaller and
smaller values of , the
magnitude of
becomes
smaller and smaller. The
instantaneous velocity is a
vector defined as v  lim s / t 
or v 
ds
dt
t 0
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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.
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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
aavg
v

t
The Δv = v’ - v represents the
difference in the velocity
during the time interval Δt
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The
instantaneous
acceleration is a vector
defined as a  lim v / t 
t 0
dv d 2 s
or a   2
dt dt
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The acceleration can be
either positive (+) or
negative (-).
The magnitude of the
acceleration is generally
expressed in units of
m/s2 or ft/s2.
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12.2 Rectilinear Kinematics: Continuous Motion
Relating the equations
v
s
t
a
v
t
It is obtained an important
differentia relation involving
displacement, velocity and
acceleration
Constant Acceleration, a=ac
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Velocity as a Function of
Time. Integrate ac=dv/dt,
assuming that initially v=v0
when t=0
a ds  v dv
v
t
 dv   a dt
c
v0
0
v  v0  act
(1)
Constant Acceleration
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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
s
t
 ds   v
0
s0
 ac dt
0
1
s  s0  v0t  ac t 2
2
(2)
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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
v
s
 vdv   a ds
c
v0
s0
v 2  v 2 0  2ac s  s0 
Constant Acceleration
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Homework1  WebPage
MECN 4600
Due, Thursday, February 01, 2012
Omar E. Meza Castillo Ph.D.
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