ENGR 3340: Fundamentals of Statics and Dynamics
Fundamentals of Statics and
Dynamics - ENGR 3340
Professor: Dr. Omar E. Meza Castillo
omeza@bayamon.inter.edu
http://facultad.bayamon.inter.edu/omeza
Department of Mechanical Engineering
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
Tentative Lectures Schedule
Topic
Lecture
Kinematics of a Particle
13
2
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
One thing you learn in science is that there is
no perfect answer, no perfect measure.
A. O. Beckman
Topic 13: Kinematics of a Particle
Position, Velocity and Acceleration
3
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
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.
4
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
Introduction. What is dynamics ?
Study the accelerated motion of a body
Dynamics
Kinematics
Kinetics
Mass
Acceleration
Work
Energy
Impulse
Moment
Analysis of the forces causing the motion
Treats only the geometric aspects of the motion
5
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
What may happen if dynamic’s is not applied properly ?
6
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
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: The displacement
of a particle is defined as the
change in its position and it is also
a vector quantity
s  s '  s
7
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
Rectilinear Kinematics: Continuous Motion
c. Velocity: If the particle moves
through a displacement Δs
during the time interval Δt, the
average velocity of the particle
during this time interval is
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 
t 0
or v 
ds
dt
8
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.
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
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
The instantaneous acceleration is
a vector defined as
a  lim v / t 
t  0
dv d 2 s
or a   2
dt dt
9
The acceleration can be
either positive (+) or negative
(-).
The
magnitude
of
the
acceleration is generally
expressed in units of m/s2 or
ft/s2.
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
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
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
10
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
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)
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
11
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
12
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
Homework6  http://facultad. bayamon.inter.edu/omeza/
Omar E. Meza Castillo Ph.D.
21
of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
¿Preguntas?
Comentarios
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of Statics and Dynamics
ENGR 3340: Fundamentals
Universidad Interamericana
MSP21
- Bayamón
GRACIAS
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