Vector Mechanics for Engineers: Dynamics MECN 3010

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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_at_bayamon.inter.edu
• http//www.bc.inter.edu/facultad/omeza

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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
Planar Kinematics of a Rigid Body



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Introduction and Basic Concepts
"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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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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12.4 General Curvilinear Motion.

• Curvilinear motion occurs when a particle moves
  along a curved path.

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12.4 General Curvilinear Motion.
c. Velocity During the time ?t, the average
velocity of the particle during this time
interval is The instantaneous velocity is
determined from this equation by letting ?t -gt 0,
an consequently the direction of ?r approaches
the tangent to the curve. Hence,
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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12.4 General Curvilinear Motion.
d. Acceleration If the particle has a velocity
of v at time t and a velocity vv?v at t?t,
then the average acceleration of the particle
during the time interval ?t, is defined
as The ?v v - v represents the difference
in the velocity during the time interval ?t The
instantaneous acceleration is a vector defined as
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12.5 General Curvilinear Motion Rectangular
Components
a. Position If the particle is at point (x,y,z)
on the curved path s shown in figure, then its
location is defined by the position vector. r
xi yj zk When the particles moves, the
x,y,z components of r will be functions of time
i.e., xx(t), yy(t), zz(t), so that
rr(t). And the direction of r is specified by
the unit vector urr/r
The magnitude of r is defined by
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12.5 General Curvilinear Motion Rectangular
Components
b. Velocity The first time derivative of r
yields the velocity of the particle.
Hence The dot notation represent the
first time derivatives of xx(t), yy(t), zz(t),
respectively.
The magnitude of v is defined by and a
direction that is specified by the unit vector
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12.5 General Curvilinear Motion Rectangular
Components
c. Acceleration The acceleration of the particle
is obtained by taking the first time derivative
of v (or the second time derivative of r). We
have Where,
The magnitude of a is defined by and a
direction that is specified by the unit vector
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12.6 Motion of a Projectile
The free-flight motion of a projectile is often
studied in terms of its rectangular components.
To illustrate the kinematic analysis, consider a
projectile launched at point (x0,y0), with a
initial velocity of v0, having components (v0)x
and (v0)y. The air resistance is neglected and
the only force acting on the projectile is its
weight, which causes the projectile to have a
constant downward acceleration of approximately
acg 9.81m/s2 32.2ft/s2
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12.6 Motion of a Projectile
Horizontal Motion Since ax0, Vertical
Motion Since ay-g,
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Application Problems
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Homework2 ? WebPage
Due, Tuesday, February 06, 2012
Omar E. Meza Castillo Ph.D.