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Lecture
6
Vector Mechanics for Engineers:
Dynamics
MECN 3010
Department of Mechanical Engineering
Inter American University of Puerto Rico
Bayamon Campus
Dr. Omar E. Meza Castillo
[email protected]
http://www.bc.inter.edu/facultad/omeza
Inter - Bayamon
Tentative Lecture Schedule
Topic
Lecture
Kinematics of a Particle
1,2,3,4
Kinetics of a Particle: Force and Acceleration
5
Kinetics of a Particle: Work and Energy
6
Kinetics of a Particle: Impulse and Momentum
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Planar Kinematics of a Rigid Body
2
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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 3: Kinetics of a particle
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Work and Energy
3
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Chapter Objectives
 To develop the principle of work and
energy and apply it to solve problems that
involve force, velocity, and displacement.
 To study problems that involve power and
efficiency.
 To introduce the concept of a conservative
force
and
apply
the
theorem
of
conservation of energy to solve kinetic
problems.
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Work of a Force
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Work of a Force
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Work of a Force
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Work of a Force
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Work of a Force
Work of a Constant Force Moving Along a Straight Line
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Work of a Force
Work of a Weight
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Work of a Force
Work of a Spring
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Work of a Force
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Principle of Work and Energy
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Principle of Work and Energy
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Principle of Work and Energy for a System of Particles
Work of Friction Caused by Sliding
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Power and Efficiency
Power
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Power and Efficiency
Efficiency
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The mechanical efficiency is always less than 1
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Conservative Forces and Potential Energy
 Conservative Force:
 It is defined by the work done in moving a
particle from one point to another that is
independent of the path followed by the
particle.
 Two examples are weight of the particle and
elastic force of the spring.
 Potential Energy:
 It is the measure of the amount of work a
conservative force will do when it moves from a
given position to the datum.
 Gravitational Potential Energy:
 If a particle is located a distance y above an
arbitrary selected datum, the particle’s weight
W has positive gravitational potential energy
V g.
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Conservative Forces and Potential Energy
 W has the capacity of
doing
positive
work
when the particle is
moved back down to
the datum.
 The particle is located a
distance y below the
datum, Vg is negative
since the weight does
negative work when the
particle is moved back
up to the datum.
 If y is positive upward,
gravitational potential
energy of the particle of
weight W is
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Conservative Forces and Potential Energy
 Elastic Potential Energy:
 When an elastic spring is
elongated or compressed a
distance
s
from
its
unstretched position, the
elastic potential energy Ve
can be expressed.
 Ve is always positive since,
in the deformed position,
the force of the spring has
the capacity for always
doing positive work on the
particle when the spring is
returned to its unstretched
position.
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Conservative Forces and Potential Energy
 Potential Function:
 If a particle is subjected to both gravitational
and elastic forces, the particle’s potential
energy can be expressed as a potential
function.
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Conservative of Energy
 Potential Function:
 When a particle is acted upon by a system of
both conservative and non-conservative forces,
the portion of the work done by the
conservative forces can be written in terms of
the difference in their potential energies using.
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 As a result, the principle of work and energy
can be written as

represent
the
work
of
the
nonconservative forces acting on the particles.
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Conservative of Energy
 If only conservative forces are applied to the
body, this term is zero and we have
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 This equation referred to as the conservation of
mechanical energy or simply the conservation
of energy.
 It states that during the motion the sum of the
particle’s kinetic and potential energies remain
constant.
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Conservative of Energy
 System of Particles:
 If a system of particles is subjected only to
conservative forces, then an equation can be
written.
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 The sum of the particle’s initial kinetic and
potential energies is equal to the sum of the
particle’s final kinetic and potential energies.
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Homework5  WebPage
Omar E. Meza Castillo Ph.D.
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