Vector Mechanics for Engineers: Dynamics MECN 3010

LectureLecture

66Vector Mechanics for Engineers: Vector Mechanics for Engineers:

DynamicsDynamics MECN 3010 MECN 3010

Department of Mechanical EngineeringDepartment of Mechanical EngineeringInter American University of Puerto RicoInter American University of Puerto Rico

Bayamon CampusBayamon CampusDr. Omar E. Meza CastilloDr. Omar E. Meza Castillo

[email protected]://www.bc.inter.edu/facultad/omeza

mailto:[email protected]

http://www.bc.inter.edu/facultad/omeza

Lecture 6Lecture 6MEC

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Tentative Lecture ScheduleTentative Lecture Schedule

TopicTopic LectureLectureKinematics of a ParticleKinematics of a Particle 1,2,3,41,2,3,4Kinetics of a Particle: Force and AccelerationKinetics of a Particle: Force and Acceleration 55Kinetics of a Particle: Work and EnergyKinetics of a Particle: Work and Energy 66Kinetics of a Particle: Impulse and MomentumKinetics of a Particle: Impulse and MomentumPlanar Kinematics of a Rigid BodyPlanar Kinematics of a Rigid Body


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Work and EnergyWork and Energy

Topic 3: Kinetics of a particleTopic 3: Kinetics of a particle

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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 AlbertEinstein Albert


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To develop the principle of work and To develop the principle of work and energy and apply it to solve problems energy and apply it to solve problems that involve force, velocity, and that involve force, velocity, and displacement.displacement.

To study problems that involve power and To study problems that involve power and efficiency.efficiency.

To introduce the concept of a To introduce the concept of a conservative force and apply the theorem conservative force and apply the theorem of conservation of energy to solve kinetic of conservation of energy to solve kinetic problems.problems.

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Work of a Constant Force Moving Along a Straight Line


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Work of a Weight


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Work of a Spring


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1313


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1414


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1515


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mon Principle of Work and Energy for a System of ParticlesPrinciple of Work and Energy for a System of Particles

Work of Friction Caused by Sliding


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1919


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2020


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2121


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2222


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Power


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Efficiency

The mechanical efficiency is always less than 1


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mon Conservative Forces and Potential EnergyConservative Forces and Potential Energy

Conservative Force:Conservative Force: It is defined by the work done in moving a It is defined by the work done in moving a

particle from one point to another that is particle from one point to another that is independent of the path followed by the particle.independent of the path followed by the particle.

Two examples are weight of the particle and Two examples are weight of the particle and elastic force of the spring. elastic force of the spring.

Potential Energy:Potential Energy: It is the measure of the amount of work a It is the measure of the amount of work a

conservative force will do when it moves from a conservative force will do when it moves from a given position to the datum.given position to the datum.

Gravitational Potential Energy:Gravitational Potential Energy: If a particle is located a distance If a particle is located a distance yy above an above an

arbitrary selected datum, the particle’s weight W arbitrary selected datum, the particle’s weight W has positive has positive gravitational potential energy gravitational potential energy VVgg..


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WW has the capacity of has the capacity of doing positive work doing positive work when the particle is when the particle is moved back down to the moved back down to the datum.datum.

The particle is located a The particle is located a distance distance yy below the below the datum, datum, VVgg is negative is negative since the since the weight does weight does negative work when the negative work when the particle is moved back particle is moved back up to the datum.up to the datum.

If y is positive upward, If y is positive upward, gravitational potential gravitational potential energy of the particle of energy of the particle of weight weight WW is is


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Elastic Potential Energy:Elastic Potential Energy: When an elastic spring is When an elastic spring is

elongated or compressed a elongated or compressed a distance distance ss from its from its unstretched position, the unstretched position, the elastic potential energy elastic potential energy VVee can be expressed.can be expressed.

VVee is always positive since, in is always positive since, in the deformed position, the the deformed position, the force of the spring has the force of the spring has the capacity for always doing capacity for always doing positive work on the particle positive work on the particle when the spring is returned when the spring is returned to its unstretched position.to its unstretched position.


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Potential Function:Potential Function: If a particle is subjected to both gravitational If a particle is subjected to both gravitational

and elastic forces, the particle’s potential and elastic forces, the particle’s potential energy can be expressed as a potential energy can be expressed as a potential function.function.


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Potential Function:Potential Function: When a particle is acted upon by a system of When a particle is acted upon by a system of

both conservative and non-conservative forces, both conservative and non-conservative forces, the portion of the work done by the the portion of the work done by the conservative forces can be written in terms of conservative forces can be written in terms of the difference in their potential energies using.the difference in their potential energies using.

As a result, the principle of work and energy As a result, the principle of work and energy can be written ascan be written as

represent the work of the represent the work of the nonconservative forces acting on the particles.nonconservative forces acting on the particles.


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If only conservative forces are applied to the If only conservative forces are applied to the body, this term is zero and we havebody, this term is zero and we have

This equation referred to as the conservation This equation referred to as the conservation of mechanical energy or simply the of mechanical energy or simply the conservation of energy.conservation of energy.

It states that during the motion the sum of the It states that during the motion the sum of the particle’s kinetic and potential energies remain particle’s kinetic and potential energies remain constant.constant.


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System of Particles:System of Particles: If a system of particles is subjected only to If a system of particles is subjected only to

conservative forces, then an equation can be conservative forces, then an equation can be written.written.

The sum of the particle’s initial kinetic and The sum of the particle’s initial kinetic and potential energies is equal to the sum of the potential energies is equal to the sum of the particle’s final kinetic and potential energies.particle’s final kinetic and potential energies.


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Omar E. Meza Castillo Ph.D.Omar E. Meza Castillo Ph.D.

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Vector Mechanics for Engineers: Dynamics MECN 3010

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