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

Lecture 6 MECN 4600 Inter - Bayamon 2 Tentative Lecture Schedule TopicLecture 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 Planar Kinematics of a Rigid Body

Lecture 6 MECN 4600 Inter - Bayamon Work and Energy Topic 3: Kinetics of a particle 3 "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

Lecture 6 MECN 4600 Inter - Bayamon 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. 4

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force Work of a Constant Force Moving Along a Straight Line

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force Work of a Weight

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force Work of a Spring

Lecture 6 MECN 4600 Inter - Bayamon Work of a Force

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Lecture 6 MECN 4600 Inter - Bayamon Principle of Work and Energy

Lecture 6 MECN 4600 Inter - Bayamon Principle of Work and Energy

Lecture 6 MECN 4600 Inter - Bayamon Principle of Work and Energy for a System of Particles Work of Friction Caused by Sliding

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Lecture 6 MECN 4600 Inter - Bayamon Power and Efficiency Power

Lecture 6 MECN 4600 Inter - Bayamon Power and Efficiency Efficiency The mechanical efficiency is always less than 1

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Lecture 6 MECN 4600 Inter - Bayamon 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. 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. 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. 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. 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.

Lecture 6 MECN 4600 Inter - Bayamon Conservative Forces and Potential Energy W has the capacity of doing positive work when the particle is moved back down to the datum. 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, V g is negative since the weight does negative work when the particle is moved back up to the datum. The particle is located a distance y below the datum, V g 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 If y is positive upward, gravitational potential energy of the particle of weight W is

Lecture 6 MECN 4600 Inter - Bayamon 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 V e can be expressed. When an elastic spring is elongated or compressed a distance s from its unstretched position, the elastic potential energy V e can be expressed. V e 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. V e 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.

Lecture 6 MECN 4600 Inter - Bayamon 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. If a particle is subjected to both gravitational and elastic forces, the particle’s potential energy can be expressed as a potential function.

Lecture 6 MECN 4600 Inter - Bayamon 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. 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. As a result, the principle of work and energy can be written as As a result, the principle of work and energy can be written as represent the work of the nonconservative forces acting on the particles. represent the work of the nonconservative forces acting on the particles.

Lecture 6 MECN 4600 Inter - Bayamon Conservative of Energy If only conservative forces are applied to the body, this term is zero and we have If only conservative forces are applied to the body, this term is zero and we have This equation referred to as the conservation of mechanical energy or simply the conservation of energy. 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. It states that during the motion the sum of the particle’s kinetic and potential energies remain constant.

Lecture 6 MECN 4600 Inter - Bayamon Conservative of Energy  System of Particles: If a system of particles is subjected only to conservative forces, then an equation can be written. If a system of particles is subjected only to conservative forces, then an equation can be written. 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. 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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Lecture 6 MECN 4600 Inter - Bayamon Omar E. Meza Castillo Ph.D. Homework5  WebPage 49