8 Conservation of Energy ay-1

8 Conservation of Energy ay-1 - 1 Chapter 8 Conservation of...

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Unformatted text preview: 1 Chapter 8 Conservation of Energy 2 Conservative and Nonconservative Forces • Forces can be categorized into two types: Conservative Nonconservative • A Force is conservative if: The work done by the force on an object moving from one point to another depends only on the initial and final positions and is independent of a particular path taken. 2 Conservative and Nonconservative Forces • Forces can be categorized into two types: Conservative Nonconservative • A Force is conservative if: The work done by the force on an object moving from one point to another depends only on the initial and final positions and is independent of a particular path taken. Gravitational force is a conservative force . W G = - mgh Gravitational Force is Conservative 4 • Since ( y 2 – y 1 ) is the vertical height h , the work done depends only on the vertical height and does not depend on the particular path taken. • This gives an alternative definition of a conservative force: A force is conservative if: The net work done by the force on an object moving around any closed path is zero. The work done by a nonconservative force is not recoverable; it is lost forever. 5 Nonconservative Forces • Friction is a nonconservative force. • Work done moving a create across floor is equal to the product of F fr and the total distance traveled • Therefore work done depends on path length. • Thus in round trip, total work by friction is never zero— always negative . 6 Example Conservation and Nonconservative Forces Conservative Forces • Gravitation • Elastic • Electric Nonconservative Forces* • Friction • Air resistance • Tension in a cord • Push or pull by a person * Also known as dissipative forces 7 Example Air resistance can be represented by a force proportional to the velocity v of an object: F = - k v . Is this force conservative? Explain. 8 8-2 Potential Energy • Kinetic energy depends on velocity. • Potential energy is energy associated with the position or configuration of objects. • Various types of potential energy can be defined. • Potential energy ( U ) only exists for conservative forces . * The change in potential energy associated with a particular conservative force F conservative is defined as the negative of the work done by that force. Δ U = - W conservative 9 W ext = mgh = U W G = - mgh = -U cos θ = 1 cos θ = -1 y v = constant 10 Elastic Potential Energy Gravitational Potential Energy: U = mgy Elastic Potential Energy: U = ½ kx 2 11 Potential Energy Summarized 1. Potential energy is always associated with a conservative force, and the difference in potential energy between two points is defined as the negative of the work done by that force....
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8 Conservation of Energy ay-1 - 1 Chapter 8 Conservation of...

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