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Unformatted text preview: Today Today s Lecture s Lecture Lecture 17: Course Review Continued; Hooks Law, Nonconservative Forces, System of Particles, Chapter 11, Impulse, Conservation of Momentum, Collisions Springs Springs and and Hook Hook s Law s Law From Hooks Law a spring exerts a force proportional to its displacement from equilibrium: This is the force by the spring by the spring on the hand stretching it. From Newtons 3 rd , the force exerted by the hand by the hand is kx . The work done by the hand is the integral: What would the work be if the hand compressed the spring? Example: Work to Stretch a Spring Example: Work to Stretch a Spring F kx W x kx dx 1 2 kx 2 xample: Springs in Series with Two Masses xample: Springs in Series with Two Masses Two springs are in series, both with a spring constant of k = 20N/m. Mass m 1 = .2kg and mass m 2 = .4kg . Find the displacement of the lower mass. Newtons 2 nd for the lower mass is: he total displacement of the lower mass is: Newtons 2 nd for the upper mass is: T l m 2 g kx l m 2 g x l m 2 g / k T u T l m 1 g kx u kx l m 1 g T u m 2 g m 1 g x u m 1 m 2 g / k x tot 2 m 2 m 1 g / k 9.8/20 .49 m 49 cm ork ork Kinetic Energy Theorem Kinetic Energy Theorem Conservation of Energy Conservation of Energy rom the WorkEnergy Theorem the work done on an object is equal to the change in its kinetic energy: W m d v dt d r F net d r K 1 2 mv f 2 1 2 mv i 2 f we consider separately the work done by conservative forces, W c , and onconservative forces, W nc : K W c W nc K U W nc otential energy was defined as the negative of the work done by onservative forces: D U =  W c . Hence: In the absence of non n the absence of nonconservative forces, the total mechanical energy is conservative forces, the total mechanical energy is onserved! onserved! K U 1 2 mv i 2 U i 1 2 mv f 2 U f E Conservative and Conservative and Nonconservative Nonconservative Forces Forces If the work done between points A and B is path independent then we can state: The work done by the force F going from A to B and back to A , W ABA , is: If the total work done by a force over a closed path vanishes, W AB A B F d r 1 A B F d r 2 W ABA A B F d r 1 A B F d r 2 A B F d r 1 B A F d r 2 W ABA F d r 0!...
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 Spring '08
 Hicks
 Force, Momentum, Work

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