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**Unformatted text preview: **Today Today ’ ’ s Lecture s Lecture Lecture 17: Course Review Continued; Hook’s Law, Nonconservative Forces, System of Particles, Chapter 11, Impulse, Conservation of Momentum, Collisions Springs Springs and and Hook Hook ’ ’ s Law s Law From Hook’s 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 Newton’s 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. Newton’s 2 nd for the lower mass is: he total displacement of the lower mass is: Newton’s 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 Work-Energy 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 Δ K 1 2 mv f 2 − 1 2 mv i 2 f we consider separately the work done by conservative forces, W c , and on-conservative forces, W nc : Δ K W c W nc Δ K Δ 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 non-conservative forces, the total mechanical energy is conservative forces, the total mechanical energy is onserved! onserved! Δ K Δ 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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