(17) Energy Diagrams

# (17) Energy Diagrams - Lecture 17 Energy Diagrams ACT:...

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Lecture 17 Energy Diagrams

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ACT: Force field The pictures below show force vectors at different points in space for two different forces. Which of these forces is conservative? A. 1 B. 2 C. Both 1 2
W = 0 W 1 W = 0 W 3 W 2 W = 0 1 2 | W 2 + W 3 | = | W 1 | W loop = 0 | W 2 ’| > | W 1 ’| loop Work along a closed trajectories (loops). W = 0 W 2 W = 0 W 1

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Relation between Relation between U U and F F (1D) f inal init ial x W F dx U = = -∆ & For a conservative force (in 1D), const ant x U F = - + & x dU F = - Examples: y x dU U mgy F mg dy U kx F dx = = - = - = = - = - The force is minus the slope of the U (x) curve.
Example: Spring 2 1 ( ) 2 U x kx = x U x x = 0, F = 0 dU/ dx = 0 Potential energy of a box attached to a spring on a horizontal, frictionless table.

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x U x x < 0, F > 0 dU/ dx < 0
x U x x > 0, F < 0 dU/ dx > 0

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x U x x > 0, F < 0 and larger in magnitude dU/ dx > 0 and steeper than before The force always points “downhill”!!!
ACT: U U vs F F A Which of the force versus position graphs matches the potential energy function shown in blue? U x F x x x F F B C + Slope: 0 0 0 Force = slope

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Relation between U and F (3D) x U F x - = 1D: , in car t esian coor dinat es f or t he r adial component in spher ical coor dinat es x y z r U U U F F F x y z U F r = - = - = - = - 3D: (minus t he gr adient of ) F U U = - r r (“downhill”) (“downhill in the steepest direction”)
Example Find the force exerted at point P (0,1,2) m if the potential energy associated with the force is: ( 29 P ˆ ˆ ˆ 3 8 12 N

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## This note was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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(17) Energy Diagrams - Lecture 17 Energy Diagrams ACT:...

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