Lect12-Phys172s11-(6.12-6.17,7.3-Energy_macroscopic)

Lect12-Phys172s11-(6.12-6.17,7.3-Energy_macroscopic) - PHYS...

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Spring 2011 PHYS 172: Modern Mechanics Lecture 12 – Energy in Macroscopic System Read 6.12 - 6.17, 7.3 Accessing your multiple choice exam: Go to CHIP Select “Link for Exams” Review your exam answers Note: You cannot change your exam score, you can only review your answers on that page! Application: escape speed Minimal condition for escape: 0 K U + = Assume: change in kinetic energy of a planet is negligible, v<<c 2 0 2 esc i i mv Mm K U G R ° ± + = + - = ² ³ ´ µ 2 2 esc mv Mm G R = 2 esc GM v R = Bound state: 0 K U + < Unbound state: 0 K U + See examples p. 241-243, 249, 259 Earth: v esc = 11.2 km/s
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Energy versus forces Energy: predict some aspects of motion Limits of possible Less details U gravitational near the Earth surface Change in potential energy: Mm U G r ° ± Δ = Δ - ² ³ ´ µ Mm Mm G G R h R ° ± ° ± = - - - ² ³ ² ³ + ´ µ ´ µ ( ) ( ) R h R U GMm R R h + - Δ = + Assumption: h << R 2 2 h M U GMm m G h R R · Δ = ¸ ¹ º » ( ) U mgh mg y mgy Δ = Δ = Δ x y y i y f g Note: motion in horizontal direction does not change U !
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