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Phys Test2 Review - Physics 2305 rev 2 s08 1 Ch 7 Potential...

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Physics 2305, rev 2, s08 1 Ch. 7 Potential Energy and Energy Conservation Gravitational Potential Energy U ( y ) = mgy Elastic potential energy U ( x ) = 1 2 kx 2 or, more generally, U ( x ) = 1 2 k ( x x 0 ) 2 . ¥ Forces that have potential energy are called conservative . For motion under conservative force: W = U 1 U 2 = K 2 K 1 K 2 + U 2 = K 1 + U 1 i..e, the total energy E = K + U = 1 2 mv 2 + mgy is constant (conserved) during motion; changes from one motion to another Relation between potential energy and force in one dimension F = dU dx , U ( x ) = Z F ( x ) dx Force from potential energy in three dimensions: F x = U x , F y = U y , F z = U z When both conservative and nonconservative forces are present then W noncons = E 2 E 1 where E includes only energy of conservative forces. ¥ Energy diagrams
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Physics 2305, rev 2, s08 2 At equilibrium points F = dU/dx = 0 . If d 2 U/dx 2 > 0 the equilibrium is stable; if d 2 U/dx 2 < 0 the equilibrium is unstable.
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