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bfinalsoln_10 - Physics 9B-C Final Exam Solutions Cole UC...

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/5 A ƒ = 2 π Physics 9B-C Final Exam Solutions Cole, UC Davis 20 points per problem/160 points total [1] (a) remain the same (b) slope (c) particle (d) halve (e) latent heat (f) negative (g) top (h) 0 (i) hotter (j) odd. [2] a) (5 pts) For a wave traveling to the left y t = v y x . õ y t v y x = 0 b) (15 pts) Making the substitution u   =  
 kx  
 +  
∑ t so that : y x = dy du u x = k dy du and y t = dy du u t = + ω dy du . Plugging into y t v y x = 0 õ ω dy du v k dy du = 0 . v = /k , so ∑

 - ∑

 = 0. [3] a) (10 pts) P = F y x y t Find the force: v = F μ õ F = μv 2 = (0.020 kg/m)(80 m/s) 2 F = 128 N. Find the derivatives: y x = kA sin kx kvt ( ) ; y t = kvA sin kx kvt ( ) where k = 2 π λ = 5.24 m -1 Subbing into the power: P = Fk 2 vA 2 sin 2 kx kvt ( ) = = 128 N ( ) 5.24 m 1 ( ) 2 80 m/s ( ) 0.03 m ( ) 2 sin 2 5.24 m 1 ( ) x 419 s 1 ( ) t ( ) = P = 253 W ( ) sin 2 5.24 m 1 ( ) x 419 s 1 ( ) t ( ) b) (3 pts) At maximal displacement the slope of the string is zero, so P y x = 0 .
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