problem18_90

University Physics with Modern Physics with Mastering Physics (11th Edition)

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18.90: a) , and ) ( 2 2 2 1 2 1 rms 2 1 2 1 av v v v v v v + = + = and ) 2 ( 4 1 ) ( 2 1 2 1 2 2 2 1 2 2 2 1 2 av 2 rms v v v v v v v v + + - + = - . ) ( 4 1 ) 2 ( 4 1 2 2 1 2 1 2 2 2 1 v v v v v v - = - + = This shows that , av rms v v with equality holding if and only if the particles have the same speeds. b) ), ( ), ( av 1 1 av 2 2 rms 1 1 2 rms u Nv v u Nv v N N + = + = + + and the given forms follow immediately. c) The algebra is similar to that in part (a); it helps somewhat to express . 1 1 ) 2 ( 1) ( 1 ) ) ) 1 (( 2 1) 1) (( ( 1) ( 1 2 2 av 2 av 2 2 av 2 av 2 av 2 2 av u N u u v v N N v N N u N N u Nv v N N N v + + - + - + + + = - + + + - + + = Then, . ) ( 1) ( ) ( 1 ) 2 ( 1) ( ) ( 1) ( 2 av 2 2 av 2 rms 2 av 2 av 2 2 av 2 rms 2 av 2 rms u v N N v v N N u u v v N N v v
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Unformatted text preview: N N v v-+ +-+ = +-+ +-+ = ′-′ If , av rms v v then this difference is necessarily positive, and . av rms v v ′ ′ d) The result has been shown for 1, = N and it has been shown that validity for N implies validity for 1; + N by induction, the result is true for all N ....
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This document was uploaded on 02/05/2008.

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