Analytical Mech Homework Solutions 35

Analytical Mech Homework Solutions 35 - v2 = v2 2 ( + + ) m...

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() 22 2 m vv α β γ = −+ + D 1 2 2 2 m αβ =− + + D (b) 2 2 0 m + = D v 1 2 2 m  =+ +   D v (c) x V mx F x == ±± mx 2 V y y my 2 3 V z z mz 4.5 (a) ˆˆ Fi xj y G on the path x y = : dr idx jdy K ( ) 1,1 1 1 1 1 0,0 0 0 0 0 1 xy F dr F dx F dy xdx ydy ⋅= + = + = K K ∫∫ K on the path along the x-axis: ˆ dr idx = K and on the line 1 x = : ˆ dr jdy = ( ) 1 1 0 0 1 Fd r x y + = K K K is conservative. F (b) yj x G on the path x y = : ( ) 1 1 1 1 0 0 0 0 F dr F dx F dy ydx xdy + = K K K and, with x y = ( ) 1 1 0 0 0 r x d x y d y K = on the x-axis: ( ) 1,0 1 1 0 0 x r x y d x = K K K and, with on the x-axis 0 y = ( ) 1,0 0 r = K K on the line 1 x = :
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