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Analytical Mech Homework Solutions 19

Analytical Mech Homework Solutions 19 - 2.17 dv dv = mv = f...

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2.17 ( ) ( ) dv dv m mv f x g dt dx = = i v ( ) ( ) mvdv f x dx g v = By integration, get ( ) dx v v x dt = = If F x : ( ) ( ) ( , t f x g t = i ) ( ) ( ) 2 2 d x d dx m m f x g dt dt dt = = i t This cannot, in general, be solved by integration. If ( ) ( ) ( ) , t f v g t = i F v : ( ) ( ) dv m f v g dt = i t ( ) ( ) mdv g t dt f v = Integration gives v v ( ) t = ( ) dx v t dt = ( ) dx v t dt = A second integration gives ( ) x x t = 2.18 ( )( ) 4 2 6 1 1.55 10 10 1.55 10 kg c s = × = × ( ) ( ) 2 2 5 2 0.22 10 2.2 10 kg c s = = × ( ) ( ) 1 2 7 2 6 6 5 5 10 9.8 1.55 10 1.55 10 2 2.2 10 2 2.2 10 2.2 10 t v × × = − + + × × × × ×
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