Analytical Mech Homework Solutions 94

Analytical Mech Homework Solutions 94 - vcm 1 m1 = =...

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1 1 2 1 1 1 cm v m v m m α = = + + Equation 7.6.11 Thus ( ) ( ) ( ) 2 2 2 1 2 1 1 1 r α γ α α α = + + + + ( ) ( ) ( ) 1 2 1 2 2 2 1 1 2 1 1 1 v r v α γ α α α = + + + + Simplifying 1 2 2 1 0 1 1 r r γ α α α + + + = Let 2 x r = and solving the resulting quadratic for x ( ) 1 2 2 2 1 1 1 1 x γ γ α α α = + + + Squaring ( ) ( ) 1 2 2 2 2 2 2 2 1 2 1 2 1 r x γ α γ γ α α = = + − + + + 1 Now ( ) ( ) 1 2 2 2 2 1 2 2 1 1 1 1 2 1 2 1 1 T r T γ α γ γ α α = = + − + + + And, after a little algebra, we get the desired solution ( ) 2 2 1 2 1 2 2 1 1 1 T T γ γ γ α α α = + + + + 7.20 From Equation 7.6.15 … ( ) ( ) 1 1 1 1 1 1 2 2 1 2 1 m v m v v m m m m m v γ = = 1 + + Now we solve for 1 1 v v 1 2 1 1 2 T v m
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