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Analytical Mech Homework Solutions 70

Analytical Mech Homework Solutions 70 - 1 r = a cos r = a =...

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Thus 1 cos 3 r a θ = ( ) @ 0 r a θ = = D (b) at 3 2 π θ = the origin of the force. To find how long it takes … 0 r 2 2 2 2 1 1 cos cos 3 3 av v l r a a θ θ θ = = = D D ± 2 1 cos 3 a dt d v θ θ = D 3 2 2 2 2 0 0 1 3 3 cos cos 3 4 a a T d d v v π π a v π θ θ φ φ = = D D = D Since 1 2 2 9 2 k v a = D 1 1 2 2 2 2 3 2 2 4 9 4 a T a k k π π = = (c) Since the particle falls into the center of the force v → ∞ (since ) l vr const = = 6.15 From Example 6.5.4 … 1 2 1 1 2 c v r v r r = + D D Letting c v v = D V we have 1 2 1 2 1 r r = + D V So: 2 2 1 1 1 2 1 2 r r dV dr V r r
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