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l14anno - Central Impact n v Bi v Ai vBni n v Ani n Blobs...

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Central Impact Blobs approach Blobs contact and attain equal normal velocity Blobs separate n Ai v Bi v AC v Af v BC v Bf v · · AC BC C v = = v n v n Ani v n Bni v n C v n Bnf v n Anf v n C v n
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t 1 Blobs contact with initial normal Normal Impulse and velocities v Ani n and v Bni n Momentum t 1 to t 2 Blobs squish together and reach a common normal velocity v C n t 2 to t 3 Blobs expand and separate with final normal velocities v Anf n and v Bnf n ( ) ( ) t F t = F n A 2 1 2 1 3 2 3 2 ( ) ( ) ( ) ( ) t A C A Ani t t B C B Bni t C C t A Anf A t t B Bnf B t F t dt m v m F t dt m v m v v F t dt m v m F t dt m v m v v = = = = B Impact loads dominate, hence neglect other loads, e.g. weight
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Manipulate above Coefficient of restitution Eliminate v C 3 2 2 1 3 2 2 1 ( ) ( ) ( ) ( ) C C t t B Bnf B A Anf A t B C B Bni A C A Ani t t t t t Bnf Anf Ani Bni F t dt m v m m v m m v m m v m F t dt F t dt F t dt v v v v v v e v e v = = = =
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e= 0 i.e. plastic impact, implies v Bfn -v Afn = 0.
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