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Elastic Collisions & Sierpinski Carpet

Elastic Collisions & Sierpinski Carpet. Anakaren Santana. Elastic Collisions. Momentum is Conserved : Kinetic Energy is Conserved : Where U’s are velocities before the collision and V’s are velocities after the collision .

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Elastic Collisions & Sierpinski Carpet

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  1. ElasticCollisions &SierpinskiCarpet Anakaren Santana

  2. ElasticCollisions • Momentum isConserved: • KineticEnergyisConserved: • WhereU’s are velocitiesbeforethecollision and V’s are velocitiesafterthecollision. • Usingtheseequationsyou can solvefor and calculatethe position of eachmass at a given time ( x = V*t)

  3. Method • Set up initialconditions (makesurebothmasseswillactuallycollide). • Forloopchanges positions of themassesaccordingtotheirrespectivevelocities. • Anifstatementchecksifthemassescollide. Whentheycollidethe new velocities are calculated and initial positions reset. • A secondforloopchangesthe positions of themassesaccordingtothese new velocities and initialcoordinates.

  4. 1D: m1=2 m2=2, U1=2 U2=0, x01=0 x02=20RunCodeWith: elasticCollision.m

  5. 2D: m1=2 m2=4, Ux1=4 Uy2=4, Ux2=-1 Uy2=-1, x01=-90 y01=-90, x02=90 y02=90RunCodeWith: elasticCollision2D.m

  6. TheSierpinskiCarpetis a fractal of fractal dimension 1.8929. • Itbeginswith a squarethatyou divide into 9 sub-squares and removethe center square. Repeattheprocesswitheachsubsquare. • Method: • Nestedforloopswithin a whileloop. • Thewhileloopensuresthatwe can keepdividingby 3. • Thenestedforloops “remove” theappropriatesquares in eachiteration.

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