Elastic Collisions & Sierpinski Carpet

1 / 7

# Elastic Collisions & Sierpinski Carpet - PowerPoint PPT Presentation

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 .

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Elastic Collisions & Sierpinski Carpet

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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.