The Simulation of a Collision of Two Spheres

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The Simulation of a Collision of Two Spheres

• Mary Tenorio
• Advisor Dr. Xusheng Wang
• HESTEC 2006
• September 25, 2006
• Computer Science

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Outline

• Purpose of Project
• Elements in Initial Design
• Concept (Layout Design, Starting Points, and
  Equations used)
• How it works
• Beginning and Final Screenshots
• Results
• Conclusion

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Purpose of the Project

• To show a physical simulation between two objects
  (spheres) relating to mass and velocity
• It will provide students and others learning
  about physics an easy approach by viewing and
  observing how spheres travel and collide with one
  another
• It will also demonstrate user-entered values and
  output the results in a visual form of two
  spheres, along with the final time for both.
• These elements will create an understanding of
  these concepts for students and others

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Elements used in the Design

• Languages used C / OpenGL
• Runs in the Windows and Unix environment
• Background flat surface with two walls (one on
  each side) that will bounce the spheres back in
  the other direction. These walls will change the
  direction of the velocity as the spheres hit
  them.

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Concept Layout Design

• Preliminary design that shows the equal distance
  each sphere can travel before colliding with the
  wall
• Each sphere is equal distance from their
  corresponding wall
• Opposite signs of velocity, which will change
  after collision
• They will also change directions when colliding
  with each other

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Concept Starting Points

• Spheres will start with opposite directions of
  velocity ( and - )
• Start equal distance from each of their
  corresponding walls
• Spheres will change colors to represent the each
  collision made
• Final times will be shown for both spheres along
  with their beginning values

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Concept Equations Used

• Momentum Conservation in One Dimensional
  Collision
• Kinetic Energy Conservation in an elastic
  collision
• Spheres colliding with each other
• Final Velocity of Sphere after Collision

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How it will Work
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Concept Beginning Screenshot

• Final Screenshot displaying the two spheres at
  starting point waiting for user input
• User input mass and velocity for each sphere
• Spheres will continue to run through until speed
  for both reaches zero

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Concept Final Screenshot after Simulation

• Final screenshot taken after both spheres have
  reached zero.
• The final times for both are displayed on the
  screen for viewing
• Different colors represent the collision made
  (change every time they collide with either the
  wall or the other sphere)
• User has the option to run the simulation again

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Final Results Conclusion

• Running the simulation many times can yield some
  final results
• The greater the velocity, the longer it took for
  the sphere to reach a speed of 0 and complete the
  simulation
• Each time the simulation is run, the elements of
  mass, velocity, time, distance, and momentum are
  all put to use
• Allowing the user to choose their values gives
  them a better understanding as to how the spheres
  function with collision