Simulating 2D Collisions: Elastic Circle Interactions and Velocity Calculation

In summary, the conversation discusses the design of a program that simulates collisions in 2 dimensions, specifically between 2 circles with known masses, velocities, and radii. The collisions are perfectly elastic, and the only unknowns are the final Vx and Vy vectors of the circles. The solution involves exchanging the component of momentum along a line joining their centers when they make contact.
  • #1
spl3001
16
0
I'm designing a program that simulates collisions in 2 dimensions, among other things. The collisions are between 2 circles, the collisions themselves are perfectly elastic. The mass of the two circles are known, and their X and Y velocity components are known. They also have specific radii. I can easily detect collisions amongst 2 circles, but I cannot solve for the final Vx or Vy vectors of the two spheres.

Any help would be greatly appreciated.
Thanks
 
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  • #2
As long as you are not including friction and spin all you have to do is exchange the component of momentum along a line joining their centers when they make contact.
 

FAQ: Simulating 2D Collisions: Elastic Circle Interactions and Velocity Calculation

How do you simulate 2D collisions between circles?

In order to simulate 2D collisions between circles, you need to use the laws of physics, specifically the conservation of momentum and energy. This involves calculating the velocities and positions of the circles before and after the collision, as well as taking into account the mass and radius of each circle.

What is an elastic collision?

An elastic collision is a type of collision in which both kinetic energy and momentum are conserved. This means that the total energy and momentum of the system before and after the collision are equal.

How do you calculate the velocities of the circles after a collision?

In order to calculate the velocities of the circles after a collision, you need to use the conservation of momentum equation: m1v1 + m2v2 = m1v1' + m2v2', where m1 and m2 are the masses of the circles, v1 and v2 are their velocities before the collision, and v1' and v2' are their velocities after the collision.

Can you simulate collisions between circles with different masses?

Yes, collisions between circles with different masses can be simulated by taking into account the mass of each circle in the calculations for velocity and energy. This will result in the larger circle having a smaller change in velocity compared to the smaller circle.

Are there any limitations to simulating 2D collisions between circles?

Yes, there are some limitations to simulating 2D collisions between circles. Some of these limitations include assuming perfectly elastic collisions, neglecting external forces such as friction, and not accounting for the shape or composition of the circles. These simplifications may not accurately represent real-world collisions, but they provide a good approximation for understanding the basic principles of 2D collisions.

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