Exploring 2D Collision Physics with Polygons: Analysis and Simulation

[beloxx89]

I am trying to analyze the physics of a 2d collision among polygons. I supplied you with an image that illustrates my attempt:

http://s278.photobucket.com/albums/kk112/beloxx/?action=view&current=collision.jpg"
http://s278.photobucket.com/albums/kk112/beloxx/?action=view&current=collision.jpg
Now, object A moves with a velocity Vi while object B is still, as indicated on the image. According to my analysis, object A will transfer its velocity (momentum) through point P to object B which will receive the velocity with a vector perpendicular to the normal (blue line). This will further decompose into angular and transitional velocities which i have no problem doing.
When I tried to simulate that with a program (when a point hits a figure, the collision looks realistic) however what I am confused about is the final velocity of object A after hitting object B, or to be more precise the direction of the final velocity...

Does anyone have any idea? Any help will be greatly appreciated.

 

[LightHero]

To answer this question, you will need to consider the conservation of momentum and energy. Momentum is defined as the product of mass and velocity, and is conserved in any collision. That means that the momentum of both objects before the collision must equal the momentum of both objects after the collision. Since Object A is moving and Object B is not, the momentum of Object A before the collision must equal the total momentum of both objects after the collision. The direction of the final velocity of Object A can then be calculated by using the momentum equation and the known data (mass and velocity) for each object before and after the collision. In addition, the conservation of energy also needs to be considered. Energy is defined as the product of mass and velocity squared, and is also conserved in any collision. That means that the energy of both objects before the collision must equal the energy of both objects after the collision. Again, since Object A is moving and Object B is not, the energy of Object A before the collision must equal the total energy of both objects after the collision. This can then be used to calculate the final velocity of Object A. By combining the conservation of momentum and energy equations, you should be able to determine the direction and magnitude of the final velocity of Object A after the collision.

 

[astrokreng]

I would first like to commend you on your attempt to analyze and simulate 2D collision physics with polygons. It is a complex and important topic in the field of physics, and your efforts to understand it are commendable.

Based on your analysis and simulation, it appears that you have a good understanding of the basic principles of collision physics. Object A will indeed transfer its momentum to object B through point P, and this will result in both angular and translational velocities for object B. However, it is important to note that the final velocity of object A will also be affected by the collision.

In order to accurately determine the final velocity of object A, you will need to consider the conservation of momentum and energy. This means that the total momentum and energy of the system (objects A and B) before and after the collision should be equal. By using this principle, you can calculate the final velocity of object A.

Additionally, the direction of the final velocity of object A will depend on the angle at which it collides with object B. If object A collides with object B at a perpendicular angle, the final velocity will be in the opposite direction of its initial velocity. However, if the collision occurs at an angle, the final velocity will have both a horizontal and vertical component.

In order to accurately simulate the collision, you may need to consider factors such as the elasticity of the objects and any external forces acting on them. These can also affect the final velocities and should be taken into account in your simulation.

I hope this helps clarify any confusion you may have about the final velocity of object A in your simulation. Keep exploring and experimenting, and don't hesitate to reach out for further assistance or guidance in your research. Good luck!