Inelastic collision in two dimensions

In summary, the conversation discusses a programmer's attempt to simulate 2D ball collisions and their search for a formula on Wikipedia. The programmer is confused by the use of x1 and x2 in the formula as they are unsure if they are scalars or vectors. They are ultimately seeking guidance on how to use this formula for their design.
  • #1
Christopher Munroe
1
0
I am a programmer trying to simulate some 2D balls bouncing about and colliding with each other. I have both the ball's velocity components before the collision and I am trying to solve for them. I went to wikipedia to find a formula to satisfy my needs and ran into this section: https://en.wikipedia.org/wiki/Elastic_collision#Two-dimensional_collision_with_two_moving_objects
I am attempting to use an angle free representation as it is more convenient for my current design:
3a70e57f4a5cc0e5e0e11be153aa4b10.png


I am somewhat confused by it. The passage states the changed velocities are computed using the centers x1 and x2 at the time of contact. Isn't x1 and x2 scalars, I'm not sure what x1 and x2 are to be quite honest. If they are scalars, then we cannot perform a dot product. I am sorry if this is trivial, I appreciate any guidance.
 
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  • #2
They are vectors, with the two components of ##\mathbf{x}_i## corresponding to ##(x_i,y_i)##.
 

Related to Inelastic collision in two dimensions

1. What is an inelastic collision in two dimensions?

An inelastic collision in two dimensions is a type of collision between two objects where kinetic energy is not conserved. This means that the total kinetic energy of the system before and after the collision is not the same. In these types of collisions, some of the kinetic energy is transferred to other forms, such as heat or sound.

2. How is momentum conserved in an inelastic collision in two dimensions?

Momentum is still conserved in an inelastic collision in two dimensions. This means that the total momentum of the system before the collision is equal to the total momentum after the collision. However, the direction and magnitude of the individual momentums of the objects may change due to the transfer of kinetic energy.

3. What is the difference between an inelastic collision and an elastic collision?

In an elastic collision, both momentum and kinetic energy are conserved. This means that the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. In an inelastic collision, only momentum is conserved and some kinetic energy is lost.

4. How is the coefficient of restitution used to analyze an inelastic collision in two dimensions?

The coefficient of restitution is a value between 0 and 1 that is used to describe the elasticity of a collision. In an inelastic collision, the coefficient of restitution will be less than 1, as some kinetic energy is lost. This value can be calculated using the initial and final velocities of the objects involved in the collision.

5. What are some real-life examples of inelastic collisions in two dimensions?

Some examples of inelastic collisions in two dimensions include a car crash, a ball hitting the ground, or a hammer hitting a nail. In these situations, some kinetic energy is lost due to the collision, resulting in a change in momentum and often the production of sound or heat.

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