Solving the 2D Collision Between Particles of Same Mass

In summary, the problem at hand is calculating a 2D collision between two particles of the same mass. To do this, the referential needs to be changed to Mcenter. However, the equations used for this process are L. Dependent, meaning the matrix related to it is not invertible. Therefore, the final velocity in the CM referential cannot be changed back to the lab referential. The solution is to reverse the process by adding (V1 + V2)/2 instead of subtracting it.
  • #1
Littlepig
99
0

Homework Statement


Ok, I'm making an algorithm to calculate some stuff, and meanwhile, i needed to compute a 2D collision between 2 particles of same mass.

To work that out, I needed to change referential to Mcenter. The problem was there...


Homework Equations


Vcm=(v1+v2)/2 (m1=m2)
velocity addition by Galileo

The Attempt at a Solution


ok, Vcm=(v1+v2)/2
so, v1cm=v1-Vcm=v1-(v1+v2)/2=(v1)/2-(v2)/2
in the same way:
v2cm=v2-Vcm=v2-(v1+v2)/2=(v2)/2-(v1)/2

Now, the problem is: this too equations are L. Dependent, that means the matrix related to it isn't invertible, so, after i calculate the Vfinal in CM referencial, i can't change it to lab referential.
 
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  • #2
Littlepig said:
so, after i calculate the Vfinal in CM referencial, i can't change it to lab referential.
Why not? Just do the reverse of what you did to get to the CM frame: Instead of subtracting (V1 + V2)/2, add it.
 
  • #3
ah, duh, yeah

Tks Doc Al
 

Related to Solving the 2D Collision Between Particles of Same Mass

What is a 2D collision between particles of same mass?

A 2D collision between particles of same mass is a scenario where two particles of equal mass come into contact with each other in a 2-dimensional space and exchange energy and momentum.

What are the factors that affect the outcome of a 2D collision between particles of same mass?

The factors that affect the outcome of a 2D collision between particles of same mass include the initial velocities of the particles, the angle of collision, and the coefficient of restitution (a measure of the elasticity of the collision).

How is the kinetic energy conserved in a 2D collision between particles of same mass?

In an ideal scenario, the total kinetic energy of the colliding particles remains the same after the collision. However, in real-world situations, some energy may be lost due to factors such as friction and deformation of the particles.

What is the difference between elastic and inelastic collisions in a 2D system?

In an elastic collision, both the kinetic energy and momentum are conserved. In an inelastic collision, the kinetic energy is not conserved, and some energy is lost to other forms such as heat or sound.

How can the outcome of a 2D collision between particles of same mass be predicted?

The outcome of a 2D collision between particles of same mass can be predicted using mathematical equations such as the conservation of momentum and conservation of kinetic energy equations. These equations take into account the initial velocities and mass of the particles to determine the final velocities after the collision.

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