hsbhsb said:Homework Statement
Why are the Center of Momentum velocities of masses after a 2D elastic collision anti-parallel? (as in the following diagram)
Homework Equations
CM_Velocity = (∑m_i*v_i)/(∑m_i)
The Attempt at a Solution
This is not actually a problem I have to do. I am just looking for a proof of this fact. I have not been able to find one online, but have probably been looking in the wrong places!
A 2D elastic collision in the CM frame refers to a collision between two objects where the total momentum and kinetic energy of the system is conserved. This frame of reference is chosen because it simplifies the equations and allows for a clearer understanding of the collision.
In a 2D elastic collision, antiparallel velocities refer to the situation where the initial velocities of the two objects are in opposite directions. This is often represented by one object moving to the left and the other moving to the right.
After a 2D elastic collision in the CM frame, the velocities of the two objects are related by the conservation of momentum and kinetic energy equations. This means that the total momentum and kinetic energy of the system before and after the collision are equal.
The equation for calculating the final velocities of two objects after a 2D elastic collision in the CM frame is given by: v1f = (m1-m2)v1i/(m1+m2) and v2f = 2m1v1i/(m1+m2) where m1 and m2 are the masses of the two objects and v1i is the initial velocity of the first object.
Some real-life examples of 2D elastic collisions in the CM frame include billiard balls colliding on a pool table, two cars colliding in opposite directions with similar masses, and two hockey pucks colliding on an ice rink.