This is a discussion of elastic collision in one dimension.
Before collision: two particles with mass and velocity as and
After collision: the velocity have been changed to and
Assume there is no external force or the interval is very short, then
total linear momentum is conserved: i.e.
For elastic collision, the total energy is also conserved.
It can be re-write as
It is the same as m_1(v_1-v_1')(v_1+v_1')= -m_2 (v_2-v_2')(v_2+v_2')
Since , so or
The result is
It means that from the coordinate of center of mass: , it reduced to
Define , the above equations can be re-write as
The following simulation plot the above two functions.
The X-axis is , it range from Vscale*xmin to 1. (There is no collision if )
The blue curve is and red curve is
You can change the ratio of with slider.
The default value is , so
, so is a horizontal line
, so is a straight line with slope 1 (function of )
if , and ,-*-
if , then and
e.g. a ball hit the wall, it will biunced back with almost the same speed (but in oppositive direction).
if , and ,
if , then and ,
e.g. a speedy car hit you while you stand still, you will be kicked by twice the velocity of the car.