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.

so

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

and

where

and or

It means that from the coordinate of center of mass: , it reduced to

and

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 )

Special case:

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.

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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