Elastic Collisions in 1 Dimension
Using the Center of Mass Reference Frame
First, switch to a frame of reference in which m2 is at
rest. Now a particle of mass m1 and velocity v collides
elastically (in one dimension) with a stationary particle of mass
m2. What are the velocities of m1 and
m2 after the collision?
A particle of mass m1 and velocity v collides
elastically with a particle of mass m2, initially
After the collision, m1 has velocity
v1, and m2 has velocity v2.
What are v1 and v2?
Here is a proof that the center of mass method works for
one-dimensional elastic collisions:
- Find the velocity of the system center of mass:
- Switch to the center of mass reference frame. To do this,
simply subtract vcm from each particle's velocity.
- Have the collision. The particles' velocities reverse.
- Switch back to the original frame of reference, by adding
vcm to each particle's velocity.
- Smile, you're done. Note the v1 and v2
shown in step 3 match
the results derived for the general solution. Q.E.D.
last update September 28, 2004 by JL