Rules for Elastic Collisions
Rule 1:
In 1-D collisions, the separation velocity always equals the velocity of approach. In other
words,
when θ2 = 0, v1i = v2 f ! v1 f
Rule 2:
In 1-D collisions, if m1 is much smaller than m2, then v2f ≈ 0 and v1f ≈ –v1i. In other words,
when θ2 = 0, lim v2 f ! 0 and lim v1 f ! "v1i
m1 !0
Rule 3:
m1 !0
In 1-D collisions, if m1 is much larger than m2, then v2f ≈ 2v1i and v1f ≈ v1i. In other words,
when θ2 = 0, lim v2 f ! 2v1i and lim v1 f ! v1i
m1 !"
m1 !"
Rule 4:
In 1-D collisions, if m1 is equal to m2, then
when θ2 = 0, v2f = v1i and v1f = 0.
Rule 5:
At any angle, if m1 is much smaller than m2, then the % of KE transferred from ball 1 to
ball 2 is close to zero. In other words,
KE2 f
lim
!0
m1 !0 KE
1i
Rule 6:
At any angle, if m1 is much larger than m2, then the % of KE transferred from ball 1 to ball
2 is close to zero. In other words,
KE2 f
lim
!0
m1 !0 KE
1i
Rule 7:
In 1-D collisions, if m1 is equal to m2, then 100% of the KE is transferred from ball 1 to ball
2. In other words,
KE2 f
=1
when m1 = m2,
KE1i
Rule 8:
At any angle, if m1 is equal to m2, the two balls will head off at right angles. So, since θ2 is
always positive (above the x-axis) and θ1 is always negative (below the x-axis), then
when m1 = m2, θ2 – θ1 = 90°