- #1
Chronos000
- 80
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my notes tell me the following, speaking about a two body collision with one particle initially stationary. However i have no clue where lines 7.23 and 7.24 come from. (big "V" is CM velocity, v* is velocity of particle relative to the CM)
Taking a Galilean transformation to the lab frame, before the collision we get:
p1= m1 v1 = m1(v∗1 + V) = p∗ + m1 V
p2= m2 v2 = m2(v∗2 + V) = −p∗ + m2 V
while after the collision we get:
q1= q∗ + m1 V (7.21)
q2= −q∗ + m2 V. (7.22)
Exploiting the fact that p2= 0 we find
p1= p∗(1 + m1/m2) (7.23)
q1= q∗ + p∗m1/m2 (7.24)
q2= p∗ − q∗. (7.25)
Taking a Galilean transformation to the lab frame, before the collision we get:
p1= m1 v1 = m1(v∗1 + V) = p∗ + m1 V
p2= m2 v2 = m2(v∗2 + V) = −p∗ + m2 V
while after the collision we get:
q1= q∗ + m1 V (7.21)
q2= −q∗ + m2 V. (7.22)
Exploiting the fact that p2= 0 we find
p1= p∗(1 + m1/m2) (7.23)
q1= q∗ + p∗m1/m2 (7.24)
q2= p∗ − q∗. (7.25)