PHY 711 – Assignment #1
August 22, 2006
V
u
v
θ
χ
1. The figure above shows a scattered particle (mass m1 ) with velocity v1f and angle χ1 as
measured in the lab frame and velocity u1f and angle θ1 as measured in the center of mass
frame with V denoting the velocity of the center of mass. Assuming that the collision of
particle m1 with the initially stationary particle m2 is elastic, show that
cos θ1 +
cos χ1 = r
m1
m2
m1
(1 + 2 m
cos θ1 +
2
and
tan χ1 =
³
m1
m2
´2
)
sin θ1
.
1
cos θ1 + m
m2
2. Derive the corresponding relationships between θ2 and χ2 , the angles for the particle of mass
m2 .
1