ELASTIC COLLISION IN 1-D
Consider two particles that undergo an elastic head-on collision
y
V1i
m1
V2i
x
V1f
m2
m1
m2
V2f
after
before
Since the collision is in 1D we will drop the vector notation for velocities and use
components for velocities which can be negative or positive.
Cons. of Momentum
m1v1i
(1)
m2v2i
m1v1 f
m1 v1i vif
m2v2 f
m2 v2 f
v2i
Conservation of Kinetic Energy
1
1
1
1
m1v12i
m2 v22i
m1v12f
m2v22 f
2
2
2
2
2
2
2
2
m1 v1i v1 f
m2 v2 f v2i
(2)
m1 v1i vif
v1i
vif
m2 v2 f
v2i v2 f
v2i
Dividing (2) by (1) gives:
v1i
v1 f
v2 f
(3)
v2 f
v1 f
v2i
v2i v1i
The relative velocity of the particles before and after the collision have the same
magnitude but opposite sign.