Asked by Shaila
how is this equation derived
V'2= V1(2M1)/(M1+M2) (elastic collision - where one object is moving and the other is stationary)
V'2= V1(2M1)/(M1+M2) (elastic collision - where one object is moving and the other is stationary)
Answers
Answered by
drwls
It is derived by requiring that both momentum and kinetic energy be conserved.
The center of mass moves forward at velocity vcm = M1*V1/(M1 + M2). After collision, the CM retains that velocity but the velocities change directions in CM-fixed coordinates.
In CM-fixed coordinates,
v2 = -V1*M1/(M1+M2)
v2' (after collision) = V1*M1/(M1+M2)
In lab-fixed coordinates
V2' = v2 -vcm
= 2 V1*M1/(M1+M2)
The center of mass moves forward at velocity vcm = M1*V1/(M1 + M2). After collision, the CM retains that velocity but the velocities change directions in CM-fixed coordinates.
In CM-fixed coordinates,
v2 = -V1*M1/(M1+M2)
v2' (after collision) = V1*M1/(M1+M2)
In lab-fixed coordinates
V2' = v2 -vcm
= 2 V1*M1/(M1+M2)
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