Question

Two particles with different masses ??1 and ??2 traveling parallel to the x-axis with the same momentum ??, but in opposite directions. They undergo a perfectly elastic collision. After the collision, what are the final speeds of the two balls, ??1′ and ??2′?

Answer 1

In a perfectly elastic collision

Using momentum conservation

Pi = Pf

P1i + P2i = m1*v1' + m2*v2'

given that P1i = m1*v1 = p

P2i = -m2*v2 = -p (given, moving in opposite direction.)

then, p - p = m1*v1' + m2*v2'

m1*v1' + m2*v2' = 0

v1'/v2' = -m2/m1 eq(1)

Now In elastic collisions,

V1f - V2f = V2i - V1i

v1' - v2' = -(p/m2) - (p/m1)

frm eq(1),

v1' + v1'*(m1/m2) = -(p/m2 + p/m1)

v1' = -(p/m2 + p/m1)/(1 + m1/m2)

v1' = -p*( 1+ m2/m1)/(m1 + m2)

v1' = -p/m1

frm eq(1),

v2' = -v1'*(m1/m2)

v2' = -(-p/m1)*(m1/m2)

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