You elastically collide 2 carts of nearly identical masses m Before the collisio

Question

You elastically collide 2 carts of nearly identical masses m Before the collision, box 2 is at rest and box 1 is moving towards box 2 with constant velocity v1i. Assume that the collision is elastic and (no kinetic energy was lost during the collision) after the collision box 1 is moving with velocity v1f and box 2 with velocity v2f. Find out v1f and v2f in terms of initial velocity v1i and carts masses m. Presume the original direction of cart 1 to be positive. So I thought all I would need to do is set the initial momentum equal to final momentum which gave me (mv1i+mv1f)/m to get v2f. and (mv1i-mv2f)/m=v1f. However, both my answers are wrong. I don't know i am on the wrong track or just entering them incorrectly.

Explanation / Answer

According to conservation of momentum

m1v1i+m2v2i =m1v1f+m2v2f

m1v1i = m1v1f+m2v2f .... (1)

From conservaion of kinetic energy in elastic collision

(1/2)m1v1i2 = (1/2)m1v1f2+ (1/2) m2v2f2

m1v1i2 = m1v1f2+ m2v2f2    ......(2)

from Equation (1) and (2) it follws that

m1v1i (v2f-v1i) = m1v1f(v2f - v1f)

v2f (v1i-v1f) =v1i2-v1f2

v2f =(v1i + v1f) ...(3)

Substituting this in equation (1) we obtain

v1f = (m1 -m2)v1i /(m1 +m2 )

v2f = 2m1v1i /(m1 +m2 )

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