an unknown number of identical railcars each of mass m are connected in a line a

Question

an unknown number of identical railcars each of mass m are connected in a line and free to roll, a single railcar of same mass collides with stationary rail cars and bounces back with a fraction f of its precollision speed. if fraction is f=0.75 and collision is very nearly elastic, how many stationary railcars were there

Explanation / Answer

using conservation of momentum we get, let the number of identical railcars be n n*m*0 + m*u = nm*v1 - m*0.75u----(a) we have v2 - v1 = u1 -u2 since ,collision is elastic => -0.75u - v1 = 0 - u =>0.25u = v1 substituting in eq (a) we get m*u = nm*0.25*u - m*0.75u => 1.75u = 0.25nu =>n = 1.75/0.25 = 7 there for, 7 identical railcars each of mass m are connected in a line

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