"Newtons laws applied to a train of 3 cars"

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A train consisting of three cars of mass 'm' each is pulled with force 'F' by a locomotive in a straight, horizontal line. Assuming there is no friction, find the force on each car.

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The whole train experiences some acceleration $A$, so $F = 3 m A$. Each car, of mass $m$ experiences the same acceleration, so $F_{{\rm car}} = m A = (1/3) F$.

Thought experiment: if you put a (very stiff) spring in each linkage between cars and between the lead car and the loc. to measure the force applied at the linkage, what would you see?