What is the tension between the first and the second wagon?

Question

A train of 10 wagons each having a mass of 4X10exp4 kg. Locomotive has a mass of 2,2X10exp5 and pulls the first wagon with a force of 8X10exp5 N. What is the tension between the first and the second wagon?

I can't seem to understand what needs to be done.

Answer 1

Hi Bangtan O.,

Let's consider what you have, and what you need. You HAVE ten wagons, plus the locomotive; the locomotive must be accelerating the entire train at once. That means, the the tension in each coupling MUST have the same proportion to the total mass of the cars "downtrain" from the coupling. Thus, the first coupling (locomotive to first car) is pulling 10 cars (mass of 10 cars), the second coupling is pulling 9 cars (mass of 9 cars), and so on down to the last coupling (mass of 1 car). So that each car accelerates at the same rate (otherwise you would have a major problem, wouldn't you!), each Force/mass must give the same answer. So the tensions step linearly down from that of the first coupling, as you pass down the train, and reach 0 for the "coupling off the end of the train", so to speak. You should be able to take it from there?

-- Cheers, --Mr. d.