Something about tensions throws me off. I can never seem to get tension problems.(adsbygoogle = window.adsbygoogle || []).push({});

A freight train consists of 250 cars each of mass 64 metric tons. The acceleration of the train is a=0.043m/s^{2}. What is the tension in the coupling that holds the first car to the locomotive? the last car? Ignore friction.

Here's a little diagram.

[___]---[___]---[___]---[___]---[___]\ ----->a

Let me treat the last car first. The free body diagram looks like this:

O-------> T

T=ma=2.75x10^3 N

Correct?

On the first car we have (ignoring normal force and weight, which cancel out),

<-----O----->

Right? Since the car pulls on the car behind it, the car behind it pulls on it. And the locomotive pulls on the first car is the forward direction.

If you treat the train as a whole, the net force is 6.88x10^5 N in the direction of a.

Considering the front boxcar,

T_{1}- T_{2}=F_{net}=ma

a is known, m is known, F_{net}is known

T_{2}must be sufficiently large to accerelate the remainder of the train of mass M by a. So

T_{1}=a(m+M)

T_{1}=6.88x10^5 N since m+M is the total mass of the train

Is my work ok? Can you give me some advice on how to deal with tension problems in a systematic way?

Thanks.

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# Deal with tension problems in a systematic way?

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