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Let me post a question from a school textbook sent to me by a friend of mine. The book has no answer scheme and googling the question is not particularly helpful because the answers seem to vary wildly.

Here is the question: A $8000$ kg engine pulls $5$ wagons, each of $2000$ kg along a horizontal track. If the engine exerts a force of $40000$N and the track exerts a frictional force of $5000$N then calculate the force exerted by wagon 1 on wagon 2

Firstly, while the question is not very clear, most people seem to assume that the friction of $5000$N is exerted on the whole train.

Now, moving onto the basics we get the resultant force on the train as $35000$N and the accelerationof the whole system as $\frac{F}{M}=35000/18000=1.944 m/s^2 $

Now is where I am confused as to how to proceed. One of my main problems with the answer given by the reputable online coaching site Byju's answer (link below) is that it does not take into account friction at all.

https://byjus.com/questions/a-8000-kg-engine-pulls-train-of-5-wagons-each-of-2000-kg-along-a-horizontal-track-if-the-engine-exerts-a-force-40000-n-and-the-track-offers-a-friction-force-of-5000-n-calculate-net-accelerating-force/

These kinds of problems are frustrating when I thought I had gotten the hang of basic newtonian physics. My inclination was to first find the resultant force on wagon 2 by doing $ma$ and then adding it to the net backward force acting on wagon two. But I am not sure how exactly to calculate this value

Any help would be appreciated

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  • $\begingroup$ Yes you are right there is no mention of where is exactly friction is being applied also i would suggest you to have a knowledge about fbd it would be very helpful in future for you $\endgroup$ – Prateek Mourya Sep 13 '20 at 17:57
  • $\begingroup$ I agree with shelton Benjamin's comment. The track exerts a friction force of 5000 N. Is all of this friction exerted on the engine? Is the friction allotted to each object in the train? If so, is this allotment based on the mass of each object? Conclusion: your question is ambiguous. $\endgroup$ – David White Sep 13 '20 at 23:12
  • $\begingroup$ I do not understand the problem. He subtracts engine force by frictional force, thus taking friction into an account. And because of center of mass theorem, that is whole mass time acceleration of center of mass is given by sum of external forces, you do not care where is the friction exerted, only about the direction. And I think it is safe to assume, that engine pushes train in forward direction, while frictional force in the backward. $\endgroup$ – Umaxo Sep 14 '20 at 14:27
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Since the wheels of the engine are driving the engine forward, it might be reasonable to assume that the engine is not subject to a backward force of friction. The 5000 N of friction would be divided equally among the 5 wagons. You need the force to accelerate 4 wagons. (Including the 4000 N of friction.)

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  • $\begingroup$ Are you saying the BYJU'S answer is incorrect? Step (c) where the force of wagon 1 on wagon 2 is calculated does not include the friction on wagons 2 through 5, and would seem to be a mistake (unless the wagons are somehow floating :-). $\endgroup$ – JohnHoltz Sep 13 '20 at 22:28
  • $\begingroup$ I,m saying that Aman is correct in thinking the friction should be considered in the final calculation. $\endgroup$ – R.W. Bird Sep 14 '20 at 13:59

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