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An 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000N , calculate the acceleration of the train.

To find the acceleration of the train , I divided 40000N by mass of 5 wagons. But in the book the mass of the engine was also included for finding the acceleration.

I cannot understand how is the force of 40000 N acting on (engine + wagons). According to me this should only act on the wagons as the engine is applying this force.

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    $\begingroup$ This is a poorly worded question. I read (like you) that the engine exerts 40000 N on the train of wagons. What they should have said is that the net force on the engine and train is 40000 N, if the mass of the engine was involved. The only correct answer is to give both situations. The book is wrong. $\endgroup$
    – Bill N
    Commented Apr 12, 2019 at 11:43
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    $\begingroup$ It's tricky but it says "the engine exerts a force" it does not say " the engine exerts a force on the cars". And that's the reason you include the engine! $\endgroup$
    – PhysicsDave
    Commented Apr 12, 2019 at 12:40
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    $\begingroup$ The problem is ambiguously worded, but I'm shocked that you have all forgotten to include the vertical force exerted by the weight of the engine on the ground! Surely, we're meant to subtract that out from the 40kN total force. Since the question does not specify what the local gravity is on the train's planet, we clearly cannot solve it. $\endgroup$
    – Xerxes
    Commented Apr 12, 2019 at 13:26
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    $\begingroup$ @Xerxes This is completely wrong. The vertical forces cancel each other and have nothing to do with the horizontal force pulling the train. You forget the normal force exerted by the ground on the train. $\endgroup$
    – nasu
    Commented Apr 12, 2019 at 15:16
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    $\begingroup$ @nasu The cancelling normal force is exerted on, not by, the engine. $\endgroup$
    – Xerxes
    Commented Apr 12, 2019 at 15:47

6 Answers 6

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The question is ambiguous, but I think we are meant to assume that the engine exerts a force of $40000$ N on the track. From the reaction force of $40000$ N on the engine some part, say $F_1$, is acting to accelerate the engine itself and some other part, say $F_2$, is exerted on the wagons. The acceleration of the engine and of the wagons is the same, so if this acceleration is $a$ then

$F_1 = 8000a \\ F_2 = 10000a \\ 40000 = F_1 + F_2 = 18000a \\ \Rightarrow a = \frac{40000}{18000}$

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    $\begingroup$ I agree, the wording includes the engine. $\endgroup$
    – PhysicsDave
    Commented Apr 12, 2019 at 12:44
  • $\begingroup$ I would argue that the engine exerts the force on the track, and the reaction force is what accelerates the (whole) train (engine+wagons). Otherwise the problem would have specified the force acting at the first coupling, or used some indication like "net". $\endgroup$
    – CCTO
    Commented Apr 12, 2019 at 15:43
  • $\begingroup$ @CCTO Agreed - I will add this to my answer. $\endgroup$
    – gandalf61
    Commented Apr 12, 2019 at 15:48
  • $\begingroup$ The OP's question is a good one, but I don't think that the test question is ambiguous in the slightest. It seems to me that the OP's misunderstanding of it is exactly the sort of misunderstanding that this question is designed to test. $\endgroup$
    – bornfromanegg
    Commented Apr 12, 2019 at 16:09
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    $\begingroup$ @bornfromanegg I think the ambiguity comes from the word "engine". if we assume that the engine is a moving engine i.e. a locomotive then the $40000$ N is accelerating both the engine and the wagons. But "engine" could possibly mean stationary engine, in which case the $40000$ N is accelerating only the wagons and the mass of the engine is irrelevant. $\endgroup$
    – gandalf61
    Commented Apr 12, 2019 at 16:17
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IMO you're right: the problem's wording is bad. It's meaningless to say "the engine exerts a force of 40000 N". The engine interacts both with the first wagon and with the rail, exerting forces on both and these forces are different. How can we know what the book's author had in mind? If the former, your answer is right, if the latter, the book's one is right. Of course in the latter case (force exerted on rail) it's not that force which accelerates the train, but the rail's reaction.

As a general rule we shouldn't say "A exerts a force" - much better "A exerts a force on B". Better yet "A exerts a force on point P of B". The point where a force acts can make a great difference.

Edit

Many things have been said but IMO it's useful to be still clearer. After further reflections I think it's not wording that's bad, but the thinking behind.

As already stated e.g. by @Farcher in mechanics problems the first thing to be done is to make clear which the (mechanical) system is. In our case, it's wagons or wagons + engine? Note that it wouldn't make difference as to acceleration, which is the same for all parts of the train, but isn't by no means the same if forces are concerned. Consider the two choices:

a) The system consists of wagons alone. Then it makes sense to say that engine (which doesn't belong to the system) applies a given force $F$ to the system and compute acceleration as $a=F/m$, where $m=10000\,\rm kg$. Given the book's answer, this isn't the author's choice.

b) The system consists of the whole train, engine included. Then there are two alternatives as to the given force $F$ (here I'm reiterating)

b1) $F$ is a force engine applies to wagons. Then it's an internal force and as such it cannot accelerate the system. Its acceleration is only due to the net external force (in computing the resultant internal forces cancel thanks to third Newton's law). Then the solution is nonsense.

b2) $F$ is a force engine applies to external world. In that case it will never accelerate the system or a part of it. It could accelerate the rail, were it not firmly fixed to ground. Not to mention that a force engine applies to rail exists, but is in the wrong direction.

So not even choice b) is acceptable. Neither as it's used in gandalf61's answer.

I'd like to add another comment. Unfortunately "engine" in English may mean two different things: either the motor proper (electric, diesel, or else) which ultimately is the cause of motion - or the car carrying it. Of course the datum of mass suggests the latter interpretation. But my suspicion is that the author - maybe without realizing - thought of the former.

I'm led to say so because it's a very common way of thinking about cars and other motorized vehicles. If you ask someone "which force causes a car move?" I bet you'll get as an answer "the motor's force". Nobody thinks that in strict mechanical meaning the motor can only produce internal forces and as such will never move a car by a cm. That the only external force which can put a car in motion is the road's friction on the wheels.

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  • $\begingroup$ Choice b is, acceptable. You just have to go one more step and apply the law of action and reaction. The force exerted on the rails accelerates the Earth, but the reaction accelerates the train. $\endgroup$
    – Jan Hudec
    Commented Apr 13, 2019 at 12:18
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You have to add mass of engine also.The force is applied on whole system.What will be the acceleration of only engine if you remove wagons?You will consider it's mass also.

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    $\begingroup$ "The force is applied on whole system." That's NOT what the words of the problem say. The engine exerts a force---that must be on something else. In this type of analysis, things don't have self-forces. It's a terrible question. $\endgroup$
    – Bill N
    Commented Apr 12, 2019 at 11:49
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    $\begingroup$ @Bill N: The engine exerts a force on the TRACK, which causes it to accelerate. Since the engine is connected to the cars, it must accelerate them as well, so the mass being accelerated is engine + cars. $\endgroup$
    – jamesqf
    Commented Apr 12, 2019 at 15:45
  • $\begingroup$ @jamesqf The engine also exerts a force on the tracks due to gravity. Since we were just given total force exerted by the engine on the tracks, don't forget to subtract the gravity portion when calculating the force accelerating the train. $\endgroup$
    – Matt
    Commented Apr 12, 2019 at 16:20
  • $\begingroup$ @Matt As long as we're being pedantic, they don't say which planet this train is on, or if it's outer space, so the gravitational force is undefined and the question is unsolvable. $\endgroup$
    – Nuclear Hoagie
    Commented Apr 12, 2019 at 18:26
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    $\begingroup$ @NuclearWang Good point! But I disagree that accounting for gravity is pedantic. (Anyway, assuming earth is a pretty standard assumption for entry level physics) The question doesnt specify what the 40kN is exerted on. It could reasonably be on the first wagon in the line, or it could be the tracks. But in fact neither of these are what the "correct" answer assumes. I dont think its fair to expect arbitrary assumptions while also expecting the OP to ignore a very real, very important, force. Especially since the engine apparently exerts a net 40 kN on presisely zero objects. $\endgroup$
    – Matt
    Commented Apr 12, 2019 at 18:32
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Imagine if you only had the engine by itself exerting the same 40,000N of thrust, to find the acceleration of the engine you would not do 40000/0kg would you? The 40,000N the engine exert is also used to thrust itself forward.

But let’s say it didn’t, and that only the wagons were pulled. Well now you have a stationary engine, pulling 5 wagons, each with an acceleration of 4m/s^2. These wagons will catch up to the engine in no time and obliterate the engine from behind. we can at least agree this is not how train works

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    $\begingroup$ If the engine is by itself,, what is exerting thrust on? It can't exert thrust on itself. There must be something else exerting thrust on the engine. Regarding your second paragraph, there is obviously some force acting on the engine, but we aren't told what it is. All we know is that the engine exerts a force of 40000 N, presumably on the train of wagons. $\endgroup$
    – Bill N
    Commented Apr 12, 2019 at 11:51
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    $\begingroup$ It's tricky but it says "the engine exerts a force" it does not say " the engine exerts a force on the cars". And that's the reason you include the engine! The problem is solvable for either situation. $\endgroup$
    – PhysicsDave
    Commented Apr 12, 2019 at 12:43
  • $\begingroup$ I do agree with Physics Dave. Though the very existence of this Q and some comments tell that the exercise could have been written more clearly. $\endgroup$
    – Alchimista
    Commented Apr 12, 2019 at 14:47
  • $\begingroup$ @BillN on the rails, naturally. $\endgroup$
    – hobbs
    Commented Apr 12, 2019 at 15:46
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The question is flawed in that can be deemed to be ambiguous and therefore requires interpretation.

Using Newton’s second law requires the system under consideration to be defined and that has not been done in this question.

Without the system being defined the statement

the engine exerts a force of 40000N

is the cause of the ambiguity.

So which is it?

1 The engine is exerting an external force of 40000N on the system of five wagons.

2 The engine exerts an internal force of 40000N on the system of five wagons and the engine.

3 There is an external force of 40000N on the engine and five wagons.

The author of the book really meant option 3 but given the way the question was written I have to agree with the OP that an external force of 40000N is acting on the five wagons whcich is option 1.

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The force of 40 kN is exerted on the rails, not the wagons

We have to assume that the engine and wagons are all coupled together, and therefore that they move together. If the engine exerted a force on the wagons but did not move with them, the wagons would provide a different force in reaction. If the train was off the track, it would not be exerting that force on the wagons.

The engine turns the wheels which exert a force backwards on the rails, which also imparts the reaction forwards on the train.

That force is transmitted from the rails through the engine and the coupling to the wagons.

To take a different circumstance, suppose the train was going uphill? The engine will still exert a force of the same magnitude, but this time the balance of forces and angles are different, so the acceleration is different too.

Thus that force must accelerate the total mass of the engine and the wagons together.

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    $\begingroup$ No, the question is flawed/ambiguous. When you specify "A exerts a force ...." you must say what that force is exerted on. $\endgroup$
    – Bill N
    Commented Apr 14, 2019 at 3:25

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