Locomotive question with three trains involving force and acceleration

[needingtoknow]

Homework Statement

A locomotive (6.4 × 10⁵ kg) is used to pull two railway
cars (Figure 11). Railway car 1 (5.0 × 10⁵ kg) is attached
to railway car 2 (3.6 × 10⁵ kg) by a locking mechanism.
A railway engineer tests the mechanism and estimates
that it can only withstand 2.0 × 10⁵ N of force. Determine
the maximum acceleration of the train that does not
break the locking mechanism. Explain your reasoning.
Assume that friction is negligible.

Homework Equations

F = ma

The Attempt at a Solution

To start I decided that it can only withstand 2.0 × 10⁵ N of force in any direction, but the train will never move backwards, so the net force can only be 2.0 × 10⁵ N in one direction, the right. (the diagram shows the train moving to the right). Furthermore, all the objects will be moving in on direction all at once. My textbook states that if they all move together then they must all have the same acceleration (by adding the masses of the carts and the engine together and dividing by the force that causes all the carts and the engine to move in the first place). So when I try to do I get an answer around 0.1 when the answer in the back is 0.56 m/s^2. Why is that so? What is wrong with my method and understanding of these types of questions?
Any help is appreciated. Thanks again.

 

[cepheid]

2.0e5 N is the maximum force between car 1 and car 2, so it basically means that it is the force with which car 1 pulls on car 2. Of course, by Newton's 3rd law, this is also the force with which car 2 pulls on car 1.

Does that help?

 

[SteamKing]

From your description of the train, it appears the coupling in question connects ONLY cars 1 and 2. Since car 1 is presumably connected to the locomotive by a stronger coupling, the mass of car 1 would not need consideration. Similarly, the mass of the locomotive can be neglected.

If you draw a free body diagram, it is easy to see that if the coupling fails, it can only do so if the acceleration of car 2 produces more force than the coupling can withstand.

 

[needingtoknow]

Ok so one scenario is that car 2 moves too fast and puts pressure on the coupling between car 2 and car 1. But what if car 1 moves too quickly and pulls away from car 2 causing the coupling between car 1 and car 2 to be put under stress eventually breaking. On top of that, how can any of these scenarios be possible if all the carts are moving at the same acceleration (because they are all joined together). Stress would only be put on the coupling if car 2 (or car 1? referencing back to the earlier part of this) moves too slowly or quickly, but if all the carts move and accelerate at the same rate then no stress should be put in the coupling right?

 

[cepheid]

Ok so one scenario is that car 2 moves too fast and puts pressure on the coupling between car 2 and car 1. But what if car 1 moves too quickly and pulls away from car 2 causing the coupling between car 1 and car 2 to be put under stress eventually breaking. On top of that, how can any of these scenarios be possible if all the carts are moving at the same acceleration (because they are all joined together). Stress would only be put on the coupling if car 2 (or car 1? referencing back to the earlier part of this) moves too slowly or quickly, but if all the carts move and accelerate at the same rate then no stress should be put in the coupling right?

No, not right.

Draw a free body diagram JUST for car 2. Some force pulls on it, and as a result it accelerates. Where does this force come from? From car 1, through the coupling.

 

[needingtoknow]

Exactly so if the force is coming from car 1, shouldn't I use the mass of car 1 in order to determine the maximum force it can exert on the coupling if it is the one providing the force?

 

[cepheid]

Exactly so if the force is coming from car 1, shouldn't I use the mass of car 1 in order to determine the maximum force it can exert on the coupling if it is the one providing the force?

No! F = ma where F is the force ON the object, and m is its mass. In this case the force is acting ON car 2. Who cares where it comes from? Your *free* body diagram has just car 2 in it, and the forces that act on car 2.