# Integral Math exercise on force diagrams and equilibriumWatch

#1
I have no idea how to do this question:

a passenger train unit has five cars. the two end cars and middle one are powered and the other two are trailers. each powered car has a mass of 120 tonnes and each trailer 80 tonnes. the resistance to the motion of each car other than the leading one is 1 kN. the tractive effort of each powered car is 10kN. The train is traveling at a constant speed of 250 km h^-1 on a level straight track.
(i) What is the resistance to the leading car?
(ii) Find the tension or compression in each coupling
if the front power car is shut off owing to a fault, the train can only maintain a lower steady speed.
(iii) assuming that the resistances fall proportionately to speed but the tractive efforts are unchanged what is that steady speed?
The leading power car is still in failure.
(iv) the rear power car's tractive effort is reduced so that the coupling by which it is attached to the car in front is to be in tension rather than compression (when traveling at a steady speed). What is the maximum value of the tractive effort for this to be achieved?
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1 week ago
#2
These sorts of train problems are very common. The general method of approach is to consider a portion of a train and think about the forces acting on it at that time.

For part (i), you know that the train is travelling at constant speed. Thus, there will be no acceleration and hence no net force (by Newton's 2nd law). Thus you can draw an FBD for the leading car and resolve horizontally to find the force. (NB. I am unsure from the wording if it is asking for resistive force as a general force that is acting in the opposite direction to motion, or just the component that arises from the 1 kN per car...). If it is the latter, I think you can just add the resistances from the 2 other cars...

For part (ii), you can also use force balancing for each member of the train. You know that there is no net force acting on any of them as they are all travelling at constant speed. I would work from back to front, but it shouldn't matter.

For part (iii), you can now write the resistive forces as something like Resistive force = R_0 - k*v. You can once again do force balance (you know no acceleration at steady speed and hence net force on whole train is 0) and you can solve for v.

I think that should be enough to get you going (I think part (iv) has to do with force balance as well, but I haven't any time to look at it properly)

To summarise:
- split train into smaller cars/ members
- use Newton's 2nd law
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