Solving the Two-Car Train Acceleration Problem

[Elvis]

Hi !

can anyone help me ?

A train locomotive is pulling two cars of the same mass behind it. Show that the tension in the coupling between the locomotive and the first car is twice that between the first car and the second car, for any nonzero accelerationv of the train .

thanks

 

[Rudipoo]

Draw yourself a little diagram of the situtation. Include the forces acting. You should have a force(say, F) coming out of the loco, between the loco and the first car call the tension T1; remember to draw two arrows for this tension, one pulling the loco towards the car, the other pulling the car towards the loco (these have the same magnitude (By Newton's Third Law) of T1. Similarly, draw in T2 for the tension between the cars. Let the mass of each car be m.

All the bodies (both the cars and the loco) must have the same ACCELERATION, otherwise they would split apart or crash. Call this acceleration a.

Consider an imaginary box around the two cars, which bisects the bar holding the first car to the loco. Now find F = ma horizontally, taking to the right as positive:

T1 + T2 - T2 = (2m)a
i.e. T1 = 2ma

Similary, imagine a box around the LAST car, which bisects the bar holding the first car to the last car. We find:

T2 = ma

hence, T1 = 2T2.

Hope this is sufficient for your needs.

 

[Elvis]

Thank you Rudipoo .