Question

A train locomotive is pulling two cars of the same mass behind it. Determine the ratio of the tension in the coupling (think of it as a cord) between the locomotive and the first car (FT1) to that between the first car and the second car (FT2), for any nonzero acceleration of the train

Answer 1

Answer:

The ratio is  $\frac{F_{T1}}{F_{T2}} = 2$

Explanation:

The diagram for this question is shown on the first uploaded image

Here we are assume the acceleration of the train is a

which makes the acceleration of each car a

From the question we are told that

      Considering the second car

 The force causing it s movement  is mathematically represented as

       $F_{T2} = ma$

 Considering the first car

 The force causing it s movement  is mathematically represented as

      $F = F_{T1} -F_{T2} = ma$

=>   $F_{T1} -ma = ma$

=>   $F_{T1} = 2 ma$

=> $\frac{F_{T1}}{ma} = 2$

=> $\frac{F_{T1}}{F_{T2}} = 2$