Tension: wat formula i'l be using?

Question

A train locomotive is pulling two cars of the same mass behind it. Determine the ratio of the tension in the coupling 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

FT1/FT2 = 2

first coupler has to pull enough to accelerate twice the mass, therefore the force has to be twice.

only formula is F = ma

.

Answer 2

The force exerted on one car is equal to the total frictional resistance of the car plus the inertial resistance of the car.. For each of the car which are identical, the frictional resistance and inertial resistance can be assumed to be the same. For the last car assume the total resistance to be equal to FT2. Hence the tension on the coupling between the last car and the first car is equal to FT2. Since there are two identical cars being pulled by the locomotive, the total resistance of the two cars is 2 x FT2 = FT1. the ratio therefore is:

FT1/FT2 = 2FT2/FT2 = 2

Of course F = ma

But F here is just the enertial resistance which is the difference between the force exerted by the locomotive on the coupling and the friction force. When the total frictional resistance and the exerted force  become equal, the inertial resistance is zero and the acceleration becomes zero. Then the entire train will be moving at a constant velocity.The equation therefore is not just a simple F = ma. Rather it is:

FT = Ff + ma

Where:

Ft = the total tension on a coupling

Ff = the total frictional resistance of the cars or cars after the coupling

ma = the inertial force of the mass after the coupling.