# Finding the Force of two objects - by using Acceleration but only ONE of the given masses?

I came across the following question in my physics textbook and wanted to try to solve it:

A 1700 kg car is towing a larger vehicle with mass 2400 kg. The two vehicles accelerate uniformly from a stoplight, reaching a speed of 15km/h in 11 s. Find the force needed to accelerate the connected vehicles, as well as the minimum strength of the rope between them.

I did get the correct answer after a while by finding Acceleration (which was 0.3788m/s^2and then multiplying it by the mass of the truck, which was 2400kg. (The answer should be 910 N)

The part that I don't understand (and I had trouble finding the answer because of this very reason) is: Why is the mass not the sum of both masses of the car AND the truck? Should it not be both, as it specifically mentions that they are tied together, and therefore they technically act as one whole system?

• The reason you are having so much trouble is that you have not drawn a free body diagram on each of the vehicles (separately), and have not written a corresponding force balance for each. – Chet Miller Feb 24 '16 at 3:37

Now if you were looking at the force between the wheels of the towing vehicle, and the road surface, that is a force that will be used to accelerate both the car and the truck. If both were of the same mass, and the force on the rope was $F$, then the force on the (sum of the four) wheels would be $2F$ - one $F$ to accelerate the truck, and one to accelerate the car.