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?

  • $\begingroup$ 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. $\endgroup$ – Chet Miller Feb 24 '16 at 3:37

Forget about the towing vehicle, and focus just on the rope connected to the truck. If you were looking at the scene through a small window, and all you could see was the rope and the truck, what force should there be on that rope in order to accelerate that truck? You don't have to know what is on the other end of the rope - it could have been a winch attached to the earth itself...

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.

  • $\begingroup$ The question to me is poorly phrased, I think what they meant was to say the towing truck is the driving force and it should be ignored $\endgroup$ – Russell Yang Feb 24 '16 at 3:28

"Force" is poorly defined here. The force the tow truck will need to exert to accelerate itself and the towed car with the desired acceleration will obviously depend on the sum of the two masses, but the force exerted by the rope on the second car (and hence the minimum required tensile strength of the rope) will only depend on the towed car's mass. The latter result is intuitively obvious: a car towing a ping-pong ball doesn't need a very strong rope.


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