# Force and Newton's Laws of Motion

1. Aug 9, 2011

### Cromptu

I came across this question, " An 8000 kg engine pulls a train of 5 wagons, each of 2000 kg along a horizontal track. If the engine exerts a force of 40000 N and the track offers a frictions of 5000 N, then calculate the force exerted by wagon 1 on wagon 2."
In this question,if we consider wagon 2 the system, the horizontal forces would be the tension T of the string by which it is attached to wagon 1 in the left direction, and tension T1 of the strig by which it is attached to the rest of the wagons in the right direction. So the force would be mass * acceleration which will be equal to T -T1. My question is that why do we need to consider the mass of the rest of the wagons 2,3,4 and 5 too? It is our choice, we can take any number of bodies or any body as a system;here I have taken wagon 2 as a system, so why do I need to consider the mass of the other wagons?

We had this question in our school textbook and when our teacher solved it, she considered the mass of the wagon 2 + wagon 3+wagon 4+ wagon 5. She might have chosen wagon 2,3,4,5 to be a system, but I have chosen wagon 2 as the system.

2. Aug 9, 2011

### cepheid

Staff Emeritus
You can of course consider a single wagon in isolation, and only the forces that act on it. However, you have no way to figure out WHAT those forces are (i.e. to solve for them) without at least considering the system as a whole first. Here's how I would go about solving it (it requires several stages):

1. First you use Fnet = Ma to figure out the acceleration of the whole system (therefore you know that each and every car has to have this acceleration). Here, M is the total mass (8000 kg + 5*2000 kg = 18,000 kg). Fnet is the net force on the system, which is the force in the direction of motion (the thrust of 40,000 N) MINUS the sum of forces in the direction opposite to the motion (which in this case is the friction force of 5000 N times 5 since each of the 5 cars is in contact with the track). This adds up to 25,000 N. So the net force is 15,000 N and the acceleration is 15,000 N / 18,000 kg = 5/6 m/s2.

2. Next, you consider just the load (the 5 wagons) and not the engine. You do this in order to solve for the tension force T in the cable that connects the engine to the load. This is one force that acts on the load. The opposite force acts to in the other direction and is the 25,000 N of friction once again. The total mass is now 10,000 kg and the acceleration must be given by 5/6 as above. Therefore, you can solve for what the net force on the load must be, and therefore what the tension force T must be.

3. NOW you consider just wagon 1 as the system. It has two forces acting on it: the tension force T in one direction (in the cable connecting to the engine), and the tension force T1 in the other direction (in the cable connecting to wagon 2). T1 is what the problem asks you to solve for. Again, since you know the mass of wagon 1 and its acceleration, you can solve for Fnet on wagon 1. Since you also know T, you can use Fnet and T to get T1.