# Newton's third Law - action reaction pair

1. Sep 19, 2014

### caligirl

Hi,

I am a little confused with the concept of action reaction pair of forces. Does this depend on mass?

For example, if a train engine is pulling a buggy with force F, what would be the force applied by the buggy on the engine? The masses of the two are different and there is force of friction on the buggy.

I know that for 2 forces to be action reaction pair, they have to act on different objects. Does this mean that the force the buggy applies on the train engine is also F (in magnitude), but since mass is different, the acceleration would vary? I am not sure if I fully understand the concept.

2. Sep 19, 2014

### willem2

The force that the buggy applies on the train engine is also F. Since the buggys is attached to the train their accelerations can't be the same. This can happen because the force F isn't the only force on the train or on the buggy.

3. Sep 19, 2014

### caligirl

Does friction play a role in this situation?

4. Sep 19, 2014

### A.T.

I guess you mean "can't be different"?

5. Sep 19, 2014

### A.T.

Both the engine and buggy can have rolling resistance, but to simplify you can neglect that. The engine has also a propelling force which is static friction (traction). For both the engine and buggy the sum of all forces acting on them must produce the same acceleration.

6. Sep 19, 2014

### Staff: Mentor

Yes, provided that is the only force acting. Remember, Newton's 2nd law is often mis-stated as f=ma, but it is actually ∑f=ma.

If you have only one force acting on an object and only the reaction force acting on the other object then the accelerations will necessarily be in opposite directions, and the accelerations will be different magnitudes if the masses differ. Consider, for example, the earth and moon interacting through gravity.

In the train-buggy example, there are other forces acting on each object, so you can have their interaction force obey the third law (equal and opposite) while having them accelerate the same. In many cases you can use that fact to determine the other forces.