# Newton's Third Law and acceleration question

1. Sep 27, 2012

### matajee66

Two wrestlers are pushing each other. Initially the wrestlers are at rest, however the small wrestler starts to move. Now in either cases, which wrestler exerts more force? My professor said that both exert the same amount of force on each other. This is really confusing as if they are applying equal forces on each other, how are they moving. Also say if the larger wrestler exerts 200 N and the smaller exerts 100 N, wouldnt the forces cancel out? If the larger one exerts 200 N, the smaller one then exerts the same force back right (the reaction force). The smaller wrestler exerts 100 N, then the larger would exert back the 100 N ( again Newton's Third Law). Doesnt this cancel out all forces, then how is there motion?

2. Sep 27, 2012

### dydxforsn

Each man puts a force on the other that pushes them apart. Further, their is a reaction to each force that each applied on one another that pushes them still further apart. There are no forces that push the two men together. Finally, each man will receive twice the force pushing them apart if both apply an equal force on each other.

You might also be confused that $F=ma$ or $a = \frac{F}{m}$. So the acceleration (their motion) is dependent not only on the force, but also on the mass of the object receiving the force. Thus each man depending on their mass will experience different acceleration or a different motion.

3. Sep 27, 2012

### matajee66

see they dont push off each other, they are continually pushing

4. Sep 28, 2012

### Bandersnatch

Think of a more simplified situation first:
A wrestler is pushing on a wall. He applies some force F to the wall, which acts with the same force on the wrestler, albeit in the opposite direction. That force is transfered through the wrestler's body to his feet, where friction acts against it. Once the push force is equal or higher than the friction, the wrestler starts to move.
The larger wrestler does the same, only he can apply higher force to the wall before he starts to move, since friction is dependent on wrestler's weight.

Now put these two together and remove the wall. As dydxforsn said, you get the reaction force of one's own push, plus the other guy's push force(which sum up to the same thing for both) acting on each of them. Since the smaller wrestler is not held so firmly in place(the friction between his feet and the ground is lower), he starts moving first.

In space, with no friction, both would start moving at the same time, each one accelerating according to F=ma.