Consider the following scenario. Your car breaks down and a friendly truck driver offers to push your car to a mechanic. Which of the following statements is true.

As the truck pushes your car down the road, the truck pushes forward 
on your car with more force then the car pushes backward on the 
truck. This is why the car moves forward. 

As the truck pushes your car down the road, the truck pushes 
forward on your car. The car doesn't push backward on the truck 
at all. This is why the car moves forward.

As the truck pushes your car down the road, the truck pushes 
forward on your car and the car pushes backward on the truck 
with exactly the same amount of force. Nevertheless, the car 
and truck both move forward down the road.

First-time physics students often believe the first or second statement is the correct statement but the third is the correct statement. The reason students often prefer the first or second is that they intuitively believe that in order for the car to move forward, the truck must push harder on the car then the car pushes on the truck. This seems logical but is missing two key concept about motion. How an object moves (accelerates) depends not on an individual force but on the total or net of all the forces acting on the object added together. At the same time, only those forces that act on the object (and not the forces the object exerts on other things) matters when it comes to determining the object’s motion. Therefore the car accelerates forward because the net or total force on the car is pointing forward. Accounting for all the individual forces on the car can be tricky because their are many of them but two forces are dominant. The first is friction between the axles and the wheels which would point backward because it opposes the motion of the car. The second is the force of the truck pushing the car forward. We can conclude that the force of the truck pushing on the car is greater then the frictional force because the car accelerates forward. Importantly, the force of the car pushing backward on the truck isn’t important when figuring out the car’s motion because this force doesn’t act on the car; it acts on the truck.

The correct statement above (the third statement) follows direction from Newton’s Third Law of Motion which states that:

 For every action force, there is a reaction force that is equal in 
magnitude but opposite in direction. Importantly, the action is 
exerted on the object generating the reaction and the reaction 
force is exerted on the object generating the action. In other 
words, the action and reaction forces are exerted on different 
objects.

Forces always occur in action/reaction force pairs. If the truck pushing on the car is defined as the action, then the car pushing on the truck is the reaction. These two forces point in opposite direction but have exactly the same magnitude. We could conversely define the car pushing on the truck as the action force and the truck pushing on the car as the reaction force. It doesn’t matter.

How to Win a Tug-Of-War

With knowledge of Newton’s Third Law, you are in a better position to figure out how to win a tug-of-war. The team that wins is definitely not the team that pulls the hardest on the rope. In fact, since one team pulls on one side of the rope and the other team pulls on the other side of the rope, the pulling forces exerted by the two teams constitute an action/reaction force pair. Thus, Newton’s Third Law tells us that these two forces are exactly the same magnitude. The team that wins is the one that has a total or net force (after accounting for the other forces acting on the team besides the pulling force) that points away from the other team. Thus, it comes down to friction. The team that can keep its feet more firmly planted on the ground can generate more friction and win the contest. Usually this is the team that is bigger and stronger and wearing cleated footwear giving the false impression that it is the team that can pull the hardest on the rope.

The moral of the story is this. Physics tells us that to win a tug-of-war, your team members should all wear cleats and your opponents should all wear slippers.