In a tug-of-war between two athletes, each pulls on the rope with a force of 412 N. What is the tension in the rope? What is the absolute value of the horizontal force that each athlete exert against the ground? Thanks Rich

Have you made a sketch? If not, then make it, draw the two forces acting on it. For tension, take only one force, that makes a tension of 412 N in the rope.

That's because if you had a hanging object, you would have the tension as the weight of that object. But the wall also pulls the thread by which the objects hangs, and by the same force (only opposite in direction) and that is not considered.

Then, you know that the athletes are not moving since one force cancels the other. To stay like this, they have to push on the ground so that their resultant motion is zero. Can you guess what could be that force now?

This is a variation on a classic question for first year physics students:

If you tie a rope that has a breaking strength of 200 pounds between a wall and a horse, and the horse pulls on the rope with 150 pounds of force, will the rope break? Most people would answer (correctly) - no, because the tension in the rope is 150 pounds, which is less than the breaking strength of the rope.

Now, if you untie the rope from the wall and instead tie that end to a second horse, and that second horse pulls with 150 pounds force in a tug-of-war against the first horse (so that both horses are pulling with the same force) will the rope break? Many peope get this wrong - they incorrectly say yes, because they think that if two horses each pull with 150 pounds then the rope is under 300 pounds tension, which exceed its breaking strength. But that is incorrect - the proper way to look at this is to consider that it doesn't matter whether you tie that one end of the rope to a wall or a horse, in both cases the first horse is pulling against 150 pound of force and is in eqiulibrium, hence that's the tension in the rope in both cases.

Thanks everyone very much. It makes sense now. I made the mistake of responding incorrectly about the two horses question on a quiz in class. It is all clear now...