Which force is responsible for victory in tug of war?

Question

I'm confused: In a tug of war game on rough ground who will win? The one who applies greater force on the rope or the one who applies greater force on ground?

Answer 1

Typically, we assume the rope itself is of negligible mass in such a situation compared to the total mass of either team. In that situation, the tension will have the same value throughout the rope (since none of the force is required to act on the rope itself, because there is negligible mass there). The rope thus must pull on each team with the same force.

If we take each team, in turn, as a system, the only horizontal forces acting on the teams from outside are the force of tension in the rope, and the horizontal component of the Newton's 3rd law reaction force from the ground, caused by the teams pushing on the ground. This reaction force is thus equal in magnitude to the force with which the team pushes on the ground.

Supposing the teams are playing in the traditional way for tug-of-war, the tension force should be opposite the horizontal reaction force. Whichever of those is greater will cause the net force to be in its direction:

F_net (horizontal) = T - F_ground = ma

(here I arbitrarily take the direction of the tension force to be positive)

Assuming the team wants to accelerate in the direction opposite the tension, so they can win, they want the force the ground exerts on them (and thus the force they exert on the ground) to be greater.

I hope this helps! Let me know if you have any other questions.