I think the reason it doesn’t work is because a tug of war is not so much about the force vectors being added together, (if it was then pulling sideways would be effective). I think it is more about which side’s members are lighter or have worse shoes, and therefore slip. If you have 1 person pulling sideways (+y direction), and another 5 each pulling in the +x and -x directions respectively, then (ignoring the x direction), we have a force (it doesn’t matter who is exerting the force) pulling 1 person in the -y direction and 10 in the +y direction. Which group is going to slide first? (The 1 person I think). And when they do you just have the other 10 not having moved (the static friction was never overcome), and 1 person who has moved closer to the rope/everyone else, but has not moved them at all.
If tug of war was about the force vectors being added together, pulling sideways should be equally effective to pulling in any other direction, I think. (Imagine the rope is under so much tension from the preexisting pullers that you can model it as a steel bar. Further imagine that you are on a frictionless plane and everyone is exerting force via rocket thrusters. Your own little thruster will slowly accelerate the whole system equally fast in whichever direction you pick.)
I think the reason it doesn’t work is because a tug of war is not so much about the force vectors being added together, (if it was then pulling sideways would be effective). I think it is more about which side’s members are lighter or have worse shoes, and therefore slip. If you have 1 person pulling sideways (+y direction), and another 5 each pulling in the +x and -x directions respectively, then (ignoring the x direction), we have a force (it doesn’t matter who is exerting the force) pulling 1 person in the -y direction and 10 in the +y direction. Which group is going to slide first? (The 1 person I think). And when they do you just have the other 10 not having moved (the static friction was never overcome), and 1 person who has moved closer to the rope/everyone else, but has not moved them at all.
If tug of war was about the force vectors being added together, pulling sideways should be equally effective to pulling in any other direction, I think. (Imagine the rope is under so much tension from the preexisting pullers that you can model it as a steel bar. Further imagine that you are on a frictionless plane and everyone is exerting force via rocket thrusters. Your own little thruster will slowly accelerate the whole system equally fast in whichever direction you pick.)