TUG OF WAR By: Alice Ju

Tug of war, also known as tug o'war, tug war, rope war or rope pulling, is a sport that directly pits two teams against each other in a test of strength. The term may also be used as a metaphor to describe a demonstration of brute strength by two opposing groups, such as a rivalry between two departments of a company. In this scenario, there is often a third party who is considered the "rope" in the tug of war.

HISTORY For 1000's of years men have enjoyed testing each other's strength according to the simple principles adopted for the sport of tug of war. In ancient Egypt, teams of 3 men would hold each other around the waist and try to pull the opposing team over a line marked on the ground. This sport, with or without the rope was adopted by many civilizations and became part of their culture such as Burma, India, Indonesia, Hawaii, Congo, Korea, New Guinea and New Zealand.  

THE PHYSICS OF TUG OF WAR 1. When the teams are equal in pull and the rope remains fixed, that is because the forces on either team are equal but opposite; so they cancel out and the rope does not move. The net force on the system is = 0; so there is no acceleration and the teams and rope do not move. That is Newton's 2nd and 3rd Laws of Motion. 2. When one team prevails over the other and it pulls the losers over the centerline, that is Newton's 2nd and 3rd Laws as well. The difference is now the net force <> 0; so there is acceleration towards the winning team. 3. Once the whole thing, teams and rope, start moving towards the winning team side, the movement will become steady state, no more acceleration, but still moving at a constant velocity. That is Newtons 1st Law about inertia and needing force to change it.

SAMPLE PROBLEM Alice and Will are playing tug-of-war. Alice wins, pulling Will into the mud puddle. Why did Alice win? a) Alice exerted a greater force on the rope than Will exerted on the rope. b) The rope exerted a greater force on Will than it exerted on Alice. c) Alice exerted a greater force on the ground than Will exerted on the ground. d) All of the above.

ANSWER At the start everyone is at rest. For someone to win, there must be an acceleration from rest to initiate motion in one direction. This acceleration does not need to be large. During the acceleration there must be a net force on each person in the direction of the acceleration.

ANSWER CONT... (a) and (b) are wrong because the rope has relatively small mass, so the tension forces at its ends are nearly the same size (F = ma where m is zero). The rope's mass is very small compared to the masses of Alice and Will, so even when it accelerates, the net force on the rope, F = ma, is negligibly small compared to the net forces on Alice and Will. (c) is correct. The net force on Alice that allows her to accelerate with respect to the ground is the force of the ground on her feet minus the force the rope exerts on her. The person with the better shoes, greater coefficient of friction at the ground underfoot, and foot control, wins. Will also accelerates, because the force of the rope on him is larger than the force of the ground on his feet. The player wins who can maintain the largest force between his or her feet and the ground.

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