In a tug of war, if the parties on both ends of the rope apply equal and opposite forces on each other...?

Question

then how can one party win?
This is not a riddle, I have a conceptual doubt in Physics. It's based on the laws of motion.

Answer 1

GREAT question, and one that bedevils a lot of first year physics students.

The source of confusion is that you're looking at a pair of forces that are acting on two DIFFERENT objects. There is (let's say) 100 lbs. of rope tension pulling on team "A", and and equal and opposite 100 lbs. of rope tension pulling on team "B".

As you point out, Newton's 3rd Law says that these two forces will ALWAYS match.

Now, the problem is that some students try to apply this idea to Newton's SECOND law. They say, "the forces are equal and opposite, so they balance out. So there is no net force, and no acceleration."

But the flaw in that reasoning is this: when you are deciding whether there is a "net force" or not, you need to concentrate
ONLY on the forces that are acting on one SINGLE object (e.g. the forces on team "A"). Whether or not there's an equal force acting on team "B" has no bearing whatsoever on whether team "A" will accelerate.

So let's look at it from that perspective. Let's look at the forces acting on each team.

A-----------B

Forces acting on Team "A":
1) 175 N eastward (due to rope tension);
2) 170 N westward (due to friction with ground);

Forces acting on Team "B":
1) 175 N westward (due to rope tension);
2) 175 N eastward (due to friction with ground).

From this, you can see that team "A" will accelerate eastward, while team "B" will stay where they are. (i.e., team "B" will win). And this is true even though each team pulls equally hard (175 N) on the other.

Answer 2

An equal force does not mean an equal result if the situations are different.

The force required to barely lift a feather (mass of the feather times the gravitational constant squared), when applied to, say, a bowling ball, will *not* lift the bowling ball. It requires a much greater force to lift.

In this tug of war, if somebody with the weight of a feather and somebody with the weight of a bowling ball felt equal force at the ends of this rope, neglecting friction, the feather would move much further than the bowling ball moves.

Now, how can two parties of equal mass have a clear winner and a clear loser? Friction comes into play in the real world. The party who is better able to fight the pull--setting their feet, getting a good grip on the rope, etc.--will be the party who wins the tug of war. Friction acts as an opposing force to the direction of pull.

The winner of the tug of war isn't solely based on the force coming from the rope--it's based on the net force (force from rope - force from friction) and the mass of each group. Basically whichever group has the lowest net force / mass ratio will win the tug of war.

Answer 3

The rope is not the only force on the team. The ground exterts an opposing force on their feet. If the net force towards the other team becomes positive, they accelerate forward into the mud pit.

Answer 4

If the ground is not level, one side is taller on average than the other, or the surface for footing is not the same, that will provide all the difference needed for one side to win, even though the participants themselves provide equal forces.

Answer 5

Like the previous answer, the side that slips, loses. If they are strong enough, the rope will break. The winner is the team with more survivors and attached limbs.

Answer 6

Food. What can I say, why would I try and pull away from food? I always end up losing because I go towards the food and cross the line. But hey, I get free food!

Answer 7

If there is less friction between the feet of one team and the ground, the other team will win