Tug-of-War Problem: Is Rope Horizontal? | Physics Explained

[hydra03]

Homework Statement

During a tug-of-war game, two teams pull in opposite directions on a heavy rope. Is it possible for the rope to be perfectly horizontal? Explain using principles of physics.

Homework Equations

None.

The Attempt at a Solution

I overheard the teacher explaining it to a peer and heard something like "there is a force of gravity acting on the rope itself, etc." I thought about it, but I can't really explain why this is the case.

 

[cbasst]

If the rope is heavy, it must have mass. Does that help? Try making a free body diagram of a point at the center of the rope. What forces are acting on the point at the center of the rope, keeping in mind that the rope has mass?

 

[lewando]

To elaborate on where cbasst is headed, assume that both sides are pulling with equal force (and they are all the same height). You would agree that the rope is not accelerating because the sum of all forces = 0.

Case 1: Draw a free body diagram of the rope if it is perfectly horizontal (straight line).
Case 2: Draw a free body diagram of the rope if it "sags" like a normal rope would sag.

In both cases (for the sake of simplicity), assume the mass is concentrated at the midpoint of the rope. This would make Case 2's rope look more like "v" than a "u".

See if this exercise sparks any insight.