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

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SUMMARY

The discussion centers on the physics of a tug-of-war scenario, specifically whether a heavy rope can be perfectly horizontal while being pulled by two teams. It is established that the rope, having mass, experiences gravitational force, which prevents it from remaining perfectly horizontal. The analysis involves creating free body diagrams for two cases: one where the rope is horizontal and another where it sags due to its weight. The conclusion is that the rope cannot be horizontal due to the forces acting on it, particularly gravity.

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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.
 
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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?
 
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.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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