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by lyesit
6405 days ago
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The only way that the water level could rise is if the average density of the submerged rope and anchor were less then the density of the water. However if this were the case then the anchor would not reach the bottom due to having insufficient mass to submerge the rope, and the water level would remain the same. |
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Scenario #1:
1. Negative buoyancy of anchor >> Positive buoyancy of rope. 2. Sufficient rope exists to reach the bottom with some additional rope remaining in the boat. 3. It's a calm enough pond without eddy currents such that, essentially, the only non-trivial forces acting on the rope once an anchorage has been established are isotonic (i.e water pressure).
Actually #3 completely obviates the need for an anchor in the first place, but I digress.
Imagine that one were to cut the rope at the anchor.
The rope begins to ascend to the surface due to its positive buoyancy and the amount of water being displaced will decrease over time until all of the rope is floating on surface and displacing its own weight.
Scenario #2:
The case is slightly different if the rope is under any kind of tension. Assuming a sufficiently strong rope and zero relative boat movement from its anchorage, the negative buoyancy forces due to the anchor are sufficient to overcome drag effects due to the current so the boat is very slightly being pulled under--hence an additional very slight increase in the water level of the pond.
Two additional edge-case visualizations that may be helpful. Think of the "perfect superdense anchor" scenario with a neutron-star and carbon nano-tube rope and a "worst-case" anchor consisting of aero-gel.