An anchor is thrown from a boat floating in a swimming pool?

Question

..but the anchor does not reach the bottom of the pool and it's still attached to the boat. What happens to the pool water level?

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Answer 1

Level remains the same because pressure of water
on the bottom of the pool remains the same
(equal to combined weight of water, boat and anhcor):

h = g(Mw + Mb + Ma) / [ρgS]

Answer 2

The displacement by the boat+anchor combination doesn't change, since the weight acting is the same in both cases.

(This seems counter-intuitive but here's the reasoning:
When thrown in the water, the anchor DOES displace an additional volume, but the corresponding upthrust REDUCES its effective weight to the boat, so those cancel out exactly.

(Similarly, I was trying to be a smartass, considering the effect of the anchor chain or cord, but that similarly nulls itself out by Archimedes' Principle.)

So the answer is: displacement and water level doesn't change - as long as anchor is attached to boat and doesn't hit bottom or get support.

(Now if the anchor was no longer attached to the boat, obviously the amount of water it displaced would only be its volume and not its weight, thus the boat would displace less volume by (rho_anchor)*anchor_volume; and the anchor would displace additional 1*anchor_volume, thus the total displacement would decrease by (rho_anchor-1)*anchor_volume, so the water level would fall, assuming rho_anchor>1 i.e. you don't have a polystyrene anchor)

Answer 3

I read in one of your answers that the level of water goes up by the weight of the anchor .
but the point is here that the level goes up by the volume of the anchore . and for your answer , when the anchor has sinked in the water , it is not important that is in the buttom of the pool or in the half depth or... . just if it is sinked completely , the level of the water goes up to the most level it can go with the volume of that anchor.

Answer 4

the water level stays the same...the pool water was already properly dispalced by the weight of the anchor, as it was still a part of the boats overall weight...