If there is a boat floating with an anchor on it, and the anchor isdropped from
ID: 1662866 • Letter: I
Question
If there is a boat floating with an anchor on it, and the anchor isdropped from the boat into a surrounding pool of water, would thepool water level remain the same?I'm confused, as I feel that the anchor displaces the samequantity of water since it has the same mass whether it is on theboat or submerged within the water.
Thanks for the help!
I'm confused, as I feel that the anchor displaces the samequantity of water since it has the same mass whether it is on theboat or submerged within the water.
Thanks for the help!
Explanation / Answer
According to Archimedes' principle, an object submerged in waterhas a buoyant force that is equal to the weight of the displacedwater., or Fb = mwaterg We can replace the mass of the water by the density of the watertimes its volume: Fb = Vdissg So the buoyant force is directly proportional to the volume of thedisplaced water. But the volume of the displaced water isjust the same as the volume of the submerged object (or thefraction of the volume that is submerged), so Fb = Vg When the anchor is on the boat, the buoyant force on the boatis Fb = Vboatg where is the density of the water, Vboat is thevolume of the boat that is submerged, and g is the acceleration dueto gravity. If the anchor is dropped, the anchor will besubject to a similar buoyant force Fb = Vanchorg and the anchor will displace an amount of water equal to itsvolume, so the water in the pool will rise.