3 ms·
Wouldn't it make a much smaller difference in volume if the anchor was unable to hit bottom? Then it would be applying a force downward on the boat (increasing
by harpastum 18y ago
Wouldn't it make a much smaller difference in volume if the anchor was unable to hit bottom? Then it would be applying a force downward on the boat (increasing volume submerged) in addition to the volume of the anchor.
- sahaj 18y agoi think what you are saying is true.
- ErrantX 18y agopossibly - though the weight would be a lot less in the water than sat on the boat (aka in air) :)
- nandemo 18y agoYeah, but then it wouldn't be called an anchor. Just as we reasonably assume the anchor is heavier than water, we can assume it will hit the bottom.
- jcl 18y agoIt is a reasonable assumption, but the term "anchor" can also reasonably be applied to an object expressly intended to anchor a boat, regardless of whether it is attached to a sufficiently long rope to work in all parts of the lake.
- jcl 18y agoIf the anchor doesn't hit bottom, the level of the lake shouldn't change at all; the boat plus the anchor should displace the same amount of water as they did when the anchor was inside the boat -- exactly enough water to equal the weight of the boat plus the anchor. The only difference is that since the anchor is now displacing a small amount water by itself, the boat doesn't need to displace as much, so it should rise a tiny bit.
- alphamule 18y agowhere tiny bit = volume of anchor / surface area of lake. if the boat moves some because it isn't properly anchored, then presumably there would be more tension on the chain and thus a net rise in water level. of course, the problem initially never describes a chain & introducing the effects of one makes the problem far less tractable.