![]() Object not under suction seal (buoyant force): P=rho g h + rhocube g hcube - rho g hcube = rho g (h-hcube) + rhocube g hcubeĪnd in all cases it works out so the pressure is sufficient to support the cube and the (possibly slightly shortened) column of water. Object under suction seal (no buoyant force): P=rho g (h-hcube) + rhocube g hcube So the buoyant force term comes from that difference between the force exerted by the actual column of water above a certain area, and the force due to the average pressure at the bottom of the tank. ![]() For a sufficiently large tank, the pressure on the bottom will be uniform, even if the actual height of the water column varies slightly, due to objects in the water displacing some water. If there is a buoyant force (in other words, the cube does NOT form a perfect seal with the ocean's floor), then there is actually more force in play than just the column of water above the tank. The addition of $4$ cubic feet of water increases the water level by $0.5$ feet, meaning that $$\pi r^2(h+0.5)=V+4.$$ Once again, we find that $$\pi r^2\cdot0.5=4.If the bottom of the ocean is perfectly smooth and watertight and the object forms a perfect "suction cup" on the ocean's floor, then you're right, there will be no buoyant force, and the force on the ocean's floor is just the weight of the column of water plus the weight of the cube. The cylindrical shape tells us that $$\pi r^2h=V,$$ where $r$ is the radius of the tank (in feet). That is, $$\pi r^2\cdot0.5=4,$$ as before.Įdit: Instead of making such an assumption, let us instead assume that $V$ is the volume of water originally in the tank and $h$ is the initial water level (in feet). ![]() More simply, we could just assume that we started with an empty tank and poured in $30$ gallons ($4$ cubic feet), so that our change in water level is exactly the water level. ![]() You seem to be starting with one cubic foot of water in the tank, so when we pour in $30$ gallons ($4$ cubic feet), we have a change in water level of $0.5$ feet, yes, but our new volume of water is $5$ gallons. $30$ gallons take up $4$ cubic feet of space, as you've determined, but the rest doesn't really make sense. ![]()
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