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jamesbiomed
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Homework Statement
(5) A person sitting in a boat floating on a small pond throws a heavy anchor overboard. Does the level of the pond rise, fall, or stay the same? Explain.
Homework Equations
FB=mass of fluid displaced times g
Fnety=Fb-mg
The Attempt at a Solution
Theoretically, the pond level should stay the same. For the boat/man system after the anchor toss, the force of gravity will be less, because the mass of the boat/man system is less without the anchor. The buoyant force since it is floating is equal to the weight of the fluid displaced. As the anchor is tossed from the boat, there will be a shift in the net force up in the positive y-direction (assuming up is positive) causing the boat to rise relative to the water, and a portion of the water once displaced by the boat to return. This will cause an overall drop in water level.
However, when the anchor is thrown in, it will sink, until it reaches the bottom, and its exact mass will displace the same mass of water, which will cause a rise in the pond level exactly the mass of the anchor.
...I wrote that based on my verbal understanding of buoyant force. But what I'm struggling with is exactly how buoyant force will affect the boat after the anchor is tossed. Like I said, it will rise so that the amount of fluid it displaces is less. But how much less? The buoyant force will decrease, because the mass of the water displaced will decrease. I know F net y=Fb-fg. So fg is going to decrease, which will cause F net y to increase. But Fb will also decrease. So how can I better explain this, and determine precisely if the amount displaced by the anchor will equal the change due to the boat being lighter?
Sorry for the length...