Fluid Displacement and the Drop in Water Level Explained

[vu10758]

Homework Statement

A small child floats in a boat in a swimming pool. The boat contains an anchor
The child drops the metal anchor into the water and watches it sink to the bottom. Meanwhile, the water level in the pool (measured by its height on the side of the pool) actually drops. Why?

Homework Equations

The Attempt at a Solution

I am thinking that if the anchor is dropped into the water, the water should rise because of Archimedes principle. However, I am told that the water level actually drop. Where did the water go? Is it because as the boat pushes down on the water, the water pushes the boat further up due to Newton's third law, causing it to appear as if the water level has dropped? Or is the reason something else? I know that the change in pressure is the same as the weight of the boat so does this have anything to do with the question?

 

[Kurdt]

Think about the mass of the anchor and its volume. When the anchor is in the water what volume of water does it displace? When the anchor is in the boat what volume of water does it displace?

 

[m2003]

I would like to clarify that the water level in the pool does not actually drop, but rather appears to drop due to the displacement of the water by the boat and the anchor. When the anchor is dropped into the water, it displaces a certain volume of water equal to its own volume. This displaced water then moves away from the anchor, causing the water level around the anchor to appear lower. This displacement of water is also the reason why the boat appears to rise higher in the water when the anchor is dropped. This is due to Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object.

Additionally, the boat pushing down on the water does not cause the water level to drop. Instead, it causes the water to be displaced, which is why the water level appears lower. The change in pressure is also not directly related to the change in water level in this scenario.

In summary, the drop in water level is a result of the displacement of water by the boat and the anchor, and is a normal occurrence according to the laws of physics.