Explain Buoyancy: A Boat, Rock, and Swimming Pool

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Homework Statement

A small boat is floating in a swimming pool. The boat contains a heavy rock. If the rock is tossed out of the boat into the pool and the rock sinks, what happens to the water level in the pool? What if the rock floats? What if the rock became submerged in water (but didn't sink)?

Homework Equations

None

The Attempt at a Solution

I'm not too familiar with the principle of buoyancy so I'd like it if someone could check and tell me whether my understanding is correct:

When the rock is still on the boat, as long as the boat is NOT SINKING, the boat is displacing an amount of water equal to mass of boat + rock. Even if the boat is submerged in water (but not sinking), the water still rises by an amount equal to mass of boat + rock. When the rock is taken out of the boat, the water level falls by an amount equal to the mass of the rock. When the rock gets tossed in the pool and it sinks, the rock displaces an amount of water LESS than the mass of the rock (because it is sinking). Thus, the water goes up by an amount less than the mass of the rock. Hence, the level of water has decreased overall.

If the rock floated or stayed submerged (but not sinking) in the water when tossed out, then the rock would be displacing an amount of water equal to its mass, so the water level goes back up by an amount of water equal to rock's mass. Hence in this case, the water level would stay the same.

 

[Stonebridge]

Your understanding is correct.
I note that the question doesn't ask you to explain your answer. That seems rather odd!
Your explanation is fine. Some small details:
Maybe you could add that it's the weight of the volume of water displaced that is equal to the upthrust. If the rock sinks, because it is denser than water, the weight of the volume of water it displaces is less than the weight of the rock. When in the boat, the weight of the volume of water displaced was equal to the weight of the rock. Therefore more water displaced.

 

[kerimek]

Your understanding of buoyancy is mostly correct. Buoyancy is the upward force exerted on an object when it is placed in a fluid, such as water. This force is equal to the weight of the fluid that the object displaces. This principle explains why objects float or sink in water.

In the case of the boat with the rock, the boat is displacing a certain amount of water equal to the combined weight of the boat and the rock. As long as the boat is not sinking, the water level will remain the same. When the rock is tossed out of the boat, the boat is now displacing less water, as the weight of the rock is no longer being supported. This causes the water level to decrease.

If the rock sinks in the pool, it is displacing less water than its mass, causing the water level to decrease even further. However, if the rock floats or stays submerged, it is displacing an amount of water equal to its mass, so the water level will remain the same.

Overall, the water level in the pool will decrease when the rock is tossed out of the boat, but the amount of decrease will depend on whether the rock sinks, floats, or stays submerged. This is because the buoyant force acting on the rock will be different in each of these scenarios, resulting in different levels of water displacement.