Does the water level rise when a boat sinks?

[glass.shards]

Homework Statement

An aluminum boat is floating in a swimming pool. A hole opens up in the bottom of the boat, and it sinks to the bottom of the pool. Does the water level rise, fall, or stay the same?

Homework Equations

(Is the buoyancy equation applicable here?)

The Attempt at a Solution

Intuitively I'd guess that water level would rise, since the boat displaces more water when it sinks... but does the weight of the boat while floating already account for this volume?

I'm further confused because when an ice cube melts in a cup of water, the water level does NOT change because the mass of the cube when melted does not change. However, throwing rocks off a boat will cause water level to FALL, because the volume displaced by the rock is less than the volume it displaces due to its weight while in the boat.

... the more I think about this the more confused I get!

 

[tiny-tim]

Hi glass.shards!

… the volume displaced by the rock is less than the volume it displaces due to its weight while in the boat.

That's right, nice and simple!

just fill out the answer by saying how much water it displaces when it's floating, and how much when it's submerged.

 

[glass.shards]

Hi tiny-tim, thanks for your reply!

The (sample exam) question is as written above, it is a MC question with no values provided. Would it be safe to assume the volume of aluminum the boat is made of is less than the water displaced by the boat's mass... thus the water level falls when the boat sinks?

Thanks so much for your help! :)

 

[Gokul43201]

Would it be safe to assume the volume of aluminum the boat is made of is less than the water displaced by the boat's mass...

You are comparing a volume with a mass. Think that through carefully, and try again. I suspect you are close.

 

[ideasrule]

Yes, it's safe to assume that. Aluminum has a density more than twice that of water.

 

[ideasrule]

You are comparing a volume with a mass. Think that through carefully, and try again. I suspect you are close.

I think the OP meant that the volume taken up by the aluminum is less than the volume displaced by the boat while it's floating.

 

[glass.shards]

Thanks for the replies!

What would happen if aluminum wasn't denser than water? (Well in this case the aluminum wouldn't sink... but for the sake of the argument, let's say it does... by being tied down, etc)

 

[ideasrule]

Maybe some numbers would clear things up. Let's say the boat weighs 1000 kg, so it has about 0.5 m^3 of aluminum. When it's afloat, it displaces 1 m^3 of water. When it sinks, it displaces 0.5 m^3 of water.

If aluminum had a density of 500 kg/m^3 instead of 2000, the 1000-kg boat would have 2 m^3 of aluminum...

 

[tiny-tim]

Hi glass.shards!

(just got up :zzz: …)

The simplest way of answering this (you've more-or-less said it, but it's best to be clear) is (complete the gaps) …

when something floats, it displaces its own … of water

when something is submerged, it displaces its own … of water
​

You then only have to point out which of its own … and … is greater!

 

[glass.shards]

Hey tiny-tim!

Since it's 1:30 AM over here, I'm guessing you're in a different timezone. To fill in the blanks, I'm going to say...

When something floats, it displaces its own -mass- of water.
When something is submerged, it displaces its own -volume- of water.

Thanks everyone for all your help, I was at my wits end this morning trying to understand this!