Does the water level rise when a boat sinks?

1. Feb 27, 2010

glass.shards

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
(Is the buoyancy equation applicable here?)

3. 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.

Last edited: Feb 27, 2010
2. Feb 27, 2010

tiny-tim

Hi glass.shards!
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.

3. Feb 27, 2010

glass.shards

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! :)

4. Feb 27, 2010

Gokul43201

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

5. Feb 27, 2010

ideasrule

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

6. Feb 27, 2010

ideasrule

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.

7. Feb 27, 2010

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)

8. Feb 27, 2010

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...

9. Feb 28, 2010

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!

10. Feb 28, 2010

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!