Puzzler

[ivyfic]

Here's another brain teaser for you (provided by my brother):

You are standing in a boat in a lake holding a rock. You throw the rock into the lake.

What happens to the level of water in the lake?

Again, assume all basic Physics 101 assumptions (no wind, no current, etc.).

Comments

[gryphonrose.livejournal.com]

Nothing--the rock would raise the water level but the boat's displacement decreases so it balances out.
How'd I do?

[ivy03.livejournal.com]

Bzzzt! Wrong! You're right -- the rock would raise the level and the boat would decrease it...but would they change it the same amount?

(This is what I said, though. I could picture my notes on buoyancy, but couldn't remember the formulas.)

[chuckro.livejournal.com]

Wouldn't the amounts depend on the density of the rock? That is, the displacement of the water by the boat is a function of the rock's weight, but the displacement of the water by the rock is a function of its volume. Maybe? It's been almost a decade since I took a physics class.

[gryphonrose.livejournal.com]

Oh, now you're being picky. I had the principles right, and that's enough for me. :)

[ivy03.livejournal.com]

See shnayder's answer below. Unless the stone is pumice, the water level would go down.

[gryphonrose.livejournal.com]

I'm confused--if the rock displaces less water after being thrown in, wouldn't the water level go up, not down?

[ivy03.livejournal.com]

The more water that is displaced, the higher the water level is. So, since the rock displaces less water when it is in the lake than when it is in the boat, the water level goes down after you throw it.

[gryphonrose.livejournal.com]

Ah yeah, I was having a brain spasm. Duh. Never mind. :)

[veryschway.livejournal.com]

Oh, darn. Yeah, I had the same answer as gryphonrose.

[gryphonrose.livejournal.com]

I think we still get door prizes. :)

[shnayder.livejournal.com]

Chuck's right--the level would go down--when the rock is in the boat, it displaces an amount of water that weighs the same, but when it's in the water it sinks and displaces only water equal to its volume. Since rocks are denser than water, it displaces less water after being thrown in.

[ivy03.livejournal.com]

Ding ding ding! And explained much better than when my brother explained it.