Imagine that you're sitting on a boat, floating in the water, and holding a rock that you then throw into the water, and it sinks.

Did you just cause the water level to rise, fall, or stay the same?

I want you to think on that for a minute.

And to make the problem a little more clear, imagine the boat is in a container not much bigger than the boat.

Will the water level rise, fall, or stay the same?

I recommend pausing the video to try to figure it out first.

Ooh.

So it was on my boat.

It, um-- And then I threw it in the water.

You would say that it would rise.

But if that were the case, then this would be an easy question.

And since it's a stumper, I'm going to say-- So I think that it should go-- It stays the same.

Down.

DIANNA COWERN: It stays the same?

Yeah, it's like the ice cube, right?

DIANNA COWERN: Like-- oh, like the melting ice cube in the water?

Yeah, similar [inaudible] already displaced the amount of the way because the weight of yourself on the boat holding the brick should be the same as it going into the water?

And then when you drop the rock into the water, the water doesn't have to support the rock anymore.

So it would go down.

Now, at this point, we could turn to Archimedes' principle, which states that the buoyant force on an object submerged in water is equal to the weight of the volume of water that object displaces.

But that seems a little excessive.

Another way to solve this problem is to consider an extreme case.

Let's imagine an extreme case where our rock is super heavy but really small-- a black hole rock.

Now, when you put that rock in the boat in the first place, the boat had to sink very low in the water to compensate.

And consequently, it pushed the water level up by a lot.

When we throw the rock in the air, the boat goes back up, but the water level goes back down.

And then when the rock drops into the water, it's pretty small.

So the water level doesn't rise back up much at all.

Easy.

So in the end, the water level goes down.

And we can make the argument that this is the case for any rock that starts out in the boat and then sinks in water.

I'll leave that to you to work out.

Considering extreme cases is a great way of solving problems like this.

In fact, research at UMass Amherst on the role of extreme cases in problem solving showed that it gives students something imageable, something that they could visualize.

Extreme cases built up intuition and gave the student something grounded in reality.

This is in contrast to using an empirical rule like Archimedes' principle to solve the problem, which may not be very intuitive.

Now, it's not always easy to figure out what the extreme case might be.

Let's consider this time that you start in the boat, and then you jump into the water and float.

What happens to the water level this time?

Does it go up, down, or stay the same?

I'll pick my extreme case to be that the boat is really, really light, like a boat of aluminum foil.

If it's that light, it won't do much to the water level until you jump in it.

Then it will sink a bit, but just to displace your weight in water.

This is where we actually do need to know Archimedes' principle.

The water displaced when a thing is floating has the same weight as the floating thing, which in this case is you plus the boat, which is pretty much just you, because I picked the case where the boat weighs next to nothing.

When you get out, the weight in the water is still just you and your itty-bitty boat.

So pretty much, it's still just you floating in the water.

So the buoyant force stays the same.

The amount of water displaced stays the same.

And so the water level is not affected.

The water level stays the same.

If you want to try solving a few more problems using extreme cases, stay tuned.

Here a few more problems.

You've got a large wooden block and a smaller lead block balanced.

So they have the same mass.

They're in an airtight glass dome.

You then suck out all the air from the dome.

What will the balance do?

Will it tip toward the wooden block, the lead block, or stay balanced?

You have a planet.

You then surround the entire planet with telephone poles that are 10 meters high.

How much longer is the wire that goes all the way around the top of the telephone poles than the circumference of the planet?

Hint-- you don't need to know the radius of the planet.

This problem was inspired by a book written by Thomas Povey called "Professor Povey's Perplexing Problems."

Thanks for checking out this video.

I release a new video almost every week, so subscribe for more physics.

Do you want to know the answer?

Yes.

DIANNA COWERN: Do you want me to tell you?

Yeah, I'd love to know.

Tell me the answer.

DIANNA COWERN: It's-- Goes down.

It goes down?

DIANNA COWERN: It does down.

Correct.

Yeah!

[grumbling] Then I just walk out and leave.

I did take a couple physics classes.

It's been a long time, actually.

DIANNA COWERN: So that when the rock goes in the water, it doesn't raise back up very far.

Make sense?

Yes, darn it.

DIANNA COWERN: So that's the difference between ice and a rock.

OK, sure.

You like tricking people, huh?

Curses.

I blame this all on Jimmy Wong.

DIANNA COWERN: Yeah.