A Sunday Morning Brain Teaser For You

Hey, I know just what you want on a Sunday morning! A physics problem!

If it helps, think of it as a brain teaser. Like many such, it’s deceptively simple, but when you start to think about it a lot of concepts collide and it’s not as obvious as you might suppose at first glance.

Here’s my friend Dianna Cowern, aka Physics Girl, with the brain-stumper. I suggest you do as she recommends and stop the video to think about it before she gives the answer.

Did you get it right? I will admit it: I did. For the right reason, too, which I almost had to laugh at; many times when I think about a physics problem like this I can argue it both ways depending on what angle I take on the problem. In those cases I know I’ve forgotten something in my deducings.

In this case, I knew that rock is denser than water (as long as it’s not pumice, I suppose), so in the boat the rock was displacing its weight, but in the water it was displacing its volume. If rock is denser than water, its weight in water is larger than its volume in rock, so it displaces less water when it’s actually in the water, and the level goes down.

That kind of reasoning can be hard to follow if you’re not used to doing it. One slip-up loses the chain of logic. I was actually thinking that as I was going through the steps, and a part of my brain whispered to me, “Do an extreme case; it’ll be easier.” Then one minute later Dianna suggested just that, and I did laugh out loud.

Extreme cases may not solve the exact problem you’re facing, but they really help with getting through the logic, because there’s an intuition you get living in the real world about how some physics works. You really do! For example, you may know that if you throw a ball at about a 45° angle it’ll go farther than if you throw it at a higher or lower angle. If you do the physics you find the equations are symmetric around that angle, meaning that really is the best angle to throw a ball for distance.

Extreme cases exploit that knowledge you’ve gained through just existing in a Universe bound by physical laws, giving you an answer that either makes sense or is absurd, allowing you to get a better grip on things. I use them all the time when trying to figure things like this boat puzzle out, and they really do help. Just remember they’re extreme cases and may not represent the actual answer you want. Apply them carefully, and remember they’re a tool, not a solution themselves.

If you liked this problem and the video, Dianna makes lots of them and they’re really good. This one about mirrors is great and generates a lot of interesting discussion (lots of people say the answer is obvious, but it clearly isn’t to a lot of people). I also like this one about hurricanes and soap bubbles.

You can find more on her website, Physics Girl, and on her YouTube channel.

Tip o’ Archimedes’ bathtub to Mental Floss via Jennifer Ouellette.