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Hey, I'm Dianna.
You're watching Physics Girl, Riddle Series.
Here's where we left off in the last video.
Michael Stevens, from V Sauce, is
in the hot seat answering a buoyancy riddle, which
I know that you already attempted
to answer in the comments of the last video.
I laid out the premise of that riddle for him
after giving him a warm up riddle, which you
should go try if you missed it.
And in case you did miss it, here again is the main riddle.
Get a glass of water and over here imagine
that you have an ice cube and inside the ice cube,
it looks normal, because it looks like everything is clear.
But inside of it, it's got a little diamond
frozen in the middle.
Got it?
Great, beautiful.
Yeah, and then you drop the ice cube
into the glass of water.
Now, when the ice cube melts and the diamond
falls to the bottom of the glass,
because carbon in diamond form is more dense than water,
does the water level go down, go up, or stay the same
from the level it was at when the ice cube was first
placed in there?
Very good question.
All right, so let's work through this.
I just--
I want to know your intuition for it.
Well, the water is--
Is that not fair?
That's what we're working through right now.
I know.
But intuition is snap judgment.
Oh, my snap judgment answer?
My intuition is that the water level will not be as high.
OK.
That intuition comes from a video
that you made about when you exaggerate things in a problem,
it can become more clear.
OK, go ahead.
You were like, imagine that you had a rock on a boat.
Yeah.
And the rock was really heavy.
Yeah.
So the boat was pushed down a lot,
but it still wasn't sinking.
Then, you throw the rock overboard
and it falls into the water.
It still has the same mass, but now,
rather than displacing a huge amount of water because
of the boat, it's only displacing
its volume, which we're imagining is very small.
It's like a black hole rock.
So, I'm thinking--
I think that is what I said.
I think I said "black hole rock".
Is that really?
It's like you watched my video, Michael.
Number one fan of Physics Girl.
So look.
The problem is that the cube becomes part of the water.
Exactly.
So the ice cube is melting, as well.
Right.
So if you feel like, if the cube is like half floating,
half of it's above and half is below,
then you have a condition where you're only displacing half
of the volume of the cube.
But then when the ice cube melts,
all of the water that was the ice cube
has been added to the glass.
So the level should be higher when the ice cube melts.
Is this talking about if there were no--
Diamond.
Diamond in it?
That's what I'm wondering.
Because this is the age-old question of what happens when
there's a glacier with water melting into the ocean,
versus an iceberg, where the water's melting.
Right.
Oh, I see.
I see.
The ice is melting.
Yeah.
The reason the ice cube floats is
that it is displacing its own weight in water, not just
the volume.
In fact, that's what determines how deeply it's
going to be submerged.
Exactly.
It's displaced its own weight in water,
which means after it melts, its own weight of water
will be in there.
So I guess it stays the same.
Yeah.
But now we have this diamond--
Good job.
Thank you.
Yeah.
But now we have this diamond to worry about.
Exactly.
The diamond is going to displace its volume in water,
because it's sinking.
Whereas when it was floating, it was displacing its weight
in water.
So the water level will go down.
Is that the right answer?
That is the right answer.
That is really cool.
Yay, Michael.
So much depends on knowing what it means to float.
Yes.
Exactly.
Knowing what Archimedes' principle means.
Michael was basically reiterating
Archimedes' principle when he reasoned
through why the ice cube floats, even before it melts.
The reason the ice cube floats is
that it is displacing its own weight in water, not just
the volume.
Yes.
That's because-- here's Archimedes' principle, which
I will try to show visually to help
it be clearer than just the normal way it's usually
written out.
So the buoyant force, which is the force pushing up
on an object floating in water, is
equal to the weight of the water displaced by the object.
Meaning that if you took that space filled up
by the ice rather than the water and then filled it with water
and weighed that water, then that weight,
which is actually a force, would be equal to the buoyant force.
That is Archimedes' principle.
Thanks, Archimedes.
Knowing also a little bit about what happens with water
when it melts, like the fact that ice
is this really, really weird solid substance that
becomes more dense.
I think that there are a few other things that freeze
into a less dense substance.
Yeah.
Not many.
And because the water is initially
supporting all of the weight of the diamond encased in the ice,
and then only the weight of the water displaced
by the diamond, which is much less,
then the level will go down.
This is a lot like the riddle that I
did with the boat and the rock, except that the boat doesn't
melt in that case.
If you like these types of riddles,
I did a really fun video--
I had fun-- with Simone [INAUDIBLE]
my good friend, where there were two spheres that
are identical in size and I asked about the force on them
when there's air resistance and they're
falling and stuff like that.
Check that one out.
And I promised you a bonus puzzle.
So here it is.
Is it possible to tell which star
is in the sky are the hottest just by looking at them?
With or without an instrument that
shows you the star's spectrum?
How?
I'll pin a comment with the answer
to the top of the comments section a day
after this video goes up.
And thanks so much to Michael Stephens.
Yeah.
He did good.
You never know.
Sometimes people trip up even when
they've got that solid physics knowledge.
But this is fun.
Thanks, Michael.
Check out the video I did with him on the [INAUDIBLE] channel
where we did magic tricks with cards and stuff and math.
Michael's Math Magic.
Mmm.
Thanks so much for watching, guys.
And happy physics-ing.
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