 Thanks to Curiosity Stream for
supporting PBS Digital Studios.
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.
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.
Right.
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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