*beeping & chirping*
Alright everyone, welcome back to Cody's Lab.
So today I'm gonna show you how to measure the density of small irregularly shaped objects.
But first lets measure the density of this rock, by using a method that you probably learned in your 8th grade class.
Were first gonna zero the scale, then I'm gonna weigh the rock and write down its weight.
Of course the scale is actually converting the weight, or force that the rock is applying on it, into mass by multiplying it by gravity.
Grams is not a unit of weight.
Now to get its volume. We're gonna take a graduated cylinder or, in this case, a beaker.
Fill it up to a known level with water.
Put the rock in.
The rock is gonna displace the water, up to an amount. Which you can then read off, is 70 milliliters.
So it started at 60, now its 70. That means, that the rocks volume is roughly 10 milliliters.
Now if I divide its mass by its volume, I get 2.8 grams per cubic centimeter.
A value which is pretty common for ordinary crystal rocks.
Now what would happen if, instead of a large rock, you had to measure the density of a tiny crystal.
You see for something this small, you'd have to a graduated cylinder with markings on the order of a hundredth of a milliliter.
I know the university does, but I don't personally own a graduated cylinder that's that accurate.
However, I do have a scale that can measure out to the milligram.
Since the scale is far more accurate than my beaker.
How about I devise a method to measure the density of something, where the scale is actually the limiting factor for the precision I can get.
So I have a beaker of water sitting on the scale.
If we zero the scale out. And then I take my finger and stick it into the water, watch what happens.
Even though I'm supporting the weight of my finger, the scale still reads an amount of weight.
This is because you'll notice that the water level goes up and down.
By sticking my finger in there, it's as if I've added extra water.
The water is trying to push up on my finger.
And so, I have to push down with a little bit of force and that force is transferred to the scale.
Now if I suspend a piece of wire down into the water
You can see that the wire displaces some of the water and I'm reading a weight on the scale.
Because again, it's pushed up on the water. And so, it's as if i've added more water to it.
Now the iron weighs more than water, but any extra weight is being supported by the frame of the scale and is not being measured.
So the only thing that I'm measuring here is the buoyant force, which is pushing up on the wire.
Now if I zero this out.
I can now add something to the wire and measure the amount of buoyant force on the object.
Now since I'm using water, the number of grams should correlate to the number of cubic centimeters that this object displaces.
Let's actually drop the object into the water.
This actually gives me it's mass, because now the object combined with the beaker, is being listed here.
So that is .333 grams, a third of a gram.
Now if I support some of the objects weight by suspending it on the wire.
I should have just the buoyant force,
right here.
Which tells me that the object is right about .1 mL in volume
Doing the math, you can see that the density of this crystal is 3.505 grams per centimeter cubed.
That value is exactly what I'd expect because this crystal is actually clear topaz.
Now, I know this piece is actually brass. But it is yellow and it's sorta heavy, so it looks a lot like gold.
Let's see if I can use this method to tell them apart.
Here's the mass of the brass nugget.
And right there is the mass of the gold.
There's how much the brass displaces.
And there's the gold, right there 0.117
The beauty about using this method. Is it doesn't actually matter if there's bubbles on the side of the glass
Or if there's a little bit of water up top. Or even if there's a little bit of water on the plate.
As long as the amount of water doesn't actually change... then it's all valid.
So doing the math on these numbers, I've come up with 19.33 for the gold and 8.23 for the brass.
The brass is less than half as much as the gold is.
Now to measure the density of the tiny piece of platinum that I got from the spark plugs is gonna be a bit more tricky.
Because it's volume is going to be on the order of 2 microliters, which is incredibly small.
In fact I wouldn't really trust this scale to measure it because this scale is only good for ± 2 milligrams.
You see it randomly changes from time to time.
I mean its still pretty good to get the weight of the pellet, which is right about 40 mg.
But the thing is, the amount of water that it's gonna displace is gonna be down into the 2 mg range. Which this scale really can' t measure.
So i'm gonna have to use a denser liquid to displace.
So here it is, the densest room temperature liquid known to man, mercury.
Well I suppose, mercury with gold dissolved into it would be slightly heavier.
So now that I've got the straw positioned inside the mercury. I'm gonna Tare that weight.
And now, I'm going to *clink*...
Drop the platinum.
And I'm gonna pick it back up. I'm gonna bring it over here
And stick it onto the little pad that I put.
Did I catch it?
Think we got it. Ok!
So now the mercury is being displaced by the platinum.
Let's bring this back over here so you can see the weight.
And there we go, 0.026 grams of mercury displaced by the platinum.
So here is the mass of the mercury displaced, divide that by the density of mercury.
And we get the number of milliliters that was displaced by the tiny platinum ball.
Dividing that by its mass of 40 mg, we have 20.822 grams per cubic cm. Which is pretty close to the actual value of platinum.
It's not surprising that I didn't get it exactly because it's just such a tiny object.
If the bead was a perfect sphere, it'd be as simple as taking the diameter of it and plugging it into this equation.
Unfortunately the bead is sorta shaped, like this.
See it's not a perfect sphere, It's slightly flattened at the bottom.
So what I need to do is take the measurement here
and here
and then average the two so that I can get something, which is more of a sphere.
Alright, Let's take the small diameter, 1.42
And the large diameter, looks like 1.50
Averaging those two numbers we get 1.46
Plugging that into our equation and we get 1.629 cubic millimeters.
Dividing the 40 milligrams by 1.63 cubic millimeters, gives us 24 and a half grams per cubic centimeter.
So there you go. I could probably do better if I took more measurements around the bead, and uh...
It is pretty close to the value of platinum and in fact I think the measurements that I took using the scale.
And the uh, mercury displacement, were actually better. So how bout that.
Hope you guys enjoyed, I'll see you next time.