Maybe you have watched Stranger Things but maybe you haven’t. I’ve seen it, and I thought it was great—and not just because there’s lots of science in it. Don’t worry, I’m not going to talk about multiple universes or quantum tunneling. Instead I am going to talk about salt.
Small spoiler alert (but not really a spoiler): In season 1, the Stranger Things kids need to build a makeshift sensory deprivation tank. The essential component of this “tank” is a kiddie pool filled with water such that a person can easily float. Of course, normal water will make a human just barely float. To fix this problem, they add a bunch of salt to increase the liquid density to accommodate a floating human. According to Mr. Clark (their science teacher), they need 1,500 pounds of salt.
But was he right? Let’s take a look at the science.
Floating and Density
Why do things float? If an object is stationary at the surface of water (or any liquid), then the net force on that object is zero. Of course there is a gravitational force pulling down, so that must mean there is some other force (with an equal magnitude) pushing up. That force is the buoyancy force. But how does it work? Let’s start with an example.
Here is a block of water floating in water. Yes, water floats.
In this diagram, the yellow arrows represent the rest of the water pushing on this floating block of water. The water pushes on the block in all directions and this force increases with depth. Notice that the forces from the water on the sides have to cancel (since they are balanced). However, the forces pushing up from the bottom are greater than the forces pushing down from the top. But since the block of water is floating, the net upward buoyancy force must be equal to the gravitational force pulling down.
Now replace the block of water with something else—it doesn’t matter what it is made of as long as it is the exact same shape. If it’s the exact same size, it must have the same buoyancy force on it. If the block is made of steel, the upward buoyancy force is going to be less than the downward gravitational force such that the steel will sink instead of float—but the buoyancy force is still there. Because a water block would float, the magnitude of this buoyancy force must be equal to the weight of the water the object displaces—this is Archimede’s principle.
The weight of the water displaced depends on three things: the volume of the object, the density of the liquid (physicists like to use the Greek leter ρ for this) and the value of the gravitational field g. Putting this all together, the buoyancy can be written as:
But wait! What if an object is not completely submerged? What if the object is a block of wood or maybe a girl named Eleven? If the weight of the object is less than the weight of the water displaced then the buoyancy force will be greater and push the block up. It will keep moving up until part of the block is out of the water. The part of the block that is out of the water doesn’t produce any buoyancy—so eventually the block will reach equilibrium with part of the object underwater and part above.
The fraction of the block that sticks above the water depends on two things: the density of the object and the density of the water. Let’s do a quick example. Suppose I have a wood block with density ρb in water with density ρw. Just for simplicity, it’s a cubic block of length L. This is what it might look like.
Remember, the weight of the block has to be equal to the weight of the water displaced—so I will start off with the weight of the block. I know the density, so the mass (and thus the weight) can be found as ρb(L3)g. This should be equal to the weight of the water displaced with a value of ρw(L2 d)g where d is the depth of the block underwater. Notice that a lot of stuff cancels and I get:
So, the amount the block floats above the water depends on the ratio of the densities of the object and the liquid. Notice that if the object has a density equal to water, then it would float with nothing sticking out above the surface. If the density of the object was half of that of water, then have the object would stick out above the water.
This is idea is what Mr. Clark used to estimate the amount of salt to add to water. For sensory deprivation, you want to increase the density of the water such that it has a much higher density than the density of a human.
How Much Salt Do You Need?
Water has a density of 1,000 kilograms per cubic meter. If you don’t want to be cool, you could say the density is 1 gram per cubic centimeter but trust me—all the cool people use units of kg/m3. But what about the density of a human? It depends on the human, but it’s normally a little bit less than 1,000 kg/m3 such that most humans float. Of course a human can float or sink depending on the lungs. If you take in a deep breath of air, your lungs get bigger and your density decreases. Blow all the air out of your lungs and you should sink.
Normal people breathe. This…