The science of shrinking cups

posted Oct 26, 2017, 5:04 AM by Beth Orcutt

By Annie Hartwell

This figure shows a simplistic representation of the forces that enable the cup to maintain the shape. The magenta arrows represent the pressure from inside the cup pushing outwards on the cup walls. The blue arrows represent the pressure from outside the cup pushing inwards on the cup walls. The magenta arrows and the blue arrows are equal, but in opposite direction so the cup maintains its shape. You also see the size of seven cups exposed to different water depths, and the graph shows the corresponding volumes of the shrunken cups versus the exposure depth. Between 0 and 2000 meters, the volumes have big changes (the points are far apart), below 2000 meters the volume only changes a little (the points are closer together). 

Drawing on Styrofoam cups and sending them down to the bottom of the ocean to make shrunken Styrofoam cups is a lot of fun for ocean going scientists. For one, coloring is a great way to relax between all the science, and for two, the scientists get to make their own souvenirs that are unique from everybody else’s. 


Why do the cups shrink?


Before we get into the nitty gritty about why the cups shrink, let’s talk about Styrofoam. The key character of why Styrofoam cups shrink is air. Between all the white parts of Styrofoam, there are little pockets of air.  If you took all the air out of the white stuff, then the cup will get smaller.  This is precisely what is happening when the cups are brought down to the bottom of the ocean – the air is forced out causing the cup to shrink. 


How does all the air get removed from Styrofoam?


Styrofoam cups shrink when they are brought to the bottom of the seafloor because there is an enormous amount of pressure pushing on them from all sides. Remember what you have already learned about pressure at the bottom of the ocean, from the activity with stacking gallons of water? Both of these factors – that the pressure is high, and that the pressure is equal from all sides – are simultaneously important.


Pressure:  The pressure forces that are acting on the cup and forcing the air to leave is from the weight of the water.  As you descend deeper into the ocean, the weight of the water above becomes greater and greater, thus adding more pressure and forcing more air out. When a cup is placed in the bottom the ocean, the pressure from the weight of the water forces the air bubbles out, enabling the white part of the Styrofoam to contract (shrink). The deeper the cup is submerged, the more water weight it is subjected too, and the smaller it will get, until all the air is removed.

Pressure From all sides is important because it enables the cup to maintain its shape. If the pressure was only coming from above, the cup would get flattened. Same thing if the cup was pushed on either side, the cup will get squished. If all the pressure is coming from inside the cup, it would cause the sides to blow out. When a cup is submerged in the water, the cup fills with water, so there is a pressure acting from above, from the sides, from the bottom, and there is an equal amount of pressure pushing back from inside the cup. 


How small can the cup get? How deep does it need to go?


The Styrofoam cups will only shrink until all the air bubbles are removed, somewhere around 2000 meters. At that depth, there is enough pressure to force all the air bubbles out, so no matter how much additional pressure you add, the cup will not shrink any further because there is no more air to squeeze out.  In 2011 on the Research Vessel Endeavor, a scientist named Dr. Dave Ullman sent a series of cups down to different depths (150 meters, 300 meters, 800 meters, 1000 meters, 2500 meters, and 4000 meters), and he documented the volume of the un-shrunken cup at zero meters and compared it to the volume the cups shrunken at each depth.  He observed that the cups do the majority of the shrinking in the top 2000 meters of the water column and below 2000 meters the volume will decrease slightly, but much less than in the upper water column.



A little bonus about Density:


Remember what you learned last week about the density of different solutions (salt water versus freshwater versus rubbing alcohol)? Do you think that the density (mass per unit volume) of the Styrofoam cups changes when the size shrinks?


To explore this concept, let’s think about ping pong balls.  Imagine you have five ping pong balls that all together weigh 5 grams (this is the mass).


Scenario A: Now imagine the 5 ping pong balls are in milk crate that is 1 cubic foot (the volume).  If you wanted to know the density of ping pong balls in your milk crate, you calculate the value as the mass (5 grams) divided by the volume (1 cubic foot), so your density would be 5 grams/cubic foot.


Scenario B: Now imagine that you took the same five ping pong balls and put them in a milk crate that is bigger than the first one (2 cubic feet). The density of the ping pong balls in this second bigger milk crate is 5 grams/2 cubic feet = 2.5 grams/cubic feet.


Comparing scenarios A and B (5 grams per cubic foot vs. 2.5 grams per cubic feet) you see that the density of the ping pong balls in the smaller milk crate is larger than the density in the bigger milk crate. Both crates have the same about of mass (5 grams) but because the volumes of the crates differ, the densities do, too. 


In the case of the Styrofoam, a normal size cup has a certain mass of white stuff in the volume of the cup. If the air between the white is removed, the white stuff condenses and the volume of the cup decreases – but not the mass. When the air is removed from between the Styrofoam, there is essentially NO change in mass (no white stuff is lost). However, the volume of the cup does get smaller, so the density of the cup will increase. The shrunken cup will have a smaller volume than an un-shrunken cup, but they will both weigh the same.