Maybe you are one of those humans that avoids all trailers because they spoil the movie too much. I am not one of those humans. Which is why I immediately watched a trailer that came out this week for the upcoming Marvel movie Ant-Man and the Wasp. Although I was a huge comic book fan growing up, I never really got into Ant-Man. But the first Ant-Man movie was better than expected—and now I'm looking forward to this sequel.
If you don't know about Ant-Man, I'll give you a quick overview. This superhero uses special technology that allows him to shrink to ant-size (or sometimes he can also get really big—as seen in Captain America: Civil War). He also has the ability to communicate with ants. Oh, and the technology used to change the size of Ant-Man can also be used to shrinkify or embigenate other objects.
In the trailer, we see Hank Pym (the creator of the size-changing technology) shrink a whole building and then roll it away on wheels. But what happens when you shrink a building? To answer that, we have to thinking about what shrinking actually does in the Marvle Universe. When an object shrinks, does its size get smaller but its mass stays constant? Perhaps the density of the object stays constant during the process—or maybe it does something weird like moving into other dimensions.
Really, the mechanics of shrinking is pretty tough to figure out. There's conflicting evidence from the first film: First, there is the case where Scott Lang (aka Paul Rudd aka Ant-Man) puts on the suit and shrinks. At one point, he falls onto the floor and cracks the tile, suggesting that he keeps the mass of a full-size human. Later, though, we see that Hank Pym has a tiny tank on his key chain—a real tank that was just reduced in size. But clearly, this tank couldn't have the same mass as a full size tank. Otherwise, how would he carry it around?
Whatever. I'm just going to go with the idea that the mass stays constant—and if I'm wrong, oh well. It's just a movie anyway.
Let's start with the full-sized building in this trailer. How big is it? What is the volume? What is the mass? Of course I am going to have to make some rough estimates, so I'll start with the size. Looking at the video, I can count 10 levels with windows. That makes it 10 stories with each story 4 meters tall, (roughly). That would put the building at a height of 40 meters. When the build shrinks down, it looks fairly cubical in shape. This would put both the length and width at 40 meters. The volume would be (40 m)3 = 64,000 m3.
Why do I even need the volume? Because I'm going to use it to estimate the mass.
I'm sure some civil engineer somewhere has a formula to calculate building mass, but I don't want to search for that. Instead, I can find the mass by first estimating the density (where density is defined as the mass divided by the volume). For me, it is easier to imagine the density of a building by pretending like it was floating in water. Suppose you took a building and put in the ocean (and the building doesn't leak). Would it float? Probably. How much of it would stick out above the water? I'm going to guess that 75 percent is above water—sort of like a big boat. From that, I get a density of 0.25 times the density of water or 250 kg/m3 (more details in this density example).
With the estimated volume and density, I get a building mass of 16 million kilograms. Again, this is just my guess.
Now let's shrink this building down to the size in the trailer. I'm going to assume it gets to a size that's just 0.5 meters on each side, putting the volume at 0.125 m3. If the mass is still 16 million kilograms, the tiny building would have a density of 512,000 kg/m3. Yes, that is huge. Just compare this to a high-density metal like tungsten (used in fishing weights). This has a listed density of 19,300 kg/m3. This building would have a density that is 26 times higher than tungsten.
But wait! There's more! What if you put this tiny and super massive building down on the ground with just two small rolling wheels, like Hank Pym does in the trailer? Let me calculate the pressure these wheels would exert on the road, where pressure is the force divided by the contact area. The size of the wheels is pretty tough to estimate—and it's even harder to get the contact area between the wheels and the ground. I'll just roughly estimate it (and guess on the large size). Let's say each wheel has a 1 cm22 contact area for a total of 2 cm2 or 0.0002 m2.
I know the force on the ground will be the weight of the building. This can be calculated by taking the mass and multiplying by the local gravitational constant of 9.8 Newtons per kilogram. Once I get this force, I just divide by the area to get a contact pressure of 3.14 x 109 Newtons per square meters, or 3.14 Gigapascals. Yes. That is huge. Let's compare this to the compressive strength of concrete at about 40 Megapascals. The compressive strength is the pressure a material can withstand before breaking. Clearly 3 Gigapascals is greater than 40 MPa. Heck, even granite has a compressive strength of 130 MPa.
If Hank wants to roll this building away so that no one will notice, he is going to have a problem. The wheels will leave behind a trail of destruction by breaking all the surfaces it rolls on. Or there is another option. Maybe the mass of the building gets smaller when it shrinks—but in that case, I don't have something fun to write about.
Superheroes are really big on this shape-shifting stuff—but is the Incredible Hulk really as hulky as he looks in Thor: Ragnarok?
You can also have shape-shifting planets, like the weird non-spherical planet Sovereign in Guardians of the Galaxy Vol. 2. Could that really work?
And for some super-nerdy density physics: Can you calculate the center of mass in Thor's hammer?
