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### The Shrinking Building in Ant-Man and the Wasp Would Cause Massive Problems

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 m^{3}.

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/m^{3} (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 m^{3}. If the mass is still 16 million kilograms, the tiny building would have a density of 512,000 kg/m^{3}. 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/m^{3}. This building would have a density that is *26* times higher than tungsten.

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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 cm^{2}2 contact area for a total of 2 cm^{2} or 0.0002 m^{2}.

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 10^{9} 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.

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