Walking on Mercury?

While many of us heard phrases like “he thinks he walks on water”, few of us have seen someone actually walk on water without some kind of special effect being used. Last night while trying to go back to sleep I started to think about ways you could reduce pressure, and for whatever reason I went from thinking about water beds to trying to sleep on a pool of mercury. Now before we go any further I want to note this was an intellectual exercise and at no point am I advocating that you try to sleep on mercury. The more I thought about this the more I wondered what other things you might be able to do with a largish pool of mercury, like can I walk on mercury without special gear aside from something to prevent heavy metal poisoning.

First let’s get a sense of mercury vs water.

Water has a density of 1 gram cubic cm

Mercury has a density of 13.6 grams cubic cm.

Cool mercury is more than 10x the density of water. So the question for today, if someone tried to walk in a pool of mercury what would happen?

First I am going to start with my assumption before I crunch the numbers. Mercury is incredibly dense, so dense that a cannonball will float on the surface. While a cannonball will float on mercury I don’t think it is dense enough for a person to walk on the surface in such a way that you could see any part of their feet while they are standing in/on the mercury. I would bet it would look something like walking in deep slushy snow.

How much an object floats/sinks in a given liquid is based on the density of the liquid the object is being dropped into, and the density of the object you are dropping in. In physics terms, an object will float when its buoyant force exceeds the downward force of gravity. What is cool is that if you try to weigh an object in any kind of fluid, air, water, mercury, to get a truly accurate weight you must account for the buoyant force of the fluid.

The average person has the same density of water, maybe a tad less maybe a tad more, but for ease we will assume our person has a density of 1 gram/cubic cm.

For a person to float their buoyant force will need to be equal to their weight.

In the case of a 100 kg person (aka a not small dude), they would have a volume of 100 liters or 0.1 cubic meters.

Now to make sure we have enough buoyant force we need to make sure that the weight of the displaced mercury is equal to the weight of our person.

A 100 kg person floating on mercury will displace 100 kg of mercury, which has a volume of 7.35 liters. The question then becomes how deeply will they sink, and for that we get a bit complicated. Depending on how they stand/position themselves the exact number will fluctuate.

Assuming a person standing upright, we are will first see their feet and then calves slide into the mercury.

According to a 1969 NASA study on human body proportions, a human foot represented about 1.5% of a human body’s overall mass. A calf represented 4.6% of the person’s mass. Now for our basic(read lazy) approximation we are equating weight to volume. By this logic an average human has roughly 12.2% of their body mass/volume in its feet and calves. For a 100 kg person their feet and calves would have a volume of 12.2 liters. This means that our person would get about 60% (7.35 liters/12.2 liters) of the way from the body of their feet to the top of their calves

So it sounds like our person walking in mercury would have mercury to about half way up their calves.

Good news while sanity checking my work I found a youtube video from 3 years ago where the host is standing/floating in mercury, and it looks like the mercury is a bit less than halfway up his calf, considering his boots and thin frame, it feels like the math was in the ball park.

TL:DR, yes you can walk on/in mercury, but you might need a lot of core strength

Thank you to Wikimedia user Bionerd for the image of liquid mercury getting poured, more info about this creative commons image can be found here https://commons.wikimedia.org/wiki/File:Pouring_liquid_mercury_bionerd.jpg