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The delights of scientific misunderstandings

I've just had published a fun little book of 50 misunderstandings and misconceptions in science. Lightning Often Strikes Twice looks beyond this tip of the iceberg when it comes to what may of us wrongly believe about the world around us. Whether it's word of mouth, myths you've read about online, or misremembered facts from school, we're bombarded by misconceptions about science all the time.

In a light way, the book explains the real science and theory that debunks these popular myths. From fears about the exponential growth of the human population to the misapprehension that we are all descended from chimpanzees or gorillas, the book separates science fact from fiction.

For your delectation here's one of the 50 articles in the book:

A coin dropped from the top of the Empire State Building can kill you

The Empire State Building doesn’t even make it into the fifty tallest buildings in the world any more. At the time of writing, it’s only the seventh tallest in NewYork City. Yet the combination of it topping the world’s building height charts for a lengthy period between 1931 and 1972 and its appearance in over two hundred and fifty films, starting with the iconic scene in King Kong, mean that it remains a visual and emotional touchpoint for anything requiring a significant measure of height.

Image by Guille Sánchez from Unsplash
It is likely that the idea that a coin dropped from the top of the building would be deadly to someone on the sidewalk below arose when the Empire State Building still held its crown as the tallest building in the world. It seems quite a reasonable assertion. After all, many coins are heavier than bullets, and a bullet can cause terrible damage. The amount of oomph with which something hits a target is measured by its momentum– the mass of the object times the velocity at which it travels. Current British coins weigh between 3.5 and 12 grams (0.12 to 0.4 ounces), while US coins range from 2.3 to 11.3 grams (0.08 to 0.4 ounces). Not a lot. But the deadly capabilities of a falling coin rest on the assumption that it can get up to a considerable speed when dropped from the height of the Empire State Building.

The exact height involved is a little vague as the Empire State Building is topped with a radio mast and a high pointy roof (added to the original design to make sure it was taller than the rival Chrysler Building) – but even if the coin thrower were to climb to the upper parts King Kong style, it would be extremely difficult to throw a coin and manage to get it over the edge of the building, so we probably have to assume that the coin would be dropped from the observation deck 320 metres (1,250 feet) above the pavement below.

How fast, then, would the coin be going when it reached its potential victim? The starting point is the acceleration due to gravity. Although the Earth’s gravitational pull drops off as you move away from the planet’s surface, the building’s height has a trivial effect. Gravity acts as if the planet’s mass were concentrated at its centre.When we stand on the Earth’s surface, we are on average 6,371 kilometres (3,959 miles) from the centre. There is not going to be much difference between 6,371 kilometres and 6,371.32 kilometres.

The acceleration due to gravity at the Earth’s surface is 9.8 metres (32 feet) per second per second. That’s to say, after 1 second you are travelling at 9.8 metres (32 feet) per second, after 2 seconds at 19.6 metres (64 feet) per second and so on. Working out the speed this implies would be reached in a fall of 320 metres is not totally trivial, but there are plenty of calculators out there. If nothing else were involved,a coin would take 8 seconds to make the drop and would arrive travelling at around 79 metres (259 feet) per second. Going for a coin of 10 grams (0.35 ounces), this would give a momentum of 79 × 0.01 = 0.79 kilogram metres per second. To put that into context, a handgun bullet can have a momentum of around 450 × 0.007 = 3.15 kilogram metres per second – around four times as much. (Converting this to non-metric units is messy and probably no more meaningful.)

In practice, though, there’s another consideration. The air. We tend to ignore it, but falling objects are slowed down by the atmosphere’s resistance to objects moving through it. As a result, any object has a ‘terminal velocity’ – the fastest speed it will fall through air, depending on how much resistance the profile of the object puts up. (This is why a parachute, with much more surface area presented to the air, slows a person’s descent, compared to falling without one.)

For a typical person, that terminal velocity is around 55 metres per second (180 feet per second) belly down – for a coin it’s likely to be around 28 metres per second (92 feet per second), which would take its momentum down to around a twelfth of that of a bullet.

Being hit by a coin falling from the Empire State Building would certainly be unpleasant – but it won’t kill you. The TV show MythBusters created a special gun to fire a coin at the appropriate rate and showed that it was survivable (please don’t try this at home). And a more comparable experiment from around 2007 showed that coins were even less dangerous than the MythBusters experiment suggested.

Louis Bloomfield, a physics professor from the University of Virginia, devised an experiment that automatically dropped a whole cache of coins from a weather balloon, high enough up for them to reach terminal velocity. He claimed that they didn’t hurt, feeling like the impact of heavy raindrops. Bloomfield used one cent coins, lighter than the weight used above, but also found an additional slowing factor. The coins’ unstable fluttering tended to reduce their speed to as little as 11 metres per second.

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