A coin dropped from a height is lethal: True/False?

Connor Haley (in a third mention here, showing that fame can be just a matter of asking the right questions) wonders if a coin dropped from the the Eiffel Tower could kill someone on the ground. It would certainly ruin their day.

It is energy that determines how much destruction any collision causes, not speed or mass alone. When a moving object slows down its energy of motion has to go somewhere and if cracking bone and pulping organs is an option, that is where it will go.

How much energy does a dropped coin have? It’s simple to work out (as experts often say, generally while while slipping several sweat-stained pages of working into a drawer). If an object accelerates smoothly, as when it is falling, then the energy it accumulates (measured in joules) is roughly ten times its mass in kilograms times the height fallen in metres.

The exact figure here depends on what coin we choose and where on the tower we drop it from. For maximum impact, let’s imagine Connor drops a New Zealand $2 coin, weighing all of ten grams. And let’s further imagine that, dissatisfied with the observation decks, Connor has clambered right to the top of the tower, some 324 metres, hotly pursued by gendarmes. The things we imagine Connor does in the name of science!

Do the maths and we get about 32 joules of energy. That’s probably just a number so to give it some meaning we can work out how heavy an object you would need to drop from just one metre to get the equivalent energy on impact. Do that and our question boils down to whether a 3.2 kilogram object dropped on your head from one metre could kill you. Yes it could, and therefore so could the coin.

Alas I don’t have enough space to imagine a daring rescue for Connor. The good thing about thought experiments, though, is that they are all all in the head anyway — which is where a coin might end up if it lands on you from a great height.

CORRECTION 16 Aug 2010

Several readers have pointed out that I should have considered air resistance when calculating the energy of the falling coin. Looking again I see that I did make a mistake when I ignored the effects of air on the coin's speed. With aerodynamics complicating matters, the matter becomes much murkier. I am no longer certain that a coin dropped from a height can kill, but I still think New Zealand's hefty currency could be lethal. I'm far from being an expert, though. As reader Peter O'Neill points out, an experimental test of the danger of coins would make a great science project, and give us the answer to boot.

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