Newton's third law/badgers/Metro

In the Metro today, someone asks (page 17):

“How many badgers would it take to support the Empire State Building?”.

The answer given is:

“The Empire State Building weights 331,818 tonnes. The average weight of an adult European badger is 11kg. So, according to Newton’s third law, you would need 30,102,040 badgers”.

Now, I am not a scientist, but this seems unsatisfactory. It seems to me that all they have done there is answer the question “how many badgers does it take to equal the weight of the Empire State Building”? Why is Newton’s law applicable?

The answer to the question actually posed depends upon what you mean by “support”. If you mean you mean “act as a foundation for”, it seems to me that the issue is one of strength (principally seperable here into compressive, tensile and sheer strength, depending upon where the load forces are applied), not weight. Badgers’ propensity to break/be squashed under load means they are insufficient to support a large building, however many badgers you have got, unless the weight of the building is spread out over a very large surface area (on the same principle that means that an elephant’s foot does not sink into a muddy field where a stiletto heel would, despite the elephant’s weight). So you need to look at the weight–bearing strength of one badger before it will squash or break (say, 50kg?) to see how many badgers you will need (6.6million?), then make sure that the weight of the building is applied down through a cross–sectional surface area sufficient to contain that number of badgers in load–bearing formation (say, roughly 825,000m², assuming 0.125m² per badger (based upon a length of about half a metre and a width of about half of that again for one badger in a load–bearing stance)). So you don’t need as many badgers as the Metro suggests, but the value of the real estate that would be necessary would be substantial, particularly given land values in Manhattan.

No doubt one of you fiendishly clever lot will tell me why I am wrong about all this.

Alternatively, we could look at the issue economically. The Empire State cost some $41m to build. To amass that amount of money (£22m) from badgers, one could go into the business of selling badger pelts to the traditional shaving brush industry. At an average profit of, I dunno, £2.50 per pelt, one could say that 8,800,000 badgers would be required to have supported the construction costs of the Empire State. One could also look at the question of support based upon current annual running costs for the Empire State, giving a smaller number of badgers but on an annualised basis.

Labels: economics, news, science

Comments:

Badgers? We don't need no stinking badgers!

# posted by  Chrishola : 3:50 PM

 

Could a pelican swallow a badger? They can swallow pigeons you know - http://www.youtube.com/watch?v=Rcg63Y1QSDk

# posted by  Anonymous : 5:19 PM

 

I also saw that article and I thought, "That's b*ollocks, that is". However that's where my thought process ended.

Oh - and it's the guys at AQA - Any Question Answered you should be dissin', not the Metro.

Good effort though, I've forwarded them your CV.

# posted by  nickyg : 8:34 AM

 

The way my career is looking these days, all offers considered...

# posted by  tucola : 9:44 AM

 

...(before anyone else says it, one might suppose that my career would be looking better were I to spend less time theorising about badgers and more time busting my ass for the good of my employer. I couldn't possibly comment.)

# posted by  tucola : 9:46 AM

 

The concern I have here is that under traditional badger foundation construction techniques liquification may occur. However if you imagine the whole tower sitting on a wide flat solid foundation which in turn sits above another wide flat foundation which is fully supported on the earth, then you apply between these foundations a very thin film of liquid badger this would only need to be one molecule thick at any point for that membrane to be considered as supporting the tower. This would probably equate to 1000 liquified badgers? If however you imagine firing a badger at just below the speed of light up from the centre of the earth then one badger alone may act to counteract the force due to gravity exerted by the building? geoff

# posted by  Anonymous : 9:29 AM

 

I think you and they are confusing weight and mass. Newton's third law is relevant, but is only the start. Newton's third law says that each action has an equal and opposite reaction. This means that, if the Empire State Building were in space, then the force exerted by one badger on the ESB would be the same as the force exerted by the ESB on that badger (i.e. equal). However, the excess mass (and the force otherwise known as inertia) means that the acceleration of the ESB would be unlikely to be affected at all by the badger. Unless it were a particularly massive badger, of course. Like that one off "The Apprentice".

# posted by  banderama : 12:20 PM

 

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