Fermi Problems

 

Physicists should be able to estimate the order of magnitude of anything; for example, if one of your friends may have said ‘I wouldn’t study physics for all the tea in China’ the physicist might be tempted to calculate how much tea there is.  To do this you have to make some assumptions and estimates…

 

‘lets see… a billion people in China, each one drinks 0.5 L of tea per day, which maybe comes from 10g of dried tea leaves. China has, maybe, a 3 month supply of tea. We now need to combine all that and do the calculation…’

 

 

A possible solution to the tea-in-China question:

 

Assumptions:

 

There are a billion or 109 people in China

Each one drinks 0.5 litres a day

Which comes from 10g or 10-2 kg dried tea

Maybe there is a 3 month or 90 day supply of tea in China. Lets call it 100 days to make it easier

 

Calculation:

 

(109 people) x (10-2 kg/person/day) x (100 days) = 109 tea !  That’s a billion kg of tea!

 

 

 

Fermi problems are named after Italian Physicist Enrico Fermi and  you can find out more about him here: http://www.fnal.gov/pub/about/whatis/enricofermi.html

 

Solving Fermi problems is a great way to work on analytical skills, your confidence with numbers, and to think about the assumptions we make when solving physics problems.

 

You can do these tasks in any order.

 

The mysterious matchbox

 

  1. Carefully remove the lid!  By just looking (not touching or measuring), guess how many ball bearings are in the box.

 

  1. Now, with the help of the measuring instruments provided, make two estimates:

 

  1. Now count them and replace.  Compare your guesses and estimates

 

 

The Bible

 

Your mission, if you should choose to accept it, is to estimate the number of words in the Old Testament.  When you have done so, draw a brief flow chart to explain how you did it!

 

 

Airballs

 

  1. Guess, without touching or removing the balls, how many there are in the box.

 

  1. Now, with the help of the measuring instruments provided, make two estimates:

 

  1. Now count them and replace.  Compare your guesses and estimates.

 

 

The Rice Challenge

 

How many grains of rice are there in an average portion (to go with curry).  Guess first, and then estimate.  The following website may help you with a sense of scale!  I would recommend assembling this cube because it really does help you visualise volumes. 

http://www.vendian.org/mncharity/dir3/dm_box/

 

Now try these:

 

 

 

 

 

Ok these questions may not have much to do with physics, but they do get you used to making reasonable estimates and handling numbers.