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.

2. Now, with the help of the measuring instruments provided, make two estimates:
• Firstly, the number of ball bearings if they were cubes!
• Secondly, the number if they are spheres

3. 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.

2. Now, with the help of the measuring instruments provided, make two estimates:
• Firstly the number of airballs if they are cubes
• Secondly, the number if they are spheres

3. 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. No equipment (or rice!) is provided for this one. However, 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:

• How many golf balls can fit in a typical suitcase?

• Pick a nearby tree. Estimate the number of leaves on the tree.

• How much milk is produced in the UK each year?

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

How Big, How Small?

You are now going to use the following website to research the following information:

http://www.vendian.org/howbig/?&page=millipaper and use it as a basis for a dimension poster.

Distance to be found	Figure and unit with prefix	Express in metres in standard form
Diameter of Neptune’s orbit
Diameter of a human hair
Distance of Earth to Moon
Thickness of typical continental crust
Diameter of human eyeball
Length of rabies virus
Distance of Sun to Sirius
Distance of Earth to Sun

As a group, we need one A3 poster per prefix. The posters need to include:

• the name of the prefix followed by ‘meter’ (e.g.nanometer)
• the factor (e.g. 10^-9)
• the symbol followed by ‘m’ for meter (e.g. nm)
• some appropriate pictures and facts (cut and stick from the website http://www.vendian.org/howbig/?&page=millipaper )

If you want to try some more Fermi problems, try these sites. They will also link you to other useful sites:

http://mathforum.org/workshops/sum96/interdisc/sheila3.html

http://www.physics.umd.edu/perg/fermi/fermi.htm