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Fermi Problems

A Garden of
Fermi Problems
at Hampton University


What is a Fermi Problem? Well you may ask...

A Fermi Problem, named for Italian physicist Enrico Fermi, is a problem in which realistic estimation and order-of-magnitude calculation are essential. For example, if someone told a physicist he wouldn't study classical mechanics "for all the tea in China" the physicist might be tempted to calculate roughly how much tea is in China. (Maybe our physicist could look the answer up somewhere but that's no fun.) So assumptions and reasonable estimates need to be made. Let's see...a billion people in China, each one drinks about 0.5 L of tea per day, which comes from, maybe, 100 g of dried tea leaves. China probably has, oh, a 3 month supply of tea...we combine all that and do the calculation. Don't like those assumptions or estimates? Try another approach....China is about 1/2 the area of the continental US and maybe 1/2 of its land is arable, etc.

The idea of a Fermi Problem is to think about what assumptions we make, how to make them as realistic as possible, how to estimate well, and how to put all of these in the service of a straightforward mathematical calculation to arrive at the answer.

Solving Fermi Problems is a great way to work on analytical skills and out-of-the-box thinking that leads to physical insight.

Below are some Fermi Problems generated by physics teachers and members of QuarkNet. At the bottom is one teacher's solution to the tea-in-China question.


Fermi Problems: Solve Them If You Dare...

1. How many frames are in a Walt Disney animated movie such as Tarzan?

2. What is the mass of a fully loaded cement truck?

3. What is the mass of a fully loaded Boeing 747?

4. If you were to stack a pile of one dollar bills corresponding to the US national debt,
A. how high would it reach?
B. how much would it weigh?
C. what would be the pressure on the bottom dollar?

5. What is the length in miles of the US Interstate Highway system?

6. How many molecules come off a car tire with each revolution?

7. How many gallons of water move down the Mississippi River in one day?

8. How many piano tuners would you expect to find in the local telephone directory?

9. How much energy is released due to latent heat of vaporization when a hurricane dumps 16 inches
of rain on North Carolina?

10. If a high explosive (e.g. TNT) releases as much energy per kilogram as food, how many people would the
energy of a 1-MT H-bomb feed for one day, if its energy could be converted to food at 100% efficiency?

11. How many square kilometers of surface would it take to supply the U.S. with all its energy needs if solar
energy could be converted with 1% efficiency? Allow for night time, cloud cover, etc. The solar constant
is 1.35 kW/m2.

12. If all the oxygen atoms breathed by Enrico Fermi over his lifetime are now distributed uniformly through the
atmosphere, how many of these atoms do you breathe in with each breath?

13. If you could get a penny for each time someone said "Ouch!" in the United States, how long would it take you to become a billionaire?

14. If all the ball-bearings in all the fishing reels in the U.S. were dumped into a single grain elevator silo, how tall
would the silo have to be?

15. If we used ALL the electrical energy in the world to operate motor that could slow down the earth with 1% efficiency,
how many days (as measured by Earth rotations) would it take to bring the rotation of the Earth to a halt?

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

17. Assuming that energy is transferred with 100% efficiency, how much soup could be heated up from room temperature to "hot soup eating temperature" by making use of all of the energy expended in playing a game of pool? Note: This problem was devised a few meters from the pool tables at the Reynolds Club at the University of Chicago, which is not far from the old squash courts. If you don't know the significance of the U of C squash courts to physics, look it up!

Fermi problems contributed by: Alex Dzierba, Stuart Briber, Ken McFarlane, Gene Oldfield, and Ken Cecire. To contribute more Fermi problems, e-mail to cecire@jlab.org.


For more Fermi Problems:

University of Maryland Fermi Problems Site

Old Dominion University Fermi Problems Site



 		To learn more about Physics at Hampton University:

Hampton University Main Page

HU Department of Physics

HU Center for the Study of the Origin and Structure of Matter

A solution to the tea-in-China question:

Assumptions
Calculation

(109 people)(10-2 kg/person/day)(102 days) = 109 kg of tea

That's a billion kg of tea!


This site is presented as an outreach of the Hampton University Center for Particle Physics and Center for the Study of the Origin and Structure of Matter. Contact information appears below.

Webmaster / Contact Person: K. Cecire, Educational Specialist, Hampton University
E-Mail: ken.cecire@hamptonu.edu
Tel: 757-728-6533
Fax: 757-728-6946

Last Updated: September 2002