Old Dominion University Fermi Problems Site 

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Physics on the Back of an Envelope

Physics 309

Prof L.B. Weinstein

Physicists should be able to estimate the order-of-magnitude of anything. How many atoms of Julius Caesar do you eat every day? How much waste does a nuclear power plant generate? This 1 credit course will develop concepts, relations and numbers useful for estimation. We will discuss the concepts as a group and attack the problems as a group. I intend to lecture as little as possible. The course will not cover new material but will make use of already acquired (or at least already taught) knowledge. It will try to help students apply physics to real-life questions and understand which physical effects are appropriate on which scales. It will be a seminar course with a maximum enrolment of 15. The corequisite is Physics 232.

Links to other Fermi problems pages are here:

General Estimation (no physics req'd)

  1. How many piano tuners are there in Hampton Roads?
  2. How many golf balls does it take to fill a suitcase?
  3. How many pieces of popcorn does it take to fill a room?
  4. How many 1 gallon buckets of water are needed to empty Loch Ness?
  5. How much dental floss does a prisoner need to escape over a wall?
  6. How many cells are there in the human body?
  7. What is the volume of human blood in the world? How does this compare to the volume of the valley at Har Meggido (Armaggedon)?
  8. How fast does human hair grow (in km/hr)?
  9. How fast do humans grow (in km/hr)?
  10. How many atoms are in the human body?
  11. What is the spacing of these atoms?
  12. Cannibalism is frowned on in most human societies. How many atoms of your great^n-grandfather who lived about 2000 years ago do you ingest with each meal?
  13. If all the people of the world were crowded together, how much area would we cover?
  14. Assuming one Santa Claus visits all Christian children on Christmas, how fast would he have to travel?
  15. How many reindeer would he need to pull his sleigh?
  16. What is the flow rate of the James River? Of the Mississippi River?
  17. How many people were at the Million Man March in Washington DC? How would you estimate this?
  18. How much carbon-dioxide does a square kilometer of forest remove from the atmosphere each year?
  19. How much carbon-dioxide does an automobile add to the atmosphere each year?
  20. How much carbon-dioxide does a human add to the atmosphere each year (by breathing)?
  21. How many dumptruck loads would it take to cart away Mt. Everest?
  22. What is the mass of the Earth?
  23. What are the relative sizes (radii) of the moon and the sun?

    24. Transportation

  24. What is the relative cost of fuel (per kilometer) of rickshaws and automobiles?
  25. What is the relative waste generated (per kilometer) of rickshaws and automobiles?
  26. What is the average speed of an automobile including overhead (maintenance, looking for parking, cleaning, etc)? Of a bicycle?
  27. How much time would be saved nationwide by increasing the speed limit from 55 to 65 mph? How does this compare to the extra lives lost?
  28. How far does a car travel before a one molecule layer of rubber is worn off the tires?

    29. Mechanics

  29. If comet Shoemaker-Levy had hit the Earth, how much energy would it have deposited? How does this compare to one year of solar radiation?
  30. How long would it take a solar sail powered spaceship to travel to a) the Moon, b) Mars, c) Pluto?
  31. How much work is done climbing a mountain (in kcal)?
  32. How long would a beanstalk (elevator to geosynchronous orbit) have to be? What tensile strength would it require? How does this compare to steel, kevlar, spider silk, the maximum theoretical material strength?
  33. What is the mass of the Earth?
  34. What is the mass of the moon?
  35. What is the rotational angular momentum of the Earth?
  36. What is the rotational angular momentum of the Moon?
  37. What is the maximum angular velocity the Earth could have without flying apart?
  38. What is the tidal drag force on the Earth?
  39. What is the revolutionary angular momentum of the Earth about the sun?
  40. What is the revolutionary angular momentum of the Moon about the Earth?
  41. What is Roche's limit (the orbital distance inside which a moon will disintegrate)?
  42. How long was the day when the moon was at Roche's limit?
  43. How long will the day be when it is equal to the month?
  44. According to one hypothesis, 20% of the mass of the asteroid that killed the dinosaurs was uniformly deposited over the surface of the Earth at a density of 0.02 gm/cm^2. What was the mass of this asteroid?
  45. What is the kinetic energy of a large (1 km^3) meteor? How does this compare to one year's insolation of the Earth? How much is this in megatons?
  46. How much would a large (1 km^3) meteor strike change the angular momentum of the Earth?
  47. How much energy is required to boil the Earth's oceans?
  48. How often is the moon struck?
  49. How large a collision is needed to split the moon in half? To split Phobos in half?
  50. How small do you have to be to walk on water?
  51. How high can mice and elephants jump?
  52. How large a moon can you jump off of?
  53. What is the kinetic energy of a drifting continent?
  54. What is the height above the surrounding water of the Gulf Stream?
  55. What is the depth below the surrounding water surface of the water surface over the Marianas Trench?
  56. How much would the ocean surface rise if the ice caps melted? How much would that change the salinity of the ocean?
  57. How much would the ocean surface rise due to global warming (in addition to ice cap melting)?
  58. Astrology claims that the position of the planets at the time of our birth influences our lives. Calculate the relative gravitional attraction and the relative tidal forces on a newborn baby of a) Jupiter, b) the hospital building, c) the obstetrician.

    59. Electricity and Magnetism

  59. How strong are the magnets in the SSC? In the Fermilab ring?
  60. How long would the Earth's magnetic field last without a dynamo?
  61. What is the lifetime of a classical atom (before the electron loses 13 eV of energy to synchrotron radiation)?
  62. What is the Schwarzchild radius of an electron?
  63. At what distance is the magnetic field from high power transmission lines the same as a) the Earth's magnetic field? b) the magnetic field from your electric blanket?

    64. Quantum Mechanics

  64. What is the probability of an object suddenly jumping up from a surface?
  65. How small can a 1 GB memory be?
  66. What is the probability of a human diffracting as it walks through a doorway?
  67. What is the probability of a human tunneling through a closed door?
  68. You walk off of a cliff. How high does the cliff have to be (assuming constant g) for you to have an appreciable probability of quantum mechanically reflecting?

    69. Energy

  69. How long would a laser have to stay focused on a missile to ignite the chemical explosives in the warhead?
  70. How much Uranium must the Earth contain to keep the core molten?
  71. How long would the sun last without thermonuclear reactions?
  72. What is the heat output of the sun?
  73. If the Sun were made out of Gerbils, the Earth would be incinerated. Explain.
  74. How much energy would be released by stellar collapse (ie: by the Sun shrinking from its present size down to a neutron star)?
  75. How much waste (solid and gas) is created each year by a 1000-MWe coal power plant?
  76. How much acid rain is caused each year by an unscrubbed 1000-MWe coal power plant?
  77. How much waste (solid and gas) is created each year by a 1000-MWe oil power plant?
  78. How much electrical power does the US use per year?
  79. If 10% of Californians drive electric vehicles, how many extra power plants will it take to recharge them each night?
  80. How much Iron, Glass, and Water does the US use per year?
  81. How much waste does the US generate per year?
  82. How much power do humans use? How does this compare to the solar energy incident on the Earth?
  83. What is the heat output of a human?
  84. What would be the resource value of a 1km^3 metallic asteroid?
  85. How much power would it take to desalinate enough water for Virginia Beach?
  86. How much flow is needed for a 1000 MegaWatt hydropower plant?
  87. How much coal is needed each year for a 1000 MegaWatt coal fired power plant?
  88. How much cooling water is needed for a 1000 MegaWatt nuclear or coal-fired power plant?
  89. How much area would a 1000 Megawatt solar power generator need?
  90. How much area would an orbital 1000 Megawatt solar power generator need?
  91. How big would the earth-based receiving antenna be for an orbital 1000 MW solar power generator?
  92. What would the power density be at the earth-based receiving antenna? Relative to the normal solar power density?

    93. Nuclear Physics

  93. How many neutrinos from the Surry nuclear power plant pass through you each year? How many interact? Is this harmful?
  94. How much high-level nuclear waste is created each year by a 1000-MWe nuclear power plant?
  95. If this waste was spread evenly over the surface of the earth, with what depth of soil would you have to mix it so that it would be safe to ingest (ie: within federal guidelines for ingestion of radioactivity)?
  96. How long do you have to store the waste until it becomes reasonably safe?
  97. What are the radiation levels a) in Norfolk, b) in Denver, c) in a commercial jetliner, d) near Three Mile Island at the time of the accident?
  98. Ten neutrinos from Supernova 1987a (which was about 150,000 light years from earth) interacted and were detected in the Kamiokanda detector. If you were standing 2 AU from the supernova, what would have killed you?
  99. What is a lower limit on the lifetime of the proton (based on the existence of life on earth)?
  100. What is an upper limit on the energy released in cold fusion (based on the fact that it didn't kill its proponents)?
  101. A biologist recently claimed to have revived a 30 million year old bacteria. How many cosmic rays would have passed through the bacteria during the last 30 million years? What is the probability that its DNA is scrambled?
  102. How accurately can you date dinosaur bones?
  103. Someone places 1 Curie of uranium on your chest. What do you die of?
  104. How much is the energy content of 10 tons of 3He worth?
  105. How much Uranium is needed each year for a 1000 MegaWatt nuclear plant?
  106. How dangerous is Radon?
  107. How dangerous was Three Mile Island?

    108. Risk Assessment, SETI, etc

  108. What is the dynamic range of the human eye?
  109. What is the typical molecular binding energy?
  110. What is the maximum size of various objects? Moons, planets, suns, white dwarfs, neutron stars, mammals, reptiles, bugs?
  111. How likely is the existence of an extraterrestrial civilization?
  112. What is the mean distance between civilizations?
  113. How many extraterrestrial visits per year can we expect?
  114. What is the probability of success for the Search for Extra-Terrestrial Intelligence?
  115. What are the relative probabilities of dying (in the United States) of a) motor vehicle accident, b) gunshot, c) nuclear power plant accident and routine operation, d) coal power plant accident and routine operation, e) power line EM radiation, f) lightning strike, g) small meteor strike, h) large meteor strike, i) oil power plant accident and routine operation, j) plane crash?
  116. What is the human power output in the radio spectrum relative to the Earth's blackbody radio radiation? Relative to the Sun's radio emission (black-body)?
  117. A balloon full of freon falls to the floor. How much freon do you expect to find in the upper atmosphere?

For more Fermi problems, go to


These problems were written and collected by L.B. Weinstein with help from John Adam, Charles Hyde-Wright, and Marc Sher. These problems may be freely used in classrooms. They may be copied and cited in published work if L.B. Weinstein is acknowledged and this URL is given.

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Larry Weinstein

 

 

Last modified: Wed Feb 18 20:51:42 MET