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Fermi Problems A Fermi Problem is a problem in calculation where not enough information appears to have been given. But by making some clever assumptions, it is often possible to make an estimate that at least is in the right order of magnitude. The story is that Enrico Fermi dropped some bits of paper just as the first atomic bomb went off. Due to the force of the blast, the paper landed behind him. Fermi estimated the force of the blast from the distance behind him that the paper landed. The exact calculation took weeks. I don’t know how true the story is. Anyway, here they are. Estimate the total number of hairs on your head. Estimate the number of square inches of pizza consumed by all the students at the University of Maryland during one semester. One suggestion for putting satellites into orbit cheaply without using rockets is to build a tower 300 km high containing an elevator. One would put the payload in the elevator, lift it to the top, and just step out into orbit. Ignoring other problems (such as structural strain on the tower), estimate the weight of such a tower if its base were the size of Washington DC and it were made of steel. (Steel is about 5 times as dense as water, which has a density of 1 gm/cm3.) Estimate the angular momentum that your body has as a result of the earth's turning on its axis. In the 1989 Loma Prieta earthquake in California, approximately 2 million books fell off the shelves at the Stanford University library. If you were the library administrator and wanted to hire enough part-time student labor to put the books back on the shelves in order in 2 weeks, how many students would you have to hire? (You may assume that the books just fell off the shelves and got a bit mixed up but books in different aisles did NOT get shuffled together.) The mass of the earth is about 6x1024 kg. Estimate the kinetic energy it has as a result of its orbiting the sun. The orbiting Hubble telescope was recently repaired by a crew of astronauts from the Space Shuttle Endeavor. The Hubble is in a circular orbit 600 km above the surface of the earth. For half of the Hubble's orbital period it is in sunlight and for half it is in the darkness of the earth's shadow. As a results of the change in fit of the various parts of the Hubble due to heating and cooling of the telescope, the astronauts could only work on certain repairs while the Hubble was in darkness. Estimate how much time the astronauts had to work on these repairs before having to stop "for a sun-break". According to Newton's law of universal gravitation, the earth's gravity gets weaker as we go further from the earth. But when we drop a ball near the top of the lecture hall it doesn't seem to fall any differently than we drop it near the floor. Let gt stand for the gravitational acceleration observed at the top of the lecture hall and gb for it at the bottom. Estimate how much Newton's universal gravitation theory predicts gt will be less than gb. (Hint: It's easier if you estimate the fractional change, gb/gt - 1.) Suppose the Army Corps of Engineers decided to put a dam across the Potomac River in order to provide power for the Washington area. Assume the dam was built to hold back the water into a lake to a height of 15 m behind the dam. (Ignore the fact that this lake would cover land occupied by houses and cities.) Estimate the total force the water would exert on the dam. (Hint: If you have never seen the Potomac and have no idea as to how wide it is across, make a reasonable guess.) In the Millikan oil drop experiment, an atomizer (a sprayer with a fine nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more excess electrons. The charge on the plates is adjusted so that the electric force on the excess electrons exactly balances the weight of the droplet. The idea is to look for a droplet that has the smallest electric force and assume that it has only one excess electron. This lets the observer measure the charge on the electron. Suppose we are using an electric field of 3x104 N/C. The charge on one electron is about 1.6x10-19 C. Estimate the radius of an oil drop for which its weight could be balanced by the electric force of this field on one electron. A ballistic rocket is shot straight up from Cape Canaveral. Its rockets fire briefly. After the firing, it has it a velocity of 8 km/sec and a mass of m. How far up will it go before it begins to fall back to earth? Calculate your answer to within 10%. Ignore the distance it travels while its rockets are firing, the resistance of the atmosphere, and the rotation of the earth. (Hint: If you don't remember the radius of the earth you can solve for d/Re where d is the distance it reaches measured from the center of the earth and Re is the radius of the earth.) After the gulf war, large areas of desert had to be cleared of mines using special bulldozers that simply sweep the sand in front of them like a snowplow, but whose blades are strong enough to withstand the explosion of a mine. Estimate how long it would take a single bulldozer to clear a patch of desert that is 10 km square. The effect of air pressure was demonstrated in 1654 in Magdeburg, Germany with an impressive experiment. Two hollow metal hemispheres with a flat metal rim (flange) were placed together and the air removed from the interior with a primitive vacuum pump. The external pressure of the air pushed them together. When they tried to pull the hemispheres apart using two rings welded to the hemispheres, they could not be pulled apart even by a number of people pulling together. The sphere produced by putting the two hemispheres together is about the size of a basketball. Estimate the force needed to pull them apart. Two hard rubber spheres of mass ~ 10 g are rubbed vigorously with fur on a dry day. They are then suspended from a rod with two insulating strings. They are observed to hang at equilibrium as shown in the figure on the right, which is drawn approximately to scale. Estimate the amount of charge that is found on each sphere.
This winter, the East coast has been hit by a number of snow storms. Estimate the amount of work a person does shoveling the walk after a snow storm. Among your estimates you may take the following: --The length of a typical path from a house to the street is 10 meters. In doing this problem, you should estimate any other numbers you need to one significant figure. Be certain to state what assumptions you are making and to show clearly the logic of your calculation. Estimate the number of blades of grass a typical suburban houses lawn has in the summer. Estimate the number of bricks that would be required to build the University chapel.
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