스포츠 경기 생중계를 본지 꽤 오래 되었다. 감정의 기복을 경험하는 것 자체가 부담스러운 까닭이다. 누구에게는 이 자체가 즐거움이자 행복이겠지만. . 어제 포루투와의 경기를 몰입하여 직접 본 사람들이 내 주변에는 얼마 안된다. 다들 듬성 듬성 보거나 결과만을 본 사람들이 대부분이다. 또한 많은 경우 이기기를 바라지만 보면 지기 때문에 보지 않는다 한다. . 이를 수학적으로 어떻게 이해해야 하나? 관객이 많은 쪽이 패할 확률이 높단 말인가? 관객과 경기력은 상관 관계가 있는 것인가? . 오늘 아침도 쓰잘데 없는 일에 머리를 한참 사용한다. 그런데 쓸모 없는 것 만큼 유용한 것은 없는 경우가 종종 있지.
포랜직 유전계보학은 범죄 현장에서 발견된 유전자를 근거로 유사 유전자를 가진 사람들을 조사하여 범인을 추적하는 방법이다. 이 방법은 가계를 찾아감에 따른 시간적 비효율성이 높다는 것이다. 수학적 알고지즘을 이용하여 기존보다 10배 효율화 하는 방법이 스탠포드재 교수팀에 의해 개발되었다. 상세한 내용은 22년 9월 국제학술지 ‘법의학지’에 실렸다.
Fermi Problems: Solve Them If You Dare... 1. How many frames are in a Walt Disney animated movie such as Tarzan?
월트 디즈니 애니메이션 영화는, 예를 들어 타잔의 경우, 얼마나 많은 프레임으로 만들어 졌을까?
2. What is the mass of a fully loaded cement truck?
시멘트 트럭의 체적은 완전히 적재 되었을 때 얼마나 될까?
3. What is the mass of a fully loaded Boeing 747?
보잉 747의 체적은 얼마나 될 것인가?
4. If you were to stack a pile of one dollar bills corresponding to the US national debt,
1불 지폐로 미국 부태를 쌓을 때, 얼마나 될 것인가? A. how high would it reach?
그 높이는?
B. how much would it weigh?
그 무게는? C. what would be the pressure on the bottom dollar?
맨 밑바닥 달러에 미치는 압력은? 5. What is the length in miles of the US Interstate Highway system?
미국 고속도로의 총 연장은 얼마나 될 것인가?
6. How many molecules come off a car tire with each revolution?
자동차 바퀴가 한 바퀴 돌때 마다, 떨어져 나가는 분자의 개수는?
7. How many gallons of water move down the Mississippi River in one day?
하루에 미시피 강을 흐르는 물의 량은 얼마나 될까? 8. How many piano tuners would you expect to find in the local telephone directory?
지역 전화번호부에서 발견할 수 있는 피아노 조율사의 숫자는?
9. How much energy is released due to latent heat of vaporization when a hurricane dumps 16 inches of rain on North Carolina?
16인치의 비를 노스 케로라이나에 허리케인이 뿌릴 때 기화에 의하여 빼앗기는 잠열의 에너지 총량은 얼마나 될까?
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?
폭약이 방출하는 에너지를 음식으로 환원할 경우 1메가톤의 폭탄으로 얼마나 많은 사람을 먹일 수 있을 것인가?
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.
태양 에너지의 1%를 에너지로 만들 수 있을 경우 미국에서 필요한 모든 에너지를 충족하기 위해 얼마나 많은 면적이 필요할 것인가? 밤, 구름에 의한 문제를 고려한다. 1.35 kW/m2.의 태양에너지가 비추는 것을 가정한다.
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?
엔리코 페르미가 평생 마신 산소 분자가 대기에 균일하게 퍼져 있다고 가정할 때, 우리는 매번 숨쉴때 마다 얼마나 많은 이들 분자를 호흡하고 있을 것인가?
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?
미국에서 누군가 아우치라고 이야기 할 때 페니를 받는다면, 빌리온에어가 되기 위하여 얼마의 시간이 필요할 것인가?
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!
General
Estimate the total number of hairs on your head. 당신의 머리카락 개수를 추정하시오.
Estimate the number of square inches of pizza consumed by all the students at the University of Maryland during one semester. 한 학기 동안 메릴랜드 대학의 모든 학생들이 소비하는 피자의 면적을 계산하시오.
When it rains, water would accumulate on the roofs of flat-topped buildings if there were no drains. A heavy rain may deposit water to a depth of an inch or more. Given that water has a mass of about 1 gm/cm 3 , estimate the total force the roof of the physics lecture hall would have to support if we had an inch of rain and the roof drains were plugged. 지붕 위에 비가 내렸다고 가정하고, 비가 온 채로 고였을 경우 어떤 걸물에 1인치 비가 내렸을 경우, 얼마의 무게를 견뎌야 할 것인가? 물의 무게는 1 gm/cm 3로 가정한다.
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/cm 3 .)
Estimate the total amount of time 19 year olds in the US spent during this past semester studying for exams in college. (Not counting finals.)
The deficit in the Federal Budget this past year was approximately $100 Billion ($10 11 ). (a)Assuming this was divided equally to every man, woman, and child in the country, what is your share of the debt? (b) Supposing the deficit were paid in $1 bills and they were layed out on the ground without overlapping. Estimate what fraction of the District of Columbia could be covered. (c) Suppose you put these $1 bills in packages of 100 each and gave them away at the rate of 1 package every 10 seconds. If you start now, when will you be finished giving them away? (d) Are any of these calculations relevant for a discussion which is trying to understand whether the deficit is ridiculously large or appropriate in scale? Explain your reasoning.
The Federal Budget Deficit is approximately $100 Billion this year. Compare this to what we spend on what we eat by estimating the total amount US consumers spend on food in grocery stores, markets, and restaurants in one year.
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.)
Estimate the total number of sheets of 8.5 x 11 inch paper used by all the students at the University of Maryland in one semester.
If the land area of the earth were divided up equally for each person on the planet, about how much would you get?
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.
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.
Assume the snow fell to a depth of 4 inches.
Assume the snow was only moderately packed so that its density was equal to 0.2 g/cm 3 -- about one fifth that of water.
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. (In this problem, the answer is only worth 2 points. Almost all of the credit is given for your showing correct reasoning clearly.)
A floppy disk for a computer stores information by magnetizing small regions of the disk. For a typical floppy disk, estimate the area of the disk that corresponds to a single bit of information. (Remember: the storage capacity of a disk is cited in bytes where 1 byte = 8 bits.)
Ali El-Ectrical is an Engineering student at your university taking a "normal" load (for Engineers!) and paying full tuition. Estimate how much he is paying for each hour of class time he spends with an instructor over one semester.
Estimate the number of blades of grass a typical suburban house's lawn has in the summer.
How many notes are played on a given radio station in a given year?
How many pencils would it take to draw a straight line along the entire Prime Meridian of the earth?
If all the string was removed from all of the tennis rackets in the US and layed out end-to-end, how many round trips from Detroit to Orlando could be made with the string?
How many drops of waters are there in all of the Great Lakes. 호수에 있는 물방울의 개수는?
How many piano tuners are there in New York? 뉴욕에 있는 피아노 조율사의 수는?
How many atoms are there in the jurisdiction of the continental US?
How far can a crow fly without stopping?
How many golf balls can be fit in a typical suitcase? 가방에 들어갈 수 있는 골프공의 개수는?
How tall is this building? 이 건물의 높이는?
Estimate the number of cars and planes entering the state at any given time.
How much air (mass) is there in the room you are in? 이 방 안에 있는 공기의 체적은?
How long does it take a light bulb to turn off?
ow much energy does it take to split a 2x4?
How much milk is produced in the US each year? 미국에서 생산되는 우유의 총량은?
If you drop a pumpkin from the top of a ten story building what is the farthest a single pumpkin seed can land from the point of impact?
How many flat tires are there in the US at any 1 time?
Mechanics
Estimate the angular momentum that your body has as a result of the earth's turning on its axis.
The mass of the earth is about 6x10 24 kg. Estimate the kinetic energy it has as a result of its orbiting the sun.
A professor of physics is going ice skating for the first time. He has gotten himself into the middle of an ice rink and cannot figure out how to make the skates work. Every motion he makes simply slips on the ice and leaves him in the same place he started. He decides that he can get off the ice by throwing his gloves in the opposite direction. (a) Suppose he has a mass M and his gloves have a mass m. If he throws them as hard as he can away from him, and they leave his hand with a velocity v. Explain whether or not he will move. If he does move, calculate his velocity, V. (b) Discuss his motion from the point of view of the forces acting on him. (c) If the ice rink is 10 m in diameter and the skater starts in the center, estimate how long it will take him to reach the edge, assuming there is no friction at all.
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 g t stand for the gravitational acceleration observed at the top of the lecture hall and g b for it at the bottom. Estimate how much Newton's universal gravitation theory predicts g t will be less than g b . (Hint: It's easier if you estimate the fractional change, g b /g t - 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.)
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/R e where d is the distance it reaches measured from the center of the earth and R e is the radius of the earth.)
For next year's Physics Open House the Department is planning to set up a bungee jump from the top of the physics building. Assume that one end of an elastic band will be firmly attached to the top of the building and the other to the waist of a courageous participant. The participant will step off the edge of the building to be slowed and brought back up by the elastic band before hitting the ground (we hope). Estimate the length and spring constant of the elastic you would recommend using.
Estimate the angular momentum an automobile tire has about its axis of rotation while the car is driving on the interstate.
In testing a design for a yo-yo, an engineer begins by constructing a simple prototype -- a string wound about the rim of a wooden disk. She puts an axle riding on nearly frictionless ball bearings through the axis of the wooden disk and fixes the ends of the axle. In order to measure the moment of inertia of the disk, she attaches a weight of mass m to the string and measures how long it takes to fall a given distance. (a) Assuming the moment of inertia of the disk is given by I, and the radius of the disk is R, find the time for the mass to fall a distance h starting from rest. (b) She doesn't have a very accurate stopwatch but wants to get a measurement good to a few percent. She decides a fall time of 2 seconds would work. How big a mass should she use? Imagine you were setting up this experiment and make reasonable estimates of the parameters you need.
According to some recent highly accurate measurements made from satellites, the continent of North America is drifting at a rate of about 1 cm per year. Assuming a continent is about 50 km thick, estimate the kinetic energy the continental US has a a result of this motion.
While on travel this past summer, I passed through Charles deGaulle airport in Paris, France. The airport has some interesting devices, including a "people mover" -- a moving strip of rubber like a horizontal escalator without steps. It became interesting when the mover entered a plastic tube bent up at an angle to take me to the next terminal. I managed to get a photograph of it. It is shown in the figure below. If you were building this people mover for the architect, what material would you choose for the surface of the moving strip? (Hint: You want to be sure that people standing on the strip do not tend to slide down it. Figure out what coefficient of friction you need to keep from sliding down and then look up coefficients of friction in tables in reference books in the engineering library to get a material appropriate for the slipperiest shoes.)
Estimate the angular momentum of the earth due to its daily rotation about its axis. The average density of the earth is about 5 grams/cm3. Estimate the angular momentum of the earth due to its daily rotation about its axis. The average density of the earth is about 5 grams/cm3.
you can have these type of in the following books for reference. "How Much is a Million" by David Schwartz "Meta magical Themas" by Douglas Hofstadter "Innumeracy" by John Allen Paulo's "Used Math" by Clifford E. Schwartz "Aha" and "Aha - Gotcha!" by Martin Gardner Thanks
