Alles by Schwarze

IES SCHAMANN Las Palmas de G.C._November 2014

ENRICO FERMI (1901-1954) is an Italian physicist best known for his contributions to nuclear physics and the development of quantum theory. In addition to his contribution to theory, he is also noted as an experimentalist. Fermi was awarded the Nobel Prize for his physics work on the nuclear process. Shortly after receiving the Nobel Prize, Fermi was forced to flee Italy. He settled in the United States, first at Columbia University and then later at the University of Chicago. During World War II he was a member of the Manhattan project team that developed the atomic bomb in Los Alamos, Mexico. Fermi Questions are problems whose solutions are either too difficult to measure or whose answers are imprecise. Fermi Question calculations require mathematical skills, logic, critical thinking, life experiences, and the ability to break down complex problems into smaller discrete, soluble parts. At some point in the solution process, the solver is expected to estimate a value which is critical to obtaining an answer. The methodology, involved in making up a Fermi Question as well as calculating an answer, is applicable not only to the fields of science and engineering but to those of finance and commerce; in short, to provide a solution to a question in any field requiring a numerical estimate. To solve a Fermi question it is suggested to complete the following steps 1. Question: State the question and clarify the interpretation. 2. Wild Guess: Make a wild guess involving no calculations. 3. Educated Guess: Make an educated guess involving a chain of reasoning and calculations based on everyday experiences and estimates and by making a series of simple assumptions to arrive at a reasonable solution 4. Variables and Formulas: Define variables and create a formula to solve the Fermi question. 5. Gathering Information: Perform experiments, conduct surveys, make measurements, and search for information to improve estimates and to find a smallest reasonable value, a largest, reasonable value, and a most likely value for the answer to the Fermi Question. 6. Conclusions: Summarize the overall conclusions, possible sources of error, interesting facts learned, and possible directions for future investigation.

Examples of Fermi Questions related to water: 1. If you combine all of the liquid from a cup of some kind you will drink over your lifetime, how many baths would it fill?

2. How many fish are there in the oceans?

3. How many drops of water are needed to fill a 50 meter swimming pool?

4. What fraction of volume does one water molecule occupy in a cup of water?

5. How many molecules of water are in a cup of water?

6. The volume of ice in Antarctica is estimated to be 26 million cubic kilometers. If all of the ice in Antarctica melted, how high would the oceans rise?

7. If all of the oceans were frozen into a single ice cube, how high, km, would it be?

Fermi questions to answer before the visit in Spain What about the water that each of the students coming to Spain uses in one year?

How many drops of water are in a glass of 250 cm続? How much has a person of 78 years has drunken in his life? How many bath tubes could be filled with it?

What about weight of this load if all water carriers were full?

What about the amount of water or liquid that can be filled into this barrel?

How many crates of mineral water can be transported in this huge shopping trolley?

WATER: FERMI questions Our question:

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

Our calculation:

Our answer:

Additional question and answer:

How many crates of mineral water can be transported in this huge shopping trolley? If the dimensions of this volkswagen car is: Height of the car: 1.5m ,

Length of the car: 4m ,Width of the

car: 1.7m Then for the shopping trolley : Height of shopping trolley: 1,5m

Width of shopping trolley:

1.7m Length of shopping trolley : (480/350) * 4 = 5,5m So the volume of it is : Volume = 1,5 * 1,7 * 5,5 = 14 m3 And if the dimensions of a crate of mineral water which contains 24 bottles of capacity 250ml is : Height : 28cm

Length : 40cm

Width : 30cm

Then its volume is : V = (0,28)(0,4)(0,3) = 0,034 m3 Number of crates = 14 / 0,034 = 412 In this huge trolley we can transport approximately 412 crates of mineral water.

WATER: FERMI questions (Latvia) Our question: How many crates of mineral water can be transported in this huge shopping trolley?

Assumptions: 1) It possible that mark of the car, which is in the trolley is Volkswagen golf, because we near see a lot of Volkswagens. 2) The trolley is trapezium shape, because when we go to a shop we can put trolley to trolley. 3) The car could have “15” wheels –it means that diameter of wheel is 38,1 cm. 4) Crates can’t occupy the whole volume of trolley, because trolley and crates have different angles.

Our calculation: Diameter of the wheel= 38,1 cm AB=8.5 d= 323 cm CD=9 d =343 cm DA=3.7 d =140 cm AA1=3 d = 114.3 cm CB=2.7 d =103 cm h² of ABCD =(1.5d)² – (d)² h=42,6 cm - CM same way H of the prism -С1F B1B=C1C=4d=152,4 cm FC= d = 38,1 cm H² = (4d)² – (d)²

I determined all sides of prism Now I create one shape of this prism

Additional question and answer:

Here are just length and height But we can see,that there is a free space, where we can’t put any crates. If size of a crate (15 bottles 500 ml) = 30 cm x 30 cm x 26 cm. There are 6x7 boxes + 5x3 boxes + 3 boxes = 60 boxes (just one row). But I also have width now I can find average width. +

Average width I = How many rows=

�.

=121,5 cm .

.�

=3,18 = 3 rows.

Our answer: 60×3=180 crates of mineral water 500 ml 15 bottles. Vladislav Khrushch, Team Latvia

WATER: FERMI questions (Switzerland) Our question:

N°5 by Nicolas Brunisholz and Jérémy Gutierez

What about the amount of water or liquid that can be filled into this barrel ?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: We consider this barrel like a cylinder. Diameter : one person + 90cm = 1,8m + 0,9m = 2,7 m Diameter = 2,7m

Rayon = 1,35m

High = 2,4 m Our calculation:

Vcyl= πr ²h= π⋅ 1,35²⋅ 2,4= 13,7m³= 13700dm³= 13700l Our answer: We can fill approximately 13'740 liters of water or wine !

WATER: FERMI questions (Belgium) Our question: How much has a person of 78 years has drunken in his life? How many bath tubes could be filled with it?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated â&#x20AC;Ś. as a base for calculation that follow â&#x20AC;Ś: We found on the internet that the average water consumption a day is 1.5 liters, so we used this to calculate our results. For the bath we found that a full bath takes 100 gallons of water to be filled, but an average person uses around 40 gallons when he/she takes a bath. We looked up how much liters 1 gallon is and we found out that 1 gallon equals 3.785 liters.

The man was born in 1936. Since 1936 there were 20 leap years which means there were 20 years with 366 days instead of 365. In each of those years he drank an additional 1.5 liter. Our calculation: 1.5 liters of water x365x58 + 1.5 liter of waterx366x20 = 42735 liters of water 3.785 gallons x 100(gallons to fill a bathtub completely) = 378.5 liters of water 3.785 gallons x 40(gallons to fill a bathtub for usage) = 151.4 liters of water Bathtubs filled completely: 42735 liters of water/378.5 liters of water = 113 Bathtubs Bathtubs filled with enough water to take a bath: 42735 liters of water/151.4 liters of water = 282 Bathtubs

Our answer: A person aged 78 has drank around 42705 liter of water in his life. This is enough to fill 113 bathtubs completely and 282 bathtubs with the average amount of water to take a bath.

WATER: FERMI questions (Germany) Our question:

5,7 cm

6 cm

What about the amount of water or liquid that can be filled into this barrel?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: The man right of the barrel may have a size of 1,8 m. The total height of the barrel (avarage) will be about 1,80 m+0,70m= 2,5 m m.On my print-out the height of the barrel is 6 cm. I measured the length of the barrel . It has 5,7 cm. I use the formula of a cylinder to calculate the volume of the barrel.

�,

� ,



x = 2,375 m.

Our calculation: V = r²*h=  *1,25² * 2,37m³ 11,652 m³ Our answer: The barrel full of water will contain about 11,5 m³ water.

The average height of a man in the decade of 1910 according to the graph is: Av. Height = (168 * 2 + 167,5 + 167 * 3 + 166 * 2) / 8 = 167cm and the average width of a man in this period is approximately 40cm In the image we have a barrel of the shape of cylinder which have a radius equal to the height of a man. So radius = 1,67m

Then if the width of the barrel is equal to the width of seven persons then: Width of barrel = 7 * (0,4) = 2,8m So the volume of this barrel is: V = Ď&#x20AC; * (1,67)2 * 2,8 = 24,5m2

WATER: FERMI questions (Latvia)

Our question: How many drops of water are in a glass of 250cm3 Assumptions: Using the following internet website http://www.dr.lv/phorum/read.php?3,245599,245600,quote=1 , I found out, that 0.5ml contains 10 drops of water. So 1 ml has 20 drops of water in it. Our calculation: 1ml – 20 drops 250 – x drops �=

5 ∗

=5000 drops in a glass of 250cm3.

Our answer:

In a glass of 250cm3 there are 5000 drops of water. Additional question and answer: In a flat tap drips. How much extra euro will I have to pay for water if the trap drains for 3 weeks? 1) As the result of the experiment, I found out that in 1 minute the glass of 250 ml is half full. 1min – 125ml 2) How many minutes are in 3 weeks? 1d=24h; 1h=60min 3weeks= 3*7=21d. 21*24=504h=504*60=30240min.

3) How many m3 of water will flow away in 3 weeks? 1min – 125ml 30240min – x ml x=125*30240=3780000 ml = 3,78 m3. 4) How much extra euro I will need to pay, if 1m3 of water costs 1.55 euro. 1.55*3.78=5,86 euro. ANSWER: I will have to pay 5,86 euro.

WATER: FERMI questions (Switzerland) Our question: N°4 by Mauro and Jonathan

What about weight of this load if all water carriers were full?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: 1 water carrier is about 15 liters 1 liter of water weight 1 kilos The load is about 45 kg

Our calculation: We count 12 arriers : 12 * 15 = 180 liters Total : 180 + 45 = 225 kg

Our answer:

=> 180 kilos

The weight is about 225 kg

WATER: FERMI questions (Belgium) Our question:

What about weight of this load if all water carriers were full?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: 1 liter = 1 kg diameter of the wheel: 17 inch = 43,18.10-2m Height of the bottle is around the diameter, the radius is around 1/3 of the diameter of the wheel m1 empty bottle=1kg

Our calculation: V1bottle (only water)=πr²h=π(14,39.10-2m)².43,18.10-2m=2,809.102

m³=2,809.10l=28,09l

V12 bottles (only water)=12.28,09=337,1l m12 bottles (only water)=337,1kg m12 empty bottles=12kg m12bottles + water = 337,1kg + 12kg= 349kg

Our answer: We estimate that the motorcycle has to carry 349 kg. Funny detail: It can’t. :P

WATER: FERMI questions (Germany) Our question:

What about the weight of this load if all water carriers were full?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

I estimated the radius of the barrel to 12 cm and the height to 50 cm. The number of carriers is 12.

Our calculation:

V=12²* 3,14 * 50 cm³= 22608 cm³= 22,608 l. Vall = 12* 22,608 l=271,296 l.

Our answer:

I think that the carriers in reality contain 20 or 25 l. Then the weight would be between 240 l and 300 l. I calculated about 270 l by estimating the measurements of the carrier.

WATER: FERMI questions (Latvia) Our question: How many liters of water does this barrel hold?

Assumptions: We have estimated, that the average height of a man is 1,80m, including 0,30m of a head and an average length between shoulders is 0,5 m. We know, that a barrel has form of Cylinder, so we need to calculate the height and radius, to count the amount of water. To calculate the height, we measured the length between shoulders of 6 people, who were standing shoulder to shoulder. To calculate the radius of circumference, we measured the height up to the shoulder of the man, who was standing near the barrel. Our calculation: V=Ď&#x20AC;r2h 1 liter= 0,001 m3 H= 6*0,5=3m; r=1,50m V= 3,14*1,502*3 = 21,195 â&#x2030;&#x2C6; 21 m3 = =21000 l

Our answer: The barrel holds 21000 liters of water.

Additional question and answer: If the average water consumption is 20 liters per day, per person, how many days will the family of 3 people consume this barrel of water? Answer: 3*20= 60 liters per day for family 21000/60=350 days

WATER: FERMI questions (Switzerland) Our questions : N°3 by Nafissa and Loïc A) How much has a person of 78 years has drunken in his life? B) How many bath tubes could be filled with it? Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: A) morning : 1 liter midday : 1 liter evening : 1 liter B)Vbath = 15 * 5 * 3 = 225 dm³ = 225 l (Fermi question 1)

Our calculation : A) Total : 3 liters per day 1 week : 7 * 3 = 21 liters 1 month : 21 * 4 = 84 liters 1 year = 12 monthes : 84 * 12 = 1008 liters 78 years : 1008 * 78 = 78'624 liters = 78,6 m3 B) Numbers of bathes : 78'624 : 225 = 350

Our answers : A) In one life we drink 78,6 m3. B) It represents 350 bathes.

WATER: FERMI questions (Belgium) Our question: How many crates of mineral water can be transported in this huge shopping trolley?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

Our calculation: volume car = 3.43 m x 1.63 m x 1.42 m = 7.939 m³= 7939 liter volume shopping trolley ( normal ) = 1m x 0.55 m x 0.80 m volume crate = 6 bottles of 1 liter + free space = 10 liter volume big trolley (estimation) = 3.70m x 1.63 m x 1.42 m = 8.56 m³= 8560 liter

Our answer: Numbers of crates = volume big trolley / volume 1 crate = 8560 l /10 l = 856 crates . We couldn’t calculate the triangle in the front , so in reality , the numbers of crates is a bit higher.

WATER: FERMI questions (Germany) Our question:

What about the water that all students coming to Spain drink in one year?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated â&#x20AC;Ś. as a base for calculation that follow â&#x20AC;Ś:

I estimated the amount of water in one year to 100 l (some students only drink water, others drink milk or coffee, juice and lemonade). So the avarage could be 100l/year. There are 21 students coming to Spain.

Our calculation: 100 l * 21* 365= 766500 l

Our answer:

766 500 liters are drunken a year by the 21 students who come to Spain.

WATER: FERMI questions (Latvia) Our question:

What about weight of this load if all water carriers were full? Assumptions: Volume of the water carriers I found on a Venden water carrier, it’s 18,9l. I think that the count of water carries on both sides is the same. So I thought that there could be 12 water carriers. Our calculation: In these conditions the density of water is approximately 1. M = V x ρ M = 18.9 x 1 M = 18.9 kg This is the weight of one water carrier. Now we need to multiple weight of one to the count of all. 18.9 x 12 = 226.8 Our answer: 226.8 kg is the approximate weight of all load. Additional question and answer: For how many people water in this carriers could be a daily rate of water? Answer: an average human needs to drink 2 l of water every day. We know that we have 226.8 l of water. 226.8 : 2 = 113.4 But there can’t be 0.4 people. So it could be a daily rate of water for 113 people.

WATER: FERMI questions (Switzerland) Our question: N°2 by Maria and Louise

How many drops of water are in a glass of 250 cm³ ? Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: We count the number of drops in a measuring glass. In 50 ml = 0,050 l we can put 170 drops.

Our calculation: 250 cm³ = 0,25 dm³ = 0,25 l 0,25 : 0,050 = 5 5 * 170 = 850

Our answer: 850 drops of waters

WATER: FERMI questions (Belgium) Our question: What about the water that each of the students coming to Spain uses in one year? Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: Each person consume around 120 l water a day for going to the toilet, to clean the house up, to drink,….. . C1day,directly=120 l If we also take into account all the we consume indirectly, we consume 7400 l a day C1day,indirectly=7400 l number days per year = 365,25 d/y  1year = 365 days and 6 hours  6 hours = ¼ a day = 0,25 day Our calculation: C1year,directly

= C1day,directly. number days per year = 120 l.365,25d/y = 43830 l

C1year,indirectly

= C1day,indirectly. number days per year =7400l.365,25d/y = 2702850l

Our answer: Each student will consume 43830 liters of water a year directly (shower, drink). If we also count the water in our food,… each student consume 2702850l a year. Additional question and answer: How many does a person who lives in a hot climate consume? Is this more or less?

WATER: FERMI questions (Latvia) Our question:

WATER: FERMI questions (Switzerland) Our question: N°1 by Kevin and Sarah

What about the water that each of the students coming to Spain uses in one year? Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

The morning : 0,5 liters At midday : 1 liter Toilette 3 times a day : 3 * 5 liters = 15 liters The evening : 2 liters The bath : high : 30 cm = 3 dm tief : 60 cm = 6 dm length : 1,5 m = 150 cm = 15 dm

Our calculation: Vbath = 15 * 5 * 3 = 225 dm³ = 225 l Total a day : 0,5 + 1 + 15 + 2 + 225 = 243,5 l

Our answer: 243,5 liters of water

WATER: FERMI questions (Belgium) Our question: How many drops of water are in a glass of 250 cm³?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: We had to look for de volume of a water drop on the internet. V1drop = min 10µl, max 50µl

Our calculation: 10µm = 0.01m³ 50 µm = 0.05m³ Number of dropsmax = Nmax = Vglas/ V1drop=250m³/0.01m³=25000 drops Number of dropsmin = Nmin = Vglas/V1drop =250m³/0.05m³=5000 drops Average number of drops = (Nmax + Nmin) /2 = (25000 drops + 5000 drops)/2 = 15000 drops Our answer: Between 5000 and 25000 drops are in a glass of 250m³. This means an average of 15000 drops.

Additional question and answer:  What is the situation of the water. (temperature, how the drop is created,…) We need to know that for the size of the drop.

WATER: FERMI questions (Germany) Our question:

What about the water that all students coming to Spain drink in one year?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated â&#x20AC;Ś. as a base for calculation that follow â&#x20AC;Ś:

Our calculation: 100 l * 21* 365= 766500 l

Our answer:

766 500 liters are drunken a year by the 21 students who come to Spain.

WATER: FERMI questions (Belgium) Our question: 1. What about the water that each of the students coming to Spain uses in one year?

2. How many drops of water are in a glass of 250 cm³?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …: 1. X 2. We had to search for the volume of 1 water drop on the internet. Our calculation: 1. X 2. 250cm³= 250 000MM³ = 250 000 000 000 000 µm³ 1 drop is at least 10 microliters 250m³ / 0,01m³ = 25 000 drops 1 drop is maximum 50 microliters 250m³ / 0,05m³ = 5 000 drops

Our answer: 1. X 2. Between 5 000 and 25 000 drops.

Additional question and answer: 1. X 2. What is the situation of the water in the glass? (temperature, how the drop is created, …)

WATER: FERMI questions (Germany) Our question:

How much has a person of 78 years drunken in his life? How many bath tubes could be filled with it?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

I estimate the amount of water drunken during one day to 2 Information in the internet: A normal sized bathtube may contain 150 l if you take a bath.

Our calculation:

2 l*365 .78= 56940 l 56940 l: 150 l=330

Our answer:

 A man of 78 years has drunken about 56940 l of water in his life.  That means he has drunken about 330 bath tubes (filled with water for a bath).

WATER: FERMI questions (Belgium) Our question: How much has a person of 78 years has drunken in his life? How many bath tubes could be filled with it?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated â&#x20AC;Ś. as a base for calculation that follow â&#x20AC;Ś: We found on the internet that the average water consumption a day is 1.5 liters, so we used this to calculate our results. For the bath, we found that a full bath can be filled with 100 gallons of water, but a normal person only uses around 40 gallons when he takes a bath. We looked up how much liters 1 gallon is and we found that 1 gallon equals 3.785 liters. The man was born in 1936, since 1936 there were 20 leap years which means there were 20 years there were 366 days he drank 1.5 liters of water.

Our calculation: 1.5 liters of water x 58 years x 365 days +1.5 liters of water x 20 years x 366 days = 42735 liters of water 3.785 liter x 100 gallons = 378.5 liters 3.785 liter x 40 gallons = 151.4 liters Bathtubs filled completely: 42735 liters of water in total / 378.5 liters of water in a bath = 113 bathtubs Bathtubs filled with enough water to take a bath: 42735 liters of water in total /151.4 liters of water in a bath = 282

Our answer: A person aged 78 has drank around 42705 liters of water in his life. This is enough to fill 113 completely full bathtubs and to fill 282 bathtubs to only take a bath in.

WATER: FERMI questions (Germany) Our question:

How many water drops are in a glass of 250 cm³?

Assumptions: This we have reflected, got to know by an experiment, measured, estimated …. as a base for calculation that follow …:

I assume that the weight of one drop is 0,05 g. We also know that 250 cm³ water weighs 250g. Alternative:

We could measure : How many drops fit in 10 ml of water?

Our calculation:

250g :0,05 g =5000

Our answer:

5000 drops fit in one glass of water of 250 cm³.

WATER: FERMI questions (Belgium) Our question: 1. What about the water that each of the students coming to Spain uses in one year? 2. How many drops of water are in a glass of 250 cm³? 3.

Our calculation: 1. X 2. 250cm³= 250 000MM³ = 250 000 000 000 000 µm³ 1 drop is at least 10 microliters 250m³ / 0,01m³ = 25 000 drops 1 drop is maximum 50 microliters 250m³ / 0,05m³ = 5 000 drops

Our answer: 1. X 2. Between 5 000 and 25 000 drops.

Additional question and answer: 1. X 2. What is the situation of the water in the glass? (temperature, how the drop is created, â&#x20AC;Ś)

WATER: FERMI questions (Belgium) Our question: How much has a person of 78 years has drunken in his life? How many bath tubes could be filled with it? Assumptions: This we have reflected, got to know by an experiment, measured, estimated â&#x20AC;Ś. as a base for calculation that follow â&#x20AC;Ś: We found on the internet that the average water consumption a day is 1.5 liters, so we used this to calculate our results. For the bath, we found that a full bath can be filled with 100 gallons of water, but a normal person only uses around 40 gallons when he takes a bath. We looked up how much liters 1 gallon is and we found that 1 gallon equals 3.785 liters. The man was born in 1936, since 1936 there were 20 leap years which means there were 20 years there were 366 days he drank 1.5 liters of water. Our calculation: 1.5 liters of water x 58 years x 365 days +1.5 liters of water x 20 years x 366 days = 42735 liters of water 3.785 liter x 100 gallons = 378.5 liters 3.785 liter x 40 gallons = 151.4 liters Bathtubs filled completely: 42735 liters of water in total / 378.5 liters of water in a bath = 113 bathtubs Bathtubs filled with enough water to take a bath: 42735 liters of water in total /151.4 liters of water in a bath = 282

Our answer: A person aged 78 has drank around 42705 liters of water in his life. This is enough to fill 113 completely full bathtubs and to fill 282 bathtubs to only take a bath in.

Additional question and answer: