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show work for full credit.
1) Consider an atom with 10 nucleons inside. (average atom)
If the atom ( including the electronic cloud) is scaled up (same shape, just larger) to a new year ball (about 1 m
diameter) a nucleon (proton or neutron) inside the nucleus would be the size of a human hair (about 10
micrometer diameter).
Find the ratio between the new year ball diameter and the hair diameter) _____ : 1
(in scientific notation)
hint: convert micrometer to meter first
That means the whole atom (nucleus + clouds of electrons) is ____________ times larger than the nucleon. In
the atom you have ____ nucleons so the diameter of the nucleus is about ________ times smaller than the
whole atom (in scientific notation)
2 ) if a nucleus is the size of a soccer ball (about 20cm across) the electronic cloud would be 9.5 miles away.
find the ratio between the size of the atom (9.5 miles) and the size of a nucleus (10cm).
Do you get about the same order of magnitude than in 1) ?
(hint: you need to convert miles to meter and cm to meter first)
3) 10 trillion cells in our body = _____________ in scientific notation.
Each cell harbors 10 microbes. So ___________ microbes (scientific notation) inhabit us.
If you take all our DNA strings, stretch them out and connect them you will
make 8000 round trips to the moon. How long is that in km (scientific notation) __________ km
(find the distance Earth-moon in km from internet)
4) It is estimated that 2 105 tons of sulfur dioxide, SO2, enters the atmosphere daily owing to the burning of
coal and petroleum products.
Assuming an even, distribution of the sulfur dioxide throughout the atmosphere, calculate in parts per million
by weights the concentration of SO2 added daily to the atmosphere. The weight of the atmosphere is 4.5
1015 tons.
hint: it is a proportion if: 2 105 is for 4.5 1015 then X is for 1 million
It takes about 40 days for the removal of acid sulfuric by rain. (acid rain that destroys trees and contaminates
lakes )
5) source: Mathematics teaching in the middle school / Vol. 15 , No2, September 2009
Ethanol is now used as an alternative fuel. It is made from corns.
A) To measure the quantity of corns, farmer use a unit of mass called a bushel. 1 bushel is 56 pounds.
1 acre of corn field yields 150.7 bushels of corns.
How many bushels can be produced on 300 acres ?
1000 acres ?
Keep these numbers, you will need them for the coming questions. (hint: set your proportion )
TAKE HOME Dr. Lankar section _______ Name_____________ grade% _____
B) Only 15% of the corn produced is sent to an ethanol rafinery.
How many bushels are sent to rafinery from the corns grown on a 300 acres ?
1000 acres ?
(hint: proportion again 15 out of 100 is sent to rafinery . so use A) )
C) From each bushel, an ethanol rafinery can produce 2.8 gallons of ethanol .
Using the numbers found in B) find the gallons of ethanol produced from the
corns grown from a 300 acres
and from a 1000 acres
D) in 2008 9 billion gallons of ethanol was produced from rafineries. Approximately, how many bushels of corn
were used in ethanol production? (hint: use question C)
5) A leaf-cutting ant weighting 1.5 grams can carry a leaf weighting 4.5 grams. If a person could proportionally
carry as much weight, how much could a 120 lbs student carry?
6) A rhinoceros beetle weighs 30 grams and can carry 850 times its body weight, that is 25,500 grams. If a
person could carry proportionally as much as the rhinoceros beetle, how much could a 120 pounds student
carry?
7) An AMerican alligator lives about 40 years and, during that time, grows about 3000 teeth, How many teeth
per year is that ?
8) One of the fastest marathon runners is Balaine Desimo, who completed 26 miles in 2.1 hours. TO the nearest
mile, what was his rate of travel ?
9) THe fruit with the highest caloric value is the avocado: 1 1/2 pounds of edible avocado contain 1110 calories.
What is the caloric rate per edible pound ?
10) The fruit with the lowest caloric value is the cucumber. A 11/2 pound cucumber as 109.5 calories. What is
the caloric rate per pound of cucumbers ?
11) Which is the fastest-growing plant you know ? A bamboo grew 36 inches in a 24 hour period. What was the
hourly growth rate for this plant (in inches per hour or in/hr)
That means: In every hour, the plant grows ______in 3 hours it grows ___________, in 1 day ______
12) According to Plato's description, the population of the lost city of Atlantis was between 6 and 10 millions
people. If the area of Atlantis was 86,400 square kilometers and he population is assumed to have been
8,640,000 inhabitants, what was the population density for Atlantis (in people/km2)
TAKE HOME Dr. Lankar section _______ Name_____________ grade% _____
13) One of the MOST densely populated cities in Macao (a Chinese territory under Portuguese administration)
with about 446,250 inhabitants living on 21 square kilometers of land. What is the population density per square
kilometer in Macaw ? (that is the number of people per square kilometers)
14) The movie Austin Powers features Dr. Evil and his clone Mini Me. Mini Me is much smaller even if
identical to Dr. Evil. Mini Me (in the movie) is said to me 1/8 of Dr Devil's size. Let's find out if this makes
sense.
If Mini Me is 32 inches and 1/8 of Dr. Evil, how tall is Dr. Evil (in inches) ? Does this make sense ?
15) density of water is 1g/ cm3. so 1,000 cm3 (1 liter) weighs ________ kg
1,000,000 cm3 weighs _________ kg or ____ ton. (1,000,000 cm3 is 1 m3)
-----------------------------------------------------------------------------------------------------------------------the following is more challenging. If you don’t do it, but do the previous problems, you still get an A-
Johannes Kepler was German and fond of Astronomy. He was an amazing mathematician too. He had a
difficult life, (He was sent to a strict protestant boarding school and hated it, his mom was trialed for being a
witch, his dad was a mercenary and abandoned his family, he lost his first loved wife and many of his children
died ( 7 out of 11 )...and on and on .. (queen Elizabeth the 1st was his contemporary as well as Shakespeare and
Galileo)
During the 30 years war in Europe (catholic were persecuting protestants and protestants were fighting each others) ,
he had to flee Germany (catholic country, he was protestant) and moved to Prague. In Prague, he met Tycho
Brahe who had collected, with the naked eye, and amazingly very accurately, positions of planets around the
Sun. Tycho Brahe hired Kepler to work on the data in search of patterns. The 2 men didn't get along and Brahe
would only give Kepler the precious data a few at a time. Kepler got lucky when Brahe suddenly died (broken
bladder) and stole the data from the family. (Brahe was an interesting man. He lost his noise in a sword fight with a
student and was wearing a fake copper noise. He used to have his own island in Copenhagen given by the king (to observe
the sky ) but was exiled by the new king to Praque).
With the data (positions of Mars relative to the Sun), Kepler was able to infer the famous 3 Kepler laws:
A) Planets move along ellipses around the Sun (most of them are almost circles). (the sun is at one focus)
B) When moving along their orbit, planets sweep the same area during the same time. (meaning they race when
they are close to the Sun and slows down when they are away from it)
C) For all the planets in our solar system, the ratio between (the orbital period)2 and (the distance from the
Sun)3 is the same or:
(the orbital period of planet)2 / (the distance from the Sun of planet )3 = K
K is a constant.
That was a major discovery. Next, Newton invents calculus sand is able to derive and explain these laws using
his universal gravitational law. (2 masses attract each other, force of gravity)
TAKE HOME Dr. Lankar section _______ Name_____________ grade% _____
The third law is about ratio. If we use Earth as a reference we can write:
(orbital period planet)2 / (distance planet-Sun)3 = (orbital period earth)2 / (distance earth-Sun)3 = K
All before was just to have you read over. For the following questions, you will only need the previous
equation. 
Let's take (distance Earth-Sun ) is 1 AU . (distance of planets will be in AUs)
(1 astronomical unit is about 150 million km but don't use 150 million km)
Let's take the orbital period of the Earth is 1 year (period of planets will be in earth years)
We know that it takes Mars 1.88 earth years to go around the sun (orbital period planet)
Use the proportion to find the (distance mars-sun)3 = ____________ .
(hint: solve the proportion above for (distance mars-sun)3 ).
So solve for (distance mars-sun) : with your TI, raise the previous number to 1/3 (that will undo the third
power)
(distance mars-sun) =_______________ AUs.
Do the same thing for Jupiter. Find in the Internet, the orbital period of Jupiter in Earth years = _____________
(distance Jupiter-sun) =_______________ AUs.
2) Thanks to Kepler's laws we can find out the relative distances of planets from the Sun.
The distance Sun- Earth is taken as being 1 AU. The relative distance Sun-Venus is then 0.7 AU.
A) When The Sun, Venus and Earth are lined up, find the distance between the EArth and Venus in AUs.
distance EArth-VEnus = ______ AUs. (draw, it will help you)
B) To find the absolute distances from Sun to planets, radio waves were sent to VEnus. The radio wave
bounced back from Venus to Earth. It took 300s for the waves to cover the round trip. Find the distance EarthVenus in km .
(radio waves are electromagnetic waves that travel at the speed of light in space (vacuum). The speed of light is 300,000 km/s ).
distance VEnus-Earth = __________________ km (scientific notation, keep 2 decimals)
(hint: you have 1s= 300,000km find 300s = ….. km
proportion again, don't forget to divide the distance by 2, it is a round trip
C) Use the distance Venus- EArth you just found to find 1AU (distance Earth-Sun) in km.
( VEnus-Earth = 0.3AU )
1 AU = _______________ km
(hint: you can set a proportion again. 0.3 AU = ... km so 1 AU = ? km )