Mixture B
Part III. Determine the Mass % of Elements in each Compound:
K2SO4 - Potassium Sulfate
(Show Math Here)
39(2) + 32(1) + 16(4)
= 78 amu + 32 amu + 64 amu
= 174 amu
Potassium= 78 amu/174 amu x 100
= 0.448 amu x 100
= 44.8%
Sulfur= 32 amu/174 amu x 100
= 0.183 amu x 100
= 18.4%
Oxygen= 64 amu/174 amu x 100
= 0.368 amu x 100
= 36.8%
Na3 PO4 - Sodium Phosphate
(Show Math Here)
23(3) + 31(1) + 16(4)
= 69 amu + 31 amu + 64 amu
= 164 amu
Sodium= 69 amu/164 amu
= 0.421 amu x 100
= 42.1%
Phosphorus= 31 amu/164 amu
= 0.189 amu x 100
= 18.9%
Oxygen= 64 amu/164 amu
= 0.39 amu x 100
= 39%
Graphs:
IV. Conclusion:
1. Explain the difference between Mixtures and Compounds using data. Compare the pie
charts.
The difference between mixtures and compounds is that mixtures have
components that retain their own molecular structure and compounds have components
that get a new molecular structure when introduced to each other, or a chemically
bonded structure. For example, the compound Na3 PO4. The sodium, phosphorus, and
oxygen atoms have formed ionic bonds with each other to make the new compound
Sodium Phosphate. In a mixture, the components (rocks and sand, for example), the
rocks would retain their own clumped silicon structure and the sand would retain it’s
crystalline silicon dioxide structure, as shown by the pie charts.
2. Explain how you separated the Salt from the Sand. Use as much new vocabulary as you
can.
I sifted away the biggest granules of sand from the salt and fine sand, and then
poured that homogeneous mixture through a coffee filter with water. The coffee filter did
not allow the sand to pass through it, so only the tiniest pieces of sand and the salt got
through. At this point, the salt (the solute) has dissolved in the water (the solvent) and
the ionic bonds in the salt have been broken so the sodium chloride has been reduced to
sodium and chlorine atoms, and by extension, sodium and chloride ions. The sodium
and chlorine atoms are being kept from forming solid sodium chloride by all it’s
interactions with the water molecules. I then took the hot plate available and used heat
energy to force a phase change in the salty water from a liquid state to a gaseous state.
By the time all the water has boiled away, or been vaporised, the sodium and the chloride
ions can become solid again and form Sodium Chloride (NaCl) at the bottom of the
beaker.
Solubility and Chemical
Compounds
Name: _Eleanor Boyd_ _____________ Class: __S3___
QUIZ: Solubility and Naming Compounds
Part I. Charge
Directions: Write the symbol of the element with the charge.
Formula
1. Sodium Na +
2. Neon Ne No charge
3. Nitrate NO3 -
4. Chlorine Cl -
5. Magnesium Mg 2+
6. Silver Ag +
7. Sulfur S 2-
8. Phosphorus P 3-
9. Aluminum Al 3+
10. Calcium Ca 2+
11. Nitrogen N 3-
Part II.
Directions: Write the name for the compounds:
11. Na3PO4 Sodium Phosphate
12. Li2( SO4) Lithium Sulfate
13. (NH4) 2C O3 Ammonium Carbonate
14. MgCl2 Magnesium Chloride
15. Ca(NO3)2 Calcium Nitrate
16. BeF2 Beryllium Fluoride
Part III.
Directions: Write the chemical formula for the following compounds (Use your ions):
17. Calcium carbonate
Ca CO3
18. Ammonium phosphate
(NH4) 3 PO4
19. Magnesium hydroxide
Mg (OH)2
20. Potassium sulfate
K2 SO4
Part IV.
Directions: Determine the Mass % of Oxygen in Al2(SO4) 3 or AgNO3
Atomic Mass: Al (27) S (32) O (16) Ag (108) N (14)
AgNO3
Ag = 108 amu
N = 14 amu
O3 = 16(3)
108+14+48 amu = 170 amu
Ag = 108/170 x 100 = 63.5%
N = 14/170 x 100 = 8.2%
O3 = 48/170 x 100 = 28.2%
Mass percentage of Oxygen in Silver Nitrate: 28.2%
Part V.
Directions: Write an essay about the graph below. U se data!
Vocabulary: Unsaturated, saturated, supersaturated, Ions, Heat, Temperature, grams,
solubility, chemical formula
The point on the solubility graph is above the line, so that means at 15 degrees C, the
water is supersaturated. There is too much CN- in the beaker at the current temperature. There
are two possible solutions to make the cyanide at the bottom of the beaker go away, or dissolve
into the water (the solvent). The water can either be heated, or some of the cyanide can be
taken away. To reach a point at which the water is completely saturated by heating it, the water
must be heated by 23 degrees C. To reach a point at which the water is completely saturated by
subtracting some cyanide, 45 grams of cyanide must be taken away. To succinctly sum up,
there are two ways to make the water (the solvent) go from supersaturated to saturated.
Subtract 45 grams of cyanide from the beaker or heat the water by 23 degrees C.
Atoms and the Periodic Table
The History of the Atom
Speculations about atoms began nearly 2500 years ago in the fifth and fourth
centuries B.C. by Democritus and Leucippus. They thought there was something that
made up everything they saw around them, and named it atomos, or uncuttable.
Then, more than 1000 years later, John Dalton made his own model of the atom in
1808. He said matter consists of indivisible atoms, and those atoms are arranged in
different ways to make different compounds. The next notable discovery in realm of
atoms came in 1904, when J.J. Thompson discovered that atoms had electrons.
Using this, he came up with his own model of the atom called the “plum pudding
model”. He thought there was a cloud of energy that was positively charged and
smaller negatively charged particles float around inside the cloud, so it looked a bit
like plum pudding (hence the name). However, seven years later in 1911, Ernest
Rutherford disproved Thompson’s plum pudding model with his own Rutherford
Nuclear Model. He discovered that protons, or particles with a positive charge, are
actually clustered together and not just a cloud of evenly distributed positive energy
like Thompson said. He also discovered that atoms have a nucleus, or a center.
In 1913, Niels Bohr came up with what is now known as the Bohr Model of the
atom. Working off of what Rutherford discovered, he said electrons were spinning
around the nucleus of the atom in a circular fashion, like an orbit. Seven years later
Erwin Schrodinger (yes, his cat is dead) came up with the Quantum Mechanical
Model. He thought that there were positive charges in the center of the atom and
electrons are buzzing around the nucleus in a random fashion that he called orbitals.
Much later in 1932, James Chadwick discovered neutrons, particles with a net charge
of zero, or a neutral charge.
So what is the most accurate way of
displaying the atomic structure? The
Quantum Mechanical Model with protons
and neutrons would be the most accurate
description of the atom, and it looks like the
image to the left. The blue is representative
of the paths electrons take around the
nucleus, purple is neutrons, and red is
protons.
Atomic Structure
Atoms consist of electrons surrounding a nucleus that contains protons and
neutrons. Electrons have a relative charge of negative one, protons have a relative
charge of positive one, and neutrons have a neutral charge or a charge of zero.
Electrons are arranged in energy levels called shells and protons and neutrons are
clustered together to make the nucleus. Electrons are arranged in shells around the
nucleus and shells are filled with electrons from the inside out. Different shells can
hold different amounts of electrons. For example, the innermost shell can hold a
maximum of two electrons, the second and third shell can hold 8 electrons at most,
the fourth shell can hold 18 electrons, and so on and so forth.
On the Periodic Table of Elements, each horizontal row has a number and
each element has an atomic number. The number of occupied shells of the elements
in that row is the same as the row number. So for example, all the elements in the
second row of the Periodic Table would have two shells occupied. As you go left to
right on the Periodic Table,
each shell becomes filled
with more and more
electrons, so that by the
time you have reached the
last element all the way on
the right, the shell is
completely filled. The size of
these atoms are
demonstrated by the graph
to the right. The peaks are
all the way on the right of the Periodic
Table and the low points are all the way
on the left of the Table.
Sometimes there are sometime
electrons that are left unpaired on the
outermost shells. These are the
electrons that will bond with other
electrons when introduced to another
element, and are called valence
electrons. These valence electrons are
also the electrons that are most easily removed from the atom. However, the
amount of energy used to take this electron away from the atom is different. As you
go across the Periodic Table from left to right, the energy required for this to
happen increases, as you can see from the graph with the orange line above. As you
go down the Periodic Table, the amount of energy gradually decreases, though as
you move left to right across the table the amount of energy increases. The peaks in
the graph reflects the energy needed for the atoms all the way on the right of the
Table, and the low points reflect the energy needed for the electrons belonging to
the atoms on the very left side.
.The atomic number depends on how many neutrons and protons there are in
this atom. Electrons do have some weight, but seeing how it’s about 0.0005 of an
atomic mass unit, it’s not counted when determining the weight of an atom.
Using models of
different molecules and
atoms, we can even
determine the difference
between molecules and
atoms. For example,
sodium sulfide is made of
two sodium atoms and
one sulfur atom as shown
in the picture. The sulfur
atom has 16 protons and
16 neutrons in its nucleus
and has six valence
electrons in its outermost
shell. The sodium atoms
have 11 protons and 12
neutrons in its nucleus
and only one valence
electron in its outermost shell.
And then this is an atomic model of Calcium Sulfide. As you can see, it is quite
different from the Sodium sulfide.
Calcium sulfide is made of one calcium atom and one sulfur atom. The calcium atom
has 10 protons and 10 neutrons in its nucleus and two valence electrons in its
outermost shell, while the sulfur atom has 16 protons and 16 neutrons in its nucleus
as well as 6 valence electrons in its outermost shell. The only differences between
sodium sulfide and calcium sulfide are the elements used in each compound. Sodium
sulfide uses two sodium atoms and calcium sulfide uses one calcium atom. In
calcium sulfide, sulfur has only one covalent bond but in sodium sulfide sulfur has
two covalent bonds, one with each sodium atom.
Isotopes
Isotopes of the same element have the same number of protons but a
different number of neutrons in the nucleus, so they vary in atomic weight.
Sometimes this can result in a radioactive isotope. The number of neutrons can
sometimes outnumber the amount of protons in the nucleus, and this can cause the
strong nuclear force holding the nucleus together to fall apart. The protons fly in
every direction, and that results in radiation. To give an idea of how many isotopes
there can be, every chemical element has at least one radioactive isotope and there
are more than 1,000 radioactive isotopes known. There are many more stable
isotopes as well. For example, carbon 12 and carbon 14 are carbon isotopes. Both
isotopes have six protons, but carbon 12 has six neutrons and carbon 14 has eight
neutrons.
Isotopes can be used in a variety of fields, including medicine, industry, and
even space travel. In medicine, radioactive isotopes are used for cancer treatment
and tracers for diagnostic and research purposes.
In industry, they are used for measuring the
thickness of metal or plastic sheets, or in place of
x-rays used to discover any defects in
manufactured metal parts. Radioactive isotopes
are even used as a source of power in spacecraft.
The heat generated in the decay of these isotopes
can be turned into electricity to power the
spacecraft. Some of the isotopes that are used
today are cobalt 60, plutonium 238, copper 64,
chromium 51, iron 59, phosphorus 32, potassium 42,
iodine 123, and krypton 81. The numbers after the
element name is the atomic weight of the isotope.
Dmitri Mendeleev and His Contributions
to the Periodic Table
Dmitri Ivanov Mendeleyev was one of
the biggest contributors to the
Periodic Table. In fact, his
contributions to the Periodic Table
were so great they have been
compared to the works of Darwin and
the development of the theory of
evolution. Dmitri Mendeleev was born
in Russia in 1834, the youngest of 17
children. His family was well-off, and
believed in a good education, so after his father died in 1847 he was sent to the
Institute of Pedagogy in St. Petersburg. Shortly after his mother died as well. There
at the Institute in St. Petersburg he taught and studied chemistry until he graduated
in 1855 and was granted a Master’s degree in 1856. His studies took him all over
Europe, from Paris to Heidelberg but returned to St. Petersburg where he started
playing around with the organisation of the elements in the current table. During his
research in Heidelberg in 1860 he discovered the absolute point of ebullition, which is
the point at which a gas will turn into a liquid solely by the application of pressure. In
1861 he published a organic chemistry textbook and received the prestigious
Domidov award for his textbook. Later on he attended The International Chemistry
Congress in Karlsruhe, where he saw the interesting research of Italian chemist
Stanislao Cannizzaro that would later inspire him to organise the Periodic Table such
as he did.
In 1867 Mendeleev became a professor of general chemistry at the University
of St. Petersburg and taught there until 1890. While still teaching, Mendeleev wrote
another textbook from 1868- 1871 called Osnovy Khimii o r The Principles of
Chemistry which was reproduced in many different
editions and languages so it could be of help around
the world. As he was writing this book, Mendeleev
noticed a pattern between the halogens and alkaline
earth metals and discovered the periodic law. Using
this knowledge, Mendeleev revealed his Periodic
Table in 1869, which he called O pyt Sistemy
Elementov, o r the System of Elements which was
organised based on atomic weight and chemical
similarity. He quickly gained recognition for his
uniquely designed table. After his Periodic Table was
unveiled Mendeleev taught chemistry and studied
thermal expansion of liquid as well as the nature of petroleum.
Mendeleev organised his Periodic Table a very special way. As you know, he
organised the elements according to atomic weight and chemical similarity but he
put them in groups or families. Each vertical column on the Periodic Table is part of
a family, and there are five families in
the Periodic Table. The alkali metals, the
alkaline earth metals, transition metals,
halogens, and noble gases. Another way
to view the Periodic Tables is in nine
groups instead of five. The nine groups
are alkali metals (Group 1), alkaline
earth metals (Group 2), transition
metals (Groups 3-12), the Boron group
or earth metals (Group 13), the Carbon
group or Tetrels (Group 14), Nitrogen group or Pnictogens (Group 15), the Oxygen
groups or Chalcogens (Group 16), the halogens (Group 17), and the noble gases
(Group 18). Group 1 has one valence electron, group 2 has 2 valence electrons,
groups 3-12 have 3 valence electrons, group 13 has four valence electrons, group 15
has five valence electrons, group 16 has six valence electrons, group 17 has seven
valence electrons, and group 18 has 8 valence electrons or a completely filled
outermost shell.
Some similarities that can be noted in the families are as follows. In the alkali
metal group, all elements in the right
conditions have a violent exothermic
reaction with water (H2 O) and produces a
hydrogen gas and an alkali metal hydroxide
metal solution. In the alkaline earth metals
group, these metals have a high thermal and
electrical conductivity and have a violent
exothermic reaction with water. This reaction
increases in violence as you move down the
column. The exceptions to this rule are
Beryllium and Magnesium. Beryllium does
not react with water and Magnesium only
reacts with steam. The next family is the
transition metals. These are all shiny and
lustrous metals that are very dense and
have high thermal and electrical conductivity as well as high melting points and
various oxidation rates. The Boron group is not all that well known. The most famous
element in this group is Aluminium. These elements exhibit diverse properties in the
middle between metals and nonmetals. The Carbon group is similar to the Boron
group in the sense that the elements within this group display diverse properties in
the middle of metal and nonmetals. The most famous element within this group is
Carbon, which is known for forming four bonds. The
nitrogen group is six elements which display diverse
properties belonging to neither metals or nonmetals,
but something in between. The Oxygen group or
Chalcogens family has six elements which display
diverse properties. They change from non metallic to
metallic as you move down the family. The Halogens
are a group of reactive nonmetals that change from
a gaseous to a liquid to a solid state as you move down the family column. For
example, fluorine is a gas at room temperature bromine is a liquid at room
temperature, and iodine is a solid at the same temperature. The noble gases (also
known as Inert gases) are a group of unreactive nonmetals like argon or helium.
These elements typically exist by themselves, though they do rarely form
compounds. This is due to the fact that they have no valence electrons for other
elements to form covalent bonds with. It is also due to this fact that they are inert
under any normal circumstances.
A Brief Summary of “Protons” from the
Live Science Website
“Protons” from the Live Science website is a paragraph on what protons are.
Protons are basically positively charged particles that are found within the nucleus
of an atom. They were discovered by Ernest Rutherford from 1911 to 1919 in an
experiment involving cathode-ray tubes. They are made of three subatomic
particles called quarks. Two of the three quarks are “up” and have a two thirds
positive charge, while the remaining quark is “down” and has a one third negative
charge. As such, protons are about 1.0072766 atomic mass units, which is slightly less
than a neutron. The number of protons in an atom is what defines the element; for
example, if an atom has five protons in the nucleus, then the element in boron.
However, if there is only one more proton added, the element will change from are
boron to carbon.
Isotopes
QUIZ: Isotopes Date: 2-6-18
Name: Eleanor Boyd
Directions construct a graph that will help you determine the age of fossils.
Isotope A Percent Isotope
Years
0 100
5730 50
11,460 25
17,190 12.5
22,920 6.25
28,650 3.125
34,380 1.06
40,110 .5
45,840 .25
51,570 .125
57,300 0
Hint: Remember to add gridlines
Graph: ( place graph here)
Questions: (Use your graph above to answer the questions below)
1. How old is the following fossil?
Fossil A - 73% of Isotope A remaining
Fossil A is about 4500-5000 years old.
2. How old is the following fossil?
Fossil B - 15% of Isotope A remaining
Fossil B is about 17,000 years old.
3. What percentage of Isotope A is remaining if the fossil is 1200 years old?
(Use your graph)
There is about 90% of Isotope A remaining if the fossil is 1200 years old.
Average Atomic Mass Calculations
1. Naturally occurring chlorine that is put in pools is 75.53 percent 35Cl (mass = 34.969
amu) and 24.47 percent 37Cl (mass = 36.966 amu). Calculate the average atomic mass
of chlorine.
75.53% ÷ 100 x 34.969 amu = 26.4120857 amu
24.47% ÷ 100 x 36.966 amu = 9.0455802 amu
9.0455802 amu + 26.4120857 amu = 35.4576659 amu
The average atomic mass of chlorine is 35.4576659 amu (about 35 amu).
2. Calculate the atomic mass of silicon. The three silicon isotopes have atomic masses and
relative abundances of 27.9769 amu (92.2297%), 28.9765 amu (4.6832%) and 29.9738
amu (3.0872%).
The average atomic mass of silicon is 28.08538954 amu (about 28 amu).
Writing:
Use one of the examples above to discuss how you determine the number of neutrons for each
isotope. You also need to discuss how the %abundance contributed to the Average Atomic
Mass of the element. (HINT: Think of the M&M Lab!)
I determined the number of neutrons in each isotope by subtracting the number of
protons (or the atomic number) from the rounded atomic mass. For example, silicon’s atomic
number is 14. Therefore, I would subtract 14 from 28 (the atomic mass of the first silicon isotope
rounded) and get 14 as a result. This means that there are 14 neutrons in the nucleus of a
silicon molecule that weighs 27.9769 amu. I would then repeat the same process for each of the
other two silicon isotopes, getting 15 neutrons in silicon isotope 2 and 17 neutrons in silicon
isotope 3.
The atomic number, or the number of protons in an element, will never change because
the number of protons in the nucleus of an element is what defines the element. Take a proton
away or add a proton to the nucleus and you have an entirely different element. However, the
number of neutrons in the nucleus can change.
The percent abundance contributed to the average atomic mass of silicon because it is
necessary for finding how abundant the silicon isotope with that specific atomic weight is. For
example, I multiplied the percent abundance of the first silicon isotope by its atomic weight to
get 25.80301094 amu, and for the second silicon isotope I multiplied 28.9765 by 0.046832 to
get 1.357027448 amu, and for the third isotope I multiplied 29.9738 by 0.030872 to get
0.9253511536 amu. I then added all three resulting numbers together and got 28.08538954
amu as a result. 28.08538954, or 28 amu rounded, is about the atomic mass of silicon stated on
the Periodic Table. As you can see, without the percent abundance of each silicon isotope, the
average atomic mass of silicon would be vastly different because it is an integral part of the
equation to find average atomic mass of an element.
Motion
Unit 1: Uniform Motion Name_______________________________
Worksheet 8 Date__________________Period________
Speed and Velocity Problems
1. What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints
50 m in 2 s?
V = D/T
V = 100 m/ 4 s
V = 25 m/ 1 s The average speed of a cheetah that sprints 100 m in 4 s is 25
m per second. The same goes for a cheetah that sprints 50 m in 2 seconds.
V = 50 m/ 2 s
V = 25 m/ 1 s
2. If a car moves with an average speed of 60 km/hr for an hour, it will travel a distance of
60 km. How far will it travel if it continues this average rate for 4 hrs?
D = VT
D = 60 km/hr x 4 hrs
D = 240 km The car will move 240 km after 4 hrs at a rate of 60 km/hr.
3. A runner makes one lap around a 200 m track in a time of 25.0 s. What was the runner's
average speed? Answer: 8.0 m/s
V = D/T
V = 200 m/ 25 s
V = 8 m/s
4. Light and radio waves travel through a vacuum in a straight line at a speed of very nearly
3.00 × 108 m/s. How far is light year (the distance light travels in a year)? Answer: 9.50
× 101 5 m.
5. A motorist travels 406 km during a 7.0 hr period. What was the average speed in km/hr
and m/s? Answers: 58 km/hr, 16 m/s.
6. A bullet is shot from a rifle with a speed of 720 m/s. What time is required for the bullet
to strike a target 3240 m away? Answer: 4.5 s.
7. Light from the sun reaches the earth in 8.3 minutes. The speed of light is 3.0 × 108 m/s.
In kilometers, how far is the earth from the sun? Answer: 1.5 × 108 km.
8. *An auto travels at a rate of 25 km/hr for 4 minutes, then at 50 km/hr for 8 minutes, and
finally at 20 km/hr for 2 minutes. Find the total distance covered in km and the average
speed for the complete trip in m/s. Answers: 9 km, 10.7 m/s.
9. *If you traveled one mile at a speed of 100 miles per hour and another mile at a speed of
1 mile per hour, your average speed would not be (100 mph + 1 mph)/2 or 50.5 mph.
What would be your average speed? (Hint: What is the total distance and total time?)
Answer: 1.98 mph.
10. *What is your average speed in each of these cases?
a. You run 100 m at a speed of 5.0 m/s and then you walk 100 m at a speed of 1.0
m/s.
b. You run for 100 s at a speed of 5.0 m/s and then you walk for 100 s at a speed of
1.0 m/s. Answers: 1.7 m/s, 3.0 m/s.
11. *A race car driver must average 200 km/hr for four laps to qualify for a race. Because of
engine trouble, the car averages only 170 km/hr over the first two laps. What average
speed must be maintained for the last two laps? Answer: 230 km/hr
12. *A car traveling 90 km/hr is 100 m behind a truck traveling 50 km/hr. How long will it
take the car to reach the truck? Answer: 9 seconds.
V = V1 - V2
V = 90 km/hr - 50 km/hr = 40 km/hr
D = 0.1 km
T = D/V = 0.1 km / 40 km/hr = 0.0025 hrs.
T = 9 seconds
13. The peregrine falcon is the world's fastest known bird and has been clocked diving
downward toward its prey at constant vertical velocity of 97.2 m/s. If the falcon dives
straight down from a height of 100. m, how much time does this give a rabbit below to
consider his next move as the falcon begins his descent? Answer: 1.03 seconds
More Speed and Velocity Problems
14. Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his
yodel back from the canyon floor 5.20 s later. Assume that the speed of sound in air is
340.0 m/s. How deep is the canyon? Answer: 884 meters.
D = (VT)/2
D = (340 m/s (5.2 s))/2
D = (1,768 m)/2
D = 884 m
15. The horse racing record for a 1.50 mi. track is shared by two horses: Fiddle Isle, who ran
the race in 143 s on March 21, 1970, and John Henry, who ran the same distance in an
equal time on March 16, 1980. What were the horses' average speeds in:
a. mi/s? - 0.01 miles per second
b. mi/hr? - 36 miles per hour
V1 = 1.5 mi / 143 s
V1 = 0.01 mi/s
V2 = 1.5 mi / 143 s
V2 = 0.01 mi/s
16. For a long time it was the dream of many runners to break the "4-minute mile." Now
quite a few runners have achieved what once seemed an impossible goal. On July 2,
1988, Steve Cram of Great Britain ran a mile in 3.81 min. During this amazing run, what
was Steve Cram's average speed in:
a. mi/min? - 0.26 miles per minute
b. mi/hr? - 15.6 miles per hour
V = D/T
V = 1 mi / 3.81 min
V = 0.26 mi/min
V = 0.26 mi/min x 60 min
17. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French
class for the third time this week. She must get from one side of the school to the other
by hurrying down three different hallways. She runs down the first hallway, a distance of
35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she covers
its 48.0 m length at an average speed of 1.20 m/s. The final hallway is empty, and
Suzette sprints its 60.0 m length at a speed of 5.00 m/s.
a. Does Suzette make it to class on time or does she get detention for being
late again? - Yes. She is 2 seconds late to class.
b. Draw a distance vs. time graph of the situation. (Assume constant speeds
for each hallway.)
T = D/V
T = 35 m /3.5 m/s
T = 10 s
T = 48 m / 1.2 m/s
T = 40 s
T = 60 m / 5 m/s
T = 12 s
60 sec = 10 sec + 40 sec + 12 sec
60 sec ≠ 62 sec
62 sec - 60 sec = 2 sec
18. During an Apollo moon landing, reflecting panels were placed on the moon. This
allowed earth-based astronomers to shoot laser beams at the moon's surface to determine
its distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent.
The speed of light is 3.0 × 108 m/s. What was the distance between the astronomers and
the moon? Answer: 3.78 x 108
D = VT
D = 3 x 108 m/s (2.52 /2) s
D = 3 x 108 m/s (1.26 s)
D = 378000000 m
D = 3.78 x 108 m
19. For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent
years some rural stretches of highway have increased their speed limit to 104.6 km/hr (65
mi/hr). In Maine, the distance from Portland to Bangor is 215 km. How much time can
be saved in making this trip at the new speed limit? Answer: 22 minutes and 11 seconds.
T = D/V
T = 215 km / 88.5 km/hr
T = 2.43 hrs.
T = 215 km / 104.6 km/hr
T = 2.06 hrs.
2.43 hr - 2.06 hr = 0.37 hr
0.37 hr x 60 min = 22.2 mins
20. The tortoise and the hare are in a road race to defend the honor of their breed. The
tortoise crawls the entire 1000. m distance at a speed of 0.2000 m/s while the rabbit runs
the first 200.0 m at 2.000 m/s The rabbit then stops to take a nap for 1.300 hr and
awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the
race and by how much time? Answer: The tortoise wins the race by 46.8 seconds.
T = D/V
T = 1000 m / 0.2 m/s
T = 5000 s = 83.34 mins
T = 200 m / 2 m/s
T = 100 s = 1.67 min
T = 800 m / 3 m/s
T = 266.7 s = 4.45 mins
T = 1.67 min + 4.45 min + 78 min
T = 84.12 mins
T = 84.12 mins - 83.34 mins
T = 0.78 mins
21. Two physics professors challenge each other to a 100. m race across the football field.
The loser will grade the winner's physics labs for one month. Dr. Rice runs the race in
10.40 s. Dr. De La Paz runs the first 25.0 m with an average speed of 10.0 m/s, the next
50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of
11.1 m/s. Who gets stuck grading physics labs for the next month? Answer: Dr. Rice
loses by 23.4 seconds.
T = D/V
T = 25 m / 10 m/s
T = 2.5 s
T = 50 m / 9.5 m/s
T = 5.26 s
T = 25 m / 11.1 m/s
T = 2.25 s
T = 2.5 s + 5.26 s + 2.25 s
T = 10.01 s
10.4 s - 10.01 s = 0.39 s
Velocity Project 2018
Due: Wednesday night February 21,2018
1. Define the following terms and include pictures if possible:
Motion - the action or Speed - the rate at which Position - a place where
someone or something is
process of moving or being someone or something is
located or has been put.
moved. able to move or operate.
Distance - an amount of Acceleration - a vehicle's Terminal Velocity - the
space between two things capacity to gain speed constant speed that a
freely falling object
or people. within a short time. eventually reaches when
the resistance of the
medium through which it is
falling prevents further
acceleration.
Time - the indefinite Initial Velocity - The Displacement - the moving
of something from its place
continued progress of velocity of an object before
or position
existence and events in the acceleration causes it to
past, present, and future change.
regarded as a whole.
Velocity - the speed of Final Velocity - the velocity Key Metric units - A system
something in a given of an object at the final of measurement in which
point in time. the basic units are the
direction. meter, the second, and the
kilometer.
2. What is the difference between Speed and Velocity? Explain using an example
in your own words.
Speed is the absolute value of velocity, or speed plus direction. You can have a positive
or negative velocity when you establish an origin, but speed does not have direction like
velocity does. For example, you are standing at a crosswalk. A car goes away from you
at a velocity of 12 meters per second. The velocity is positive 12 meters per second and
the speed is 12 meters per second. Then the car stops and starts reversing towards
you. It is going at the same speed, but now the velocity is negative 12 meters per
second because the car is going in the opposite direction.
3. Pick 2 cities (minimum 500 miles apart) in the United States or world and
construct a data table and graph showing the amount of hours that it would take
to travel between the 2 cities with the following modes of transportation:
A. Fastest Runner (Velocity 10.58 m/s)
B. Model T Ford (Velocity 20.12 m/s)
C. Hindenburg (Velocity 37.55 m/s)
D. Tesla top speed (Velocity 69.44 m/s)
E. Fastest train (Velocity 97.22 m/s)
F. F35 Fighter Jet (Velocity 536.11 m/s)
G. Mobility scooter from Stop and Shop (Velocity 1.79 m/s)
*Provide a map showing your cities
*Show Detailed Math Steps
Cities to see: Port Louis, Tokyo
Distance between Port Louis and Tokyo: 6600.82618 miles or 10,623,000 meters
Fastest Runner:
T = D/V
T = 10623000 m / 10.58 m/s
T = 1004064.27221 s / 60 s
T = 16734.4045369 mins / 60 mins
T = 278.906742281 hours
Ford Model T:
T = D/V
T = 10623000 m / 20.12 m/s
T = 5 27982.107356 s / 60 s
T = 8798.80178927 mins / 60 mins
T = 146.6466965 hours
Hindenburg:
T = D/V
T = 10623000 m / 37.55 m/s
T = 282902.7963 s / 60 s
T = 4715.046605 mins / 60 mins
T = 78.58411008 hours
Tesla Top Speed:
T = D/V
T = 10623000 m / 69.44 m/s
T = 152980.9908 s / 60 s
T = 2549.68318 mins / 60 mins
T = 42.49471966 hours
Fastest Train:
T = D/V
T = 10623000 m / 97.22 m/s
T = 109267.6404 s / 60 s
T = 1821.12734 mins / 60 mins
T = 30.35212233 hours
F 35 Fighter Jet:
T = D/V
T = 10623000 m / 536.11 m/s
T = 19814.96335 s / 60 s
T = 330.2493891 mins / 60 mins
T = 5.504156485 hours
Stop and Shop Mobility Scooter:
T = D/V
T = 10623000 m / 1.79 m/s
T = 5934636.872 s / 60 s
T = 98910.61453 mins / 60 mins
T = 1648.510242 hours Time (hours)
Mode of Transportation
Fastest Runner 278.906742281 hours or 278 hours and
Model T Ford 54 minutes
Hindenburg 146.6466965 hours or 146 hours and 40
minutes
Tesla top speed
78.58411008 hours or 78 hours and 35
Fastest Train minutes
F 35 Fighter Jet 42.49471966 hours or 42 hours and 29
minutes
Stop and Shop Mobility Scooter
30.35212233 hours or 30 hours and 21
minutes
5.504156485 hours or 5 hours and 30
minutes
1648.510242 hours or 1648 hours and 31
minutes
4. What would you like to see in this city when you arrive? What tourist
attraction? What restaurant would you like to visit in this city? Provide pictures
What is the basic history of this city?
When I arrive in Port Louis I would like to go see my family first and then go to
the beaches. Then I would eat food made by my family and sleep in a hotel by the
beach. After that I would just walk around town, visit my aunt’s boutique, and go to the
beach with my cousins and catch minnows in the shallows. I would eat lots of street
food like dal puri and samosa and onion bhaji.
Port Louis was founded in the 17th century by Dutch mariners, who called their
town Noordt Wester Haven. However, in 1736, the French took it over and renamed the
town after King Louis XV. The French used the town as a port for all of their ships that
needed to go between Asia and Europe. The island was also used for sugar production
where slaves imported from Madagascar worked in the fields. During the Napoleonic
Wars, the British occupied the island. In 1968, Mauritius gained its independence from
the UK and Port Louis became the capital of Mauritius.
When I travel to Japan, I would like to see all the otaku shops in Tokyo and then
the Ninja Kyogoku Shinobi no Sato restaurant. I would also like to attend all the local
otaku conventions in Tokyo and surrounding districts. In the Harajuku district I would
like to go to the clothing and accessory stores and be involved with Japanese fashion.
After that, I would get ramune and crepes from the stands on the sides of streets. Then I
would go to the Sumire Dori shopping district and eat lunch at a small diner called
Yukihira. On the last day of my travels to Japan, I would just travel around Tokyo and
see the city.
Tokyo was originally a small fishing village called Edo. Later on, a man named
Tokugawa Ieyasu became shogun and began a peaceful era that lasted 250 years. In
1867, the last Tokugawa shogun was overthrown by a political movement catalyzed by
the arrival of American Commodore Matthew C. Perry in 1850. After the reign of the last
shogun was ended, Emperor Meiji left Kyoto and moved to Edo. He renamed the village
Tokyo which means “Eastern Capital” and Tokyo became the official capital of Japan. In
1923, there was a devastating earthquake in the Kanto region. During WW2, Japan was
bombed in Hiroshima and Nagasaki. There was an earthquake in Japan in 2011 which
did little damage itself but caused a tsunami, which in turn caused coolant failure at a
nuclear plant and caused a nuclear crisis near Tokyo.
5. Determine and graph an 18% increase in Velocity for each vehicle - Show how
the Times would be affected by the increase in speed. Show a double bar graph
with the 2 different times for each vehicle.
*Include pictures and brief description of each mode of transportation
Method of Transportation Original Time 18% Increased Time
Fastest Runner 278.906742281 hours 236.361646 hours or 236
hours and 22 minutes
Ford Model T 146.6466965 hours
124.29 hours or 129 hours
Hindenburg 78.58411008 hours and 17 minutes
Tesla Top Speed 42.49471966 hours
66.6 hours or 66 hours and
36 minutes
36.01 hours or 36 hours
and 1 minute
Fastest Train 30.35212233 hours 25.72 hours or 25 hours
and 43 minutes
F 35 Fighter Jet 5.504156485 hours
4.66 hours or 4 hours and
Mobility Scooter from 1648.510242 hours 40 minutes
Stop and Shop
1397.04 hours or 1397
hours and 2 minutes
Fastest Runner:
V = V x 1.18
V = 10.58 m/s x 1.18
V = 12.4844 m/s
T = D/V
T = 10623000 m / 12.4844 m/s
T = 850901.926 s
T = 850901.926 s / 3600 s
T = 236.361646 hours
Model T Ford:
V = V x 1.18
V = 20.12 m/s x 1.18
V = 23.7416 m/s
T = 10623000 m / 23.7416 m/s
T = 447442.4638609024 s
T = 447442.4638609024 s / 3600 s
T = 124.29
Hindenburg:
V = V x 1.18
V = 37.55 m/s x 1. 18
V = 44.309 m/s
T = 10623000 m / 44.309 m/s
T = 239748.13 s
T = 239748.13 s / 3600 s
T = 66.6
Tesla Top Speed:
V = V x 1.18
V = 69.44 m/s x 1.18
V = 81.94 m/s
T = 10623000 m / 81.94 m/s
T = 129643.64 s
T = 129643.64 s / 3600 s
T = 36.01 hours
Fastest Train:
V = V x 1.18
V = 97.22 m/s x 1.18
V = 114.7196 m/s
T = 10623000 m / 114.7196 m/s
T = 92599.7 s
T = 92599.7 s / 3600 s
T = 25.72 hours
F 35 Fighter Jet:
V = V x 1.18
V = 536.11 m/s x 1.18
V = 632.6098 m/s
T = 10623000 m / 632.6098 m/s
T = 16792.3418 s
T = 16792.3418 s / 3600 s
T = 4.66 hours
Stop and Shop Mobility Scooter:
V = V x 1.18
V = 1.79 m/s x 1.18
V = 2.1122 m/s
T = 10623000 m / 2.1122 m/s
T = 5029353.28 s
T = 5029353.28 s / 3600 s
T = 1397.04 hours
Usain Bolt (Fastest Runner)
Usain Bolt is a retired Jamaican sprinter. He holds the 100 metre and 200 metre world
records since fully automatic time became mandatory.
The Model T Ford
The Model T Ford was built by the Ford company from 1908 to 1927. It was praised as
practical affordable transportation for the common man and quickly became prized for
its low cost, durability, versatility, and ease of maintenance.
The Hindenburg
The Hindenburg was a German rigid passenger airship (zeppelin). It was the lead
airship in the Hindenburg class and the longest class of flying machine and largest ship
by envelope volume.
Tesla Roadster (Tesla Top Speed)
The Tesla Roadster is a car developed by Elon Musk’s company Tesla. It has a horse
power of 228 hp, a torque of 273-295 lb.-ft, a curb weight of 2,723 pounds, and a range
of 245 miles using the battery only.
Fuxing Train (Fastest Train)
The Fuxing Train is an electric multiple unit high speed train developed by the China
Railway Corporation and finished in 2014. The train is 209 metres or 686 feet long and
operates at a maximum speed of 350 km/h or 217 mph.
F 35 Fighter Jet
The F-35 Lightning II Fighter Jet was developed from the X-35 jet and designed to
replace most fighter jets with one common design to all branches of the military. It is a
fifth generation fighter jet, combining stealth with agility and speed. As of January 5,
2018, there are more than 265 of these jets made. The first flight of the F 35 jet was
December 15, 2006.
Mobility Scooter from Stop and Shop
A mobility scooter is a motorised equivalent of a wheelchair. It is also known as an
electric scooter or a power-operated vehicle/scooter.
6. Use a math calculation to show how long it would take the F35 Fighter Jet to
get to
A. Sun
T = D/V
T = 1.5 x 1011 m / 536.11 m/s
T = 2 79793326 s / 3600 s
T = 77720.3683333 hours / 24 hours
T = 3238.34868056 days / 365 days
T = 8.87 years
It takes the F 35 fighter jet almost 9 years, or 2.8 x 108 seconds to reach the Sun
from Earth.
B. Saturn
T = D/V
T = 1.2 x 1012 m / 536.11 m/s
T = 2 238346607.97 s / 3600 s
T = 621762.946659 hours / 24 hours
T = 25906.7894441 days / 365 days
T = 70.98 years
It takes the F 35 fighter jet almost 71 years, or 2.2 x 109 seconds to reach Saturn
from Earth.
C. Neptune
T = D/V
T = 4.3 x 1012 m / 536.11 m/s
T = 8 020742011.9 s / 3600 s
T = 2227983.89219 hours / 24 hours
T = 92832.6621748 days / 365 days
T = 254.34 years
It takes the F 35 fighter jet a little more than 254 years, or 8.2 x 109 seconds to
reach Neptune from Earth.
(Use scientific notation)
Velocity Story
Name: Eleanor Boyd Date: 2-12-18
Directions: Work in a group to tell a story of a classmate in motion. You must include 3 turns
(change in direction) and 3 different velocities. Your story must also have an amount of time
where the classmate does not move. What did the person do when they stopped? Where were
they going?
Data Table:
Example: Velocity = Distance/Time
V = 12 m/3 sec
V = 4 m/sec.
Description Distance (m) Time (sec.) Velocity (m/s)
Walking but dragging something 0.75 m/s
behind them 45 60
Crab walk 0.66 m/s
Taking a break 69 0 m/s
Skipping 0 300 2.133 m/s
Crawling 32 15 0.208 m/s
Sneaking around 25 120 0.016 m/s
1 60
Graph: (X-axis is Time; y axis is Distance)
Story:
Note: The story’s velocity follows Ciel with the exception of the first velocity mentioned.
It was an ordinary day at 15 year old Earl Ciel Phantomhive’s manor. He was doing
some paperwork when his butler Sebastian walked in, toting a cart bearing Ciel’s tea-time snack
at a velocity of 0.75 meters per second. “My lord,” Sebastian said, “We seem to have run out of
tea, but the Earl Grey is he-”
And the hallway behind Sebastian burst into flames.
Sebastian, being the special butler that he is, leapt out of the way and disappeared. Ciel
began coughing as his office filled with smoke, his eye not covered by the eye patch watering.
“Sebastian! Butler! Where are you?” He shouted. “Tch. That shoddy excuse of a butler never
does anything right.” Ciel muttered as he covered his face with his sleeve, trying to block out the
stinging smoke. Ciel crab walked out of his office, looking for a way to escape the burning
manor, but there was only one thin line clear of fire leading out of the manor. Luckily, Ciel could
still crab walk because they smoke hadn’t hurt his lungs too badly yet. So he turned to the side
and crab walked the 45 meters in a minute out of his manor while the only home he had ever
known crashed and burned behind him.
As Ciel beheld the tragedy that used to be his house, a tear streamed down his face.
Everything, including his fortune and the case files he had been working on for the Queen, was
lost to the raging flames in front of him. Ciel collapsed to the ground as he despaired, letting his
tears water the ground that used to belong to his ancestors. Obviously someone had figured out
he was the Queen’s Watchdog, patrolling and maintaining London’s underground Black Market,
and decided to take action. Normally Ciel was quite a level-headed person with a calm
countenance and a mien belonging to that of a statue, seeing as how he had to be in his line of
work, but his last home burning in front of him was too much for the young boy.
“Young lord!” Sebastian shouted, for he had just appeared near the earl, “Young lord, are you
uninjured?” Ciel waved the black haired man away as he sat looking at his manor. “I am quite
alright, Sebastian. Just a bit singed.” He lay in the grass and was just about to close his eyes
when he felt a gentle tap on his shoulder. Sitting up suddenly, he whirled around to face the
person behind him, pulling his sleek metal tool from his pocket as he did so.
“I will defeat you!” he shouted. “You burned down everything I have ever known! You
will-” He stopped himself mid-sentence. “What?” he muttered. He cocked his head, staring at the
strange creature that stood before him. Sebastian, now standing behind Ciel, did the same as
he slowly reached into his tailcoat pocket to get his silverware.
“I am Grell, the hamster crime lord of China. I also happen to work for the Reaper
Society. But I guess you knew that, considering that I am the one you were investigating,” Grell
the hamster said in a high-pitched, sly voice. Ciel’s eyes widened as he recognised what the
hamster was saying was true.
“You,” he said in disbelief and growing rage. “You are the one who burned my house
down! How dare y-”
Grell clicked his tongue as he interrupted the boy sitting in front of him. “I am not the one who
destroyed your house. But,” the hamster said as Ciel opened his mouth to say something,
“I know the person who burned down your mansion and it just so happens I am after him too.”
Ciel stood up after the five minutes he had spent on the ground, fists clenched. “Why?” asked
Ciel hotly. “Why are you after him and why should I work with you when I know you are a
convicted criminal?”
“Why I am after him is none of your concern, little earl. I also know where he is. Or rather, I
know where he will be and where to find him. So. Are you coming with me or not, young lord?”
Ciel hesitated. He looked to Sebastian. “Sebastian?” he asked.
The butler just looked at him and shrugged with an awkward half-smile on his face.
“Fine then,” Ciel said. “I will work with you for the time being. Though,” Ciel smirked, letting his
ebony bangs fall over his good eye, “I suppose I don’t have to tell you that you are the one who
will suffer the consequences if you decide to trick me in any way.”
Grell smiled. “Of course not, little earl. Shall we continue on our way then?”
“But of course. After you. Oh, and Grell,” Ciel said. “How did you get here so fast?”
Grell shrugged with a hamstery half smile. “I rode my chainsaw.”
Ciel looked at the hamster again, noticing the lump that stood up underneath his black cloak on
his back. “Well ok then.”
Ciel turned back to the burning manor behind him, sadness softening his sapphire blue eye for a
moment before he turned to Sebastian.
“Sebastian!”
“What is it, young master?”
“This is an order: Put out the fire and save the manor!”
Sebastian smiled as he knelt on the manicured lawn, raising his right hand to his heart as he did
so.
“Yes, my lord.”
And Sebastian disappeared.
Ciel turned back to Grell the hamster. “I have set traps around the lawn so things like
this,” he gestured to the now smoking ruins of the house behind him, “don’t happen. We need to
be careful, so I suggest we skip, then crawl, then finally sneak around the brick columns holding
up the gate. Understand? I hope you do, because you are going first.”
Grell smiled, his twitching eyebrows belaying his annoyance. “Of course, little earl.” And Grell
began skipping towards the gates in the distance, which looked like it was a challenge to Ciel
because he had such short legs. Oh well. I suppose it can’t be helped, Ciel thought. He began
skipping after the hamster (which was about 32 meters in 15 seconds or a velocity of 2.13
meters per second) until he reached the tulip patch which his clumsy gardener Finnian had
planted. “Stop!” Ciel said. “This is where we crawl. There is another trap here that requires us to
do so.”
“Well then, little earl,” Grell said. “On our knees.”
“On our knees indeed, Grell.”
So as the pair crawled along the grass, they made the 25 meters to the gate in about 2 minutes,
which was a velocity of about 0.208 meters per second. There they stood up again, where they
found Sebastian balanced on the apex of the gates. “Sebastian!” Ciel said. “Get down from
those gates and stop being ridiculous.” Sebastian merely chuckled and raised his right hand to
his heart as he lightly jumped down from the 20 foot gates. “Of course, my lord. I should have
thought that it would be inappropriate for a butler to stand higher than his master.”
“Quite so, Sebastian.” Ciel remarked, a bit miffed. “Open the gates now. We need to go around
these brick pillars.”
“Yes, my lord.” And Sebastian opened the gates, which folded outward soundlessly. “Ok,” Ciel
said. “Now we need to press our backs up against these pillars and move carefully around them
so we can get outside.”
“I know, little earl. I am, in fact, the crime lord of China. I should think I would know how to
sneak.” Ciel ignored Grell as they backed themselves up against the pillars and moved carefully
around them at a velocity of about 0.016 meters per second. Sebastian, who stood behind them
until they had moved beyond the gates, now jumped up and quite literally launched himself
between the gates, moving so quickly the traps didn’t have time to activate. The gates shut with
a clang behind the trio once Sebastian had passed through. “So,” Ciel said to Grell, “Who is the
man who burned down my manor?” Grell chuckled. “You haven’t figured it out already? I believe
you know them, little earl. His name is Levi Ackerman, ruler of the underground, with his
henchmen Farlan Church and Isabel Magnolia.” Ciel gasped, then clenched his teeth. “I thought
I put them in jail!” Ciel said angrily. “You did, but then they escaped. I guess even the stone
walls of the Queen couldn’t hold him,” the hamster remarked with a smirk. “Shall we get going,
little earl? I don’t believe Levi Ackerman is going to catch himself.”
Ciel sighed and fingered the sapphire ring on his thumb.
“Let’s go.”
GPE/KE
QUIZ REVIEW2: GPE/KE
Scenario: You are an engineer for a major engineering firm that will design the lift motor and
safety restraints for the next roller coaster on the planet Hoth in Star Wars. Hoth has a gravity
equal to 37% greater than Earth’s. The Star Wars Theme Park needs to provide you with the
velocity of the roller coaster on this planet to help you with your design. Your roller coaster will
be called the Millenium Falcon and will have a height of 125 m. Your roller coaster “The
Falcon” will have a mass of 7000 kg. You will need to compare the needs for safety on Earth to
the needs on Hoth. Explain your reasoning for the changes on Hoth.
Hoth:
Directions: Provide a data table showing the comparisons between the Millenium Falcon Roller
Coaster on Earth and Hoth. Describe the types of restraints that you would need on the faster
coaster.
Calculations: Hoth
Earth 9.807 m/s2 x 1.37 = 13.43559
GPE = mgh GPE = mgh
GPE = 7000 kg x 125 m x 9.807 GPE = 7000 kg x 125 m x 13.43559
GPE = 8581125 joules GPE = 11756141 joules
GPE = KE GPE = KE
KE = 0.5 mv2 KE = 0.5 mv2
8581125 joules = 0.5(7000 kg)v2 11756141 joules = 0.5(7000 kg)v2
8581125 joules = 3500v2 11756141 joules = 3500v2
8581125/3500 = 3500/3500 v2 11756141/3500 = 3500/3500 v2
2451.75 joules = v2 3358.8975 joules = v2
√2451.75 = √v2 √3358.8975 = √v2
V ≈ 49.521 m/s V ≈ 57.96 m/s
Data Table: Earth Hoth
Planet 49.521 57.96
Velocity
Graph:
Conclusion:
The purpose of this experiment was to find out on which planet the roller coaster would
be more exciting on, or in other words, on which planet the Falcon had a higher velocity.
My hypothesis was that the roller coaster on Hoth would have a greater velocity because
the gravity is stronger there, and because gravity is part of one of the equations needed
for finding velocity, I can hypothesise that the stronger the gravity, the higher the
velocity. In other words, there is a positive linear correlation between the gravity of the
planet and the velocity of the roller coaster. My hypothesis was proven correct when I
looked at the data. The variables used in this experiment are gravity (or the planet) and
velocity. The planet and its corresponding gravity are the independent variable and the
velocity is the dependent variable. This is because as I said before, gravity is part of one
of the equations needed for finding velocity, so if you change the gravity, the velocity will
change as well. The conclusion gathered from this experiment is that the Millenium
Falcon roller coaster will be more exciting (have a higher velocity) on Hoth because of its
stronger gravity. The equations I used for finding this out are the equations for GPE (GPE
= mass(height)(gravity)) and the equation for finding velocity, which include using the
number of joules found in the GPE equation and setting that equal to
0.5(mass)(velocity2), and I isolated the v2 variable and found the square root of it, and that
is how I found the velocity for each roller coaster on the different planets. As you can
see, GPE is needed to find velocity, so if I change the GPE the velocity will change as
well. This also means that if I change the gravity used in the GPE equation, the velocity
will end up different. For finding the velocity of the MIllenium Falcon roller coaster on
Earth, I used the value 9.807 m/s2 which gave me a GPE of 49.521 joules. When I found
the velocity of the Millenium Falcon roller coaster on Hoth, I used the value of 13.43559
m/s2 for the gravity because Hoth’s gravity is 37% stronger than the gravity on Earth. To
find this number, I multiplied Earth’s gravity (9.807 m/s2) by 1.37 to get Hoth’s gravity of
13.43559 m/s2. The velocity of the roller coasters on each planet are 49.521 m/s on Earth
and 57.96 m/s on Hoth. As you can see, the velocity of the Millenium Falcon on Hoth is
greater than the velocity on Earth by 8.439 m/s and will therefore make a better and more
exciting ride on Hoth than on Earth. To briefly sum up, the purpose of this experiment
was to find out on which planet the Millenium Falcon roller coaster was more exciting on,
the variable used in this experiment are the planets (independent variable) and velocity
(dependent variable), and the velocity of the roller coaster on Hoth is greater than on
Earth because of the stronger gravity on Hoth.
Extra Problems:
1. The Millenium Falcon Roller Coaster has a mass of 3200 kg on Planet Tatooine.
The height of the roller coaster is 15 m which results in a Potential Energy of
800,000 J. What is the gravity on Planet Tatooine? The gravity on the planet
Tatooine is 16.67 m/s2.
GPE = mgh
800000 joules = 3200 kg x (g) x 15 m
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