Dylan Bettencourt Portfolio

Science Portfolio 2018

Dylan Bettencourt

Isotopes



How Old Are The Fossils

Fossil E - Many legs, looks like it has a shell.
Graph # 1
Fossil E - Isotope A - 12% = 6900 years old
Fossil E - Isotope B - 93% = 1550 years old
Graph # 2
Fossil E - Isotope A - 12% = 4500 years old
Fossil E - Isotope B - 93% = 750 years old

Fossil B - Looks like a dragonfly
Graph # 1
Fossil B - Isotope A - 82% = 2000 years old
Fossil B - Isotope B - 39% = 4400 years old
Graph # 2
Fossil B - Isotope A - 82% = 1300 years old
Fossil B - Isotope B - 39% = 2250 years old

Fossil D - Looks like an amphibious animal with a long neck
Graph # 1
Fossil D - Isotope A - 15% = 6700 years old
Fossil D - Isotope B - 81% = 2100 years old
Graph # 2
Fossil D - Isotope A - 15% = 4300 years old
Fossil D - Isotope B - 81% = 1300 years old

Activity:​ Determine which fossil is older

Directions: Watch videos, take notes and construct the graphs
below using your spreadsheet.
Film:

https://www.bing.com/videos/search?q=radiometric+dating&&vi
ew=detail&mid=0913F60FB719BC5912690913F60FB719BC591269&&FO
RM=VDRVRV
Film #2:
https://www.bing.com/videos/search?q=radiometric+dating&&vi
ew=detail&mid=33AAFAE1F005C0E7E25833AAFAE1F005C0E7E258&&F
ORM=VDRVRV

Take notes:

Isotope #1 100
0 50
25
2300 12.5
4600 6.25
6900 3.125
9200 1.06
11,500 .5
13,800 .25
16,100 .125
18,400 0
20,700
23,000

Isotope #2 100
0 50
25
1500 12.5
3000 6.25
4500 3.125
6000 1.06
7500 .5
9000
10,500

12,000 .25
13,500 .125
15,000
0

Graphs:

Write an Essay that explains which fossil is older: (use your
graphs)
Fossil A
18% of Fusarus remaining
5300

Fossil B
35% of Montanosaurus remaining
2500

Quiz Review Isotope Aging

Isotope - Radiometric Dating

Directions:​ Use the following Isotopes and decay rates to
determine the age of the fossils in the room.

Isotope #1 Isotope #2

% %

Remainin Years Remainin

Years g (millions) g

0 100 0 100

2800 50 3.2 50

8,000 25 6.4 25

8400 12.5 9.6 12.5

11,200 6.25 14 6.25

14,600 3.125 16 3.125

20,000 1.56 20 1.56

20,200 0.78 22.4 0.78

23,000 0.39 25.6 0.39

26,000 0.19 29 0.19

28,600 0.095 32 0.095

30,000 0 35 0

Questions:

1. How old is Fossil 1 =
each fossil if 7,800
there is 29% Fossil 2 =
remaining? 4.5 Million

Fossil 1 =
2. How old is 6,000
each fossil if Fossil 2 =
there is 46%? 6 Million

3. How much

of Isotope #1

is remaining

if the fossil is

8000 years

old? 25%

4. How much

of

Cabrerianite

is remaining

if the fossil is

11,000 years

old? 6%

5. How old is

each fossil if

there is 23% Fossil 1 =

remaining of 8,200

both Fossil 2 =

isotopes? 6.8 Million

% Isotope #2
remainin Isotope
g #1

Fossil A 32% 5.4 Million
Fossil B remainin
Fossil C g 7,600
Fossil D
Fossil E 18%
Fossil F remainin
g 8,300

75%
remainin
g

65%
remainin
g

20%
remainin
g

42%
remainin
g

Average Atomic Mass Practice Problems

1. Calculate the atomic mass of lead. The four lead isotopes have
atomic masses and relative abundances of 203.973 amu (1.4%),
205.974 amu (24.1%), 206.976 amu (22.1%) and 207.977 amu
(52.4%).
How many neutrons would each isotope have in its nucleus?

2. Calculate the average atomic mass of sulfur if 95.00% of all sulfur
atoms have a mass of 31.972 amu, 0.76% has a mass of
32.971amu and 4.22% have a mass of 33.967amu.

How many neutrons would each isotope have in its nucleus?

Quiz: Isotopes

QUIZ:​ Isotopes
Name: Dylan Bettencourt
Date:
Directions​ construct a graph that will help you determine the age
of fossils.

I​ sotope A Percent
Years Isotope

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

4,900 years old
2. How old is the following fossil?
Fossil B - 15% of Isotope A remaining

16,200 years old
3. What percentage of Isotope A is remaining if the fossil is 1200
years old?
(Use your graph)
24%

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.

(34.969 x .7553) + (36.966 x .2447) = 35.457 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%).

(27.9769 x .922297) + (28.9765 x .046832) + (29.9738 x .030872) = 28.085
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!)

To determine the number of neutrons in each chlorine isotope,
you must first know the atomic mass, in this case, 35. You then
subtract the number of protons (which is also the atomic number)
from it. The number of neutrons is the answer you get after that.
So for the element chlorine 35, the equation would be 35 - 17 = 18.
For chlorine 37, 37 - 17 = 20. However, if you get the atomic mass
wrong, this would be hard to do. Instead of calculating just the
atomic masses of the different isotopes, you must also take into
account the percent abundance of each isotope something like
silicon that has three isotopes would normally be affected greatly
by a big number, but if it is only 3% of all silicon isotopes, it won't
make that much of a difference. In the M&M lab, we had to count
the neutrons in the nucleus of the M&M “isotope”, which could
change based on the amount of pretzel M&M’s inside

Velocity



Velocity: Tell a story using velocity

Velocity Story

Name: Dylan Bettencourt 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 Time (sec.) Velocity
(m) 11.48 (m/s)
11.83 .29
Walking from table to 3.5 2.88 .53
back counter. 8.51 2.08
12 1.12
Walking from back 6.25 34.5 8.33
counter to teachers desk. .46

Walking from teachers 6
desk to pencil sharpener.

Pencil sharpener to locker 9.49
949.

Locker 949 to bathroom 10
door.

Bathroom door back to 16

desk.
Graph:​ (X-axis is Time; y axis is Distance)

Story:
Charlie left his pencil on the back counter so he got up to get it he
walked at a velocity of .29 m/s. When he got there, he noticed that
it was missing, so he went up to Mr. Lopez as a pace of .53 m/s and
asked to go to his locker. Walking at a pace of 2.08 m/s, he walked
to the pencil sharpener, talked to Emily, than went to his locker
moving at 1.12 m/s. He got a pencil, than went to the bathroom at
8.33 m/s, turned around and went back to his desk at .46 m/s.

Velocity Project

Velocity Project 2018
Due: Wednesday night February 21,2018

1. Define the following terms and include pictures if possible:

Motion - Speed - Position -

Distance - Acceleration - Terminal Velocity -

Time - Initial Velocity - Displacement -

Velocity - Final Velocity - Key Metric units -

2. What is the difference between Speed and Velocity? Explain
using an example in your own words.
3. Hartford -> Rio De Janeiro (7802 kilometers apart) 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 - 45 km/h
T = D/V
T = 7802 km/45 km/hr
T = 173.38 hours

B. Model T Ford - 72 km/h
T = D/V
T = 7802 km/72 km/h
T = 108.36 hours

C. Hindenburg - 135 km/h
T = D/V
T = 7802 km/135 km/h
T = 57.79 hours

D. Tesla top speed - 249 km/h
T = D/V
T = 7802 km/249 km/h
T = 31.11 hours

E. Fastest train - 603 km/h
T = D/V
T = 7802 km/ 603 km/h
T = 12.94 hours

F. F35 Fighter Jet - ​1,930 km/h
T = D/V
T = 7802 km/1,930 km/h
T = 4.04 hours

G. Samson Switchblade Flying Car - 322 km/h
T = D/V
T = 7802 km/ 322 km/h
T = 24.23 hours

4. What would 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?
I would like to see the statue Cristo Redentor (Christ the
Redeemer). I would love to see a game of soccer, or as it is called in
the rest of the world, futbol. I would love to eat at M​ arius
Degustare.​ It is a restaurant with some Portuguese style food and
some interesting seafood. The city was founded March 1, 1565 by
the Portuguese. Brazil became independent in 1822.

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

A. Fastest Runner:

T = D/(V x 1.18)
T = 7802 km/(45 x 1.18)
T = 7802 km/53.1 km/h
T = 146.93032 hours

B. Model T Ford: 72 k/m x 1.18 = 84.96
T = D/(V x 1.18)
T = 7802 km/(72 x 1.18) km/h
T = 7802 km/84.96 km/h
T = 91.8314501 hours

C. Hindenburg - 135 km/h x 1.18
T = D/(V x 1.18)
T = 7802 km/159 km/h
T = 49.07 hours

D. Tesla top speed - 249 km/h x 1.18
T = D/(V x 1.18)
T = 7802/(249 x 1.18)
T = 7802 km/293.82 km/h
T = 26.5536723 hours

E. Fastest train - 603 km/h
T = D/(V x 1.18)
T = 7802 km/ (603 x 1.18) km/h
T = 7802 km/711.54km/h
T = 10.9649493 hours

F. F35 Fighter Jet - ​1,930 km/h
T = D/(V x 1.18)
T = 7802 km/(1,930 x 1.18) km/h
T = 7802 km/​2277.4 km/h
T = ​3.42583648 hours

Use a math calculation to show
A. Sun - Distance from Earth to Sun = 149.6 million
149600000 kilometers = ​1.496 × 10​8​ g

B. Saturn - Distance from Earth to Saturn = 1​ ,200,000,000​ km
Scientific Notation: 1​ ,200,000,000 = 1.2 × 10​9

T = D/V
T = 1.2​ ​x 10​9​ /1,930
T = 621,761.66 hours

C. Neptune - Distance from earth to neptune - 4.3 billion
kilometers
4,300,000,000 = 4.30 x 109​
Scientific notation: 4.30 x 10

T = D/V
T=

Unit 1: Uniform Motion Name: ​Dylan Dowcett Bettencourt
Worksheet 8 Date: ​2/15/2018​ Period: ​Science 3

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 = 100m/4s
V = 25 m/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=VxT
D = 60 km/hr x 4 hrs

D = 240 km
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 = 200/25
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 × 10​8​ m/s. How far is light
year (the d​ istance​ light travels in a year)? Answer: 9.50 × 10​15
m.
D = 3 x 108​ ​ x 60
D = ​1.8 x 10​9 x​ 60
D = 1.08 x 101​ 0 x​ 24
D = 2.592 x 108​ ​ x 365
D = 9.50 x 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.
V = D/T
V = 406/7
V = 58 km/hr
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 × 10​8​ m/s. In kilometers, how far is the
earth from the sun? Answer: 1.5 × 10​8​ 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?

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?

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?

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?

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?
b. mi/hr?

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?
b. mi/hr?

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?
b. Draw a distance vs. time graph of the situation.
(Assume constant speeds for each hallway.)

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?
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?
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?
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?

QUIZ: Motion
Name:​ ________________________
Date:​ ___________
Formulas:

A= v2 −v1 V2 = V1 + (a * T) T= V2−V1
T2 a

1. After traveling for 14.0 seconds, a bicyclist reaches a speed of 89
m/s. What is the runner’s acceleration?

A = v2 −v1
T2

A = 89 m/s − 0 m/s
14

A = 6.357 m/s

2. A car starting from rest accelerates at a rate of 18.0 m/s/s.
What is its final speed at the end of 5.0 seconds?

V2 = V1 + (a * T)
V2 = 0 m/s + (18 m/s/s x 5.0 Sec)
V2 = 90 m/s/s

3. A cyclist accelerates at a rate of 16.0 m/s2. How long will it take
the cyclist to reach a speed of 49 m/s?

T= V2−V1
a

T= 49 m/s − 0 m/s
16 m/s/s

T = 3.063 Sec

3. 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 4.6 seconds after the laser
pulse was sent. The speed of light is 3.0 × 10​8​ m/s. What was the
distance between the astronomers and the moon?

D=V*T

D = 3.0 x 108​ ​ m/s * 4.6 sec

D = ​1380000000 m

D = ​1.38 × 109​ m​

Directions:​ Choose 4 or 5
4. 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 65.0 m, at a speed of 5.2 m/s. The second hallway
is filled with students, and she covers its 32.0 m length at an
average speed of 1.46 m/s. The final hallway is empty, and
Suzette sprints its 60.0 m length at a speed of 7.3 m/s.

a. Does Suzette make it to class on time or does she get
detention for being late again?

5. 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 0.35 m/s while the rabbit runs the first 200.0 m at 1.85
m/s The rabbit then stops to take a nap for 1.200 hr and
awakens to finish the last 800.0 m with an average speed of 4.2
m/s. Who wins the race and by how much time?

Tortoise
T = D/V
T = 1000 m/ 0.35 m/s
T = 2857.14286 Seconds

Hare
T1 = D/V
T1 = 200 m/ 1.85 m/s
T1 = 108.108108 Seconds
T2 = 4320 Seconds
T3 = D/V
T3 = 800 m/ 4.2 m/s
T3 = 190.47619 Seconds
Overall Time = 108.108108 + 4320 + 190.47619 = 4618.5843 Seconds

The Tortoise won the race by 1,761.44144 seconds
6. What is the Acceleration of the Car on the Ramp? Determine the

Angle of the Ramp (A).

50 m/100 m = 30%

100 m/100 m = 90%

Angle Chart:
https://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSD
NSMXc

Which Angle had the greatest Acceleration? Write a Conclusion
based on your findings. Create a Graph if you have time.

Height
of Ramp

(Opposit Time Velocit Dist. Velocit Acceleratio
e) Dist. 1 1 y 1 2 Time 2 y 2
n

10 20 10 m/s
50 m 100 m sec. 10/ms 100 m 5 sec. m/s

100 m 5 20 50 30 m/s
Graph: 100 m sec. m/s 100 m 2 sec. m/s

Conclusion:

The 90% angle had the greatest acceleration traveling 100 m in 5
sec, and then the second 100 m in 2 seconds, generating an
acceleration of 30 m/s. The 30% angle did the first 100 m in 10
seconds and the second 100 m in 5 seconds, getting an
acceleration of 10 m/s.

EXTRA CREDIT:

Light from the​ another star in the galaxy reaches the earth in 46
minutes. The speed of light is 3.0 × 10​8​ m/s. In k​ ilometers​, ​how far
is the earth from the star?
Answer must be in scientific notation







Energy



Potential Energy Project
Due: Friday 3/17

Define and make note cards or QUIZLET for the following words:

Energy Joules Chemical Law of
Potential Conservation
Energy of Energy

Kinetic Energy Kilojoules Elastic Gravity
Potential
Energy

Potential Gravitational Mechanical
Energy Potential Energy
Energy

Resource:

http://www.physicsclassroom.com/class/energy/Lesson-1/Po

tential-Energy

Gravitational Potential Energy

Determine the Gravitational Potential Energy (GPE) of 3 different

masses (g) at 3 different ​heights.
3 objects: Y​ ou, African Elephant, Chevy Camaro (research the

masses)

*2.2 lbs = 1 kg

Data Table:

Your data table will need: Object, mass, gravity, height, GPE

Videos: ​http://www.youtube.com/watch?v=x5JeLiSBqQY

*Video shows you how to use the GPE equation.

Determine the GPE of one of the masses on the following planets:
Saturn - 10.44 m/s​2
Pluto - 0.62 m/s2​

Ceres - 0.27 m/s2​

*Use the height of your favorite Roller Coaster. You will use this to
figure out the Velocity at the bottom of the hill on the planets.

Diamondback, Kings Island, Ohio
● Drop - 70 m
● Weight of Train - 735 kg
● Gravity - (Depends on planet)

GPE on planets with full train

Saturn GPE - 537,138 Joules
Pluto GPE - 31,899 Joules
Ceres GPE - 13,891.5 Joules

SAMPLE
GPE = KE
M x G x H = .5mv​2
10 kg x 12 m/s x 39 m = .5 x 10kg x v​2
4680/.5 = 5/.5v2​
Square root of 936 = Square root of v2​
30.6 m/s = V

GPE = KE
735 kg x 0.27 m/s​2​ x 70 m = .5 x 735 kg x v2​
13,891.5 = 5/.5v​2
Square root of 2,778.3 = Square root of v2​

52.7095816716​ m/s = V

Data Table:

Saturn

Object mass (kg) gravity ? H1 = your GPE
Dylan 43 kg 10.44 m/s coaster
Bettencour
70 m 31,424
t Joules

Pluto mass (kg) gravity H1 = your GPE
1,865 kg 0.62 m/s coaster 80,941
Object Joules
Chevy 70 m
Camaro

Ceres

Object mass (kg) gravity H1 = your GPE
African 6,350 kg 0.27 m/s coaster 120,015
Elephant Joules
70 m

Use the formula: GPE = mass * acceleration due to gravity
(Earth is 9.8 m/s2) * height of object

Graph:

X - axis: Planet
Y -axis: Potential Energy

Critical Thinking Questions:
1. What factors affect Gravitational Potential Energy?
2. Why did the GPE change on the other planets?
3. Which planet would you be able to hit a golf ball further?
Explain using data.
4. How does GPE relate to Chemical Potential Energy?
5. How do Energy companies use GPE to generate Electrical
Energy? Give an example
6. What happens to the GPE when the object falls to the
ground? Describe the Energy transformations along the
way. Use a diagram.

Worksheet 1:
http://glencoe.mheducation.com/sites/0078600510/student_vie
w0/unit1/chapter4/math_practice_2.html
Worksheet 2:
http://go.hrw.com/resources/go_sc/ssp/HK1MSW65.PDF

*We will use our information to see how a roller coaster would be
different on those planets.

FINAL PART - Roller Coaster Physics
Objective:

1. When energy is transformed, the total amount of energy
stays constant (is conserved).

2. Work is done to lift an object, giving it gravitational potential
energy (weight x height). The gravitational potential energy
of an object moving down a hill is transformed into kinetic
energy as it moves, reaching maximum kinetic energy at the
bottom of the hill.

Determine the velocity of a full roller coaster of riders at the
bottom of the largest hill. You can use the following roller
coasters:
Watch these Videos for help:
http://www.youtube.com/watch?v=Je8nT93dxGg
http://www.youtube.com/watch?v=iYEWIuQBVyg

Use either:
GPE​top​ = KE​bottom

QUIZ:​ 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: Earth Hoth
G = 9.8 m/s2​
G = 9.8 x 1.37

GPE = mgh G = 13.426 m/s2​
GPE = GPE = mgh
KE = 0.5mV2​ GPE = 7000 x 13.426 x 125
8,575,000 = 0.5(7,000) V​2 KE = 0.5mV​2
8,575,000 = 3,500 V2​ 11,747,750 = 0.5(7,000) V2​
2,450 = V2​ 11,747,750 = 3,500 V2​
49.4974747 = V 3,356.5 = V2​
57.9353088 = V
Data Table:
Planet Velocity
Earth 49.4974747 m/s
Hoth 57.9353088 m/s

Graph:

Conclusion:
We would need stronger magnets and support beams to compensate for the addition
velocity gained by moving to a planet with stronger gravity. We would also need to have
a more powerful motor to pull the coaster up to the top of the hill as there will be more
gravity trying to pull us back. We will also need stronger restraining bars to compensate
for the additional weight of the people that are riding. As the dependent variable is the
velocity, we need to remember that by changing the gravity, we must be cautious about
the velocity. My hypothesis is that if we went to a planet that the gravity exceeds 20 m/s​2​,
then it would become unsafe, but also that by raising the gravity, the velocity will also go
up on a downhill slope, but​ loose v​elocity on an uphill slope.

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?

GPE = mgh
800,000 = (3,200)(g)(15)
800,000 = 48,000 g
16.6666667 = g

GPE = mgh
800,000 = (m)(16.6666667)(15)
800,000 = 250 m
3,200 = m

2. The Tie Fighter Roller Coaster has a height of 150 m. on Planet Hoth. Hoth has a
gravity of 5.2 m/s​2.​ This roller coaster has a Potential Energy of 600,000 J. What is the
mass of the Tie Fighter?

GPE = mgh
600,000 = (m)(5.2)(150)
600,000 = 780 m
769.230769 = m

GPE = mgh
600,000 = (769.230769)(g)(150)
600,000 = 115,384.615 g
5.2 = g

Scenario: S​ uppose you would like to bring a 175 N box up to a height of 29 m. You decide to
use an inclined plane because you just learned about them in science class. The ramp you
design has a distance of 48 m. You also measure the Force (N) needed to push the box up the
ramp which is 85 N. What is the Work Output, Work Input, Ideal Mechanical Advantage, Actual
Mechanical Advantage, and Efficiency of the machine?

A. Use “Drawing” to label a triangle (Inclined Plane)

B. Calculate the angle of the ramp.
38o​

C. Calculate the Ideal Mechanical Advantage (IMA)
1.651

D. Calculate the Actual Mechanical Advantage (AMA)
2.04

E. Calculate the Efficiency (%)
124

Questions:
1. Is this machine possible? Explain using evidence from the problem.
2. How could you change the Input Force or Distance or to make it possible?
3. How would this problem be different on another planet?

QUIZ: Inclined Plane 
QUIZ: ​Wednesday and Thursday 

 
Directions: ​Analyze the Inclined Plane Data Table that is shared on Classroom and 
determine which machine has the greatest Actual Mechanical Advantage (AMA). 
Problem Statement: 

How does the angle of an inclined plane affect the Mechanical Advantage? Is 
there a machine that is impossible? Explain using data. 

 
Hypothesis: ​(Use proper form!) 

If the angle of an inclined plane decreases, then the distance of the inclined plane will increase. 
Additionally, if the input work decreases, the efficiency will increase as well. If the AMA is greater 
than the IMA, than the machine is impossible. 

 
Diagrams of Inclined Planes:​(Use DRAWING - Label Diagrams) 

Possible Machine  Impossible Machine 

   

Angle Chart: h​ttps://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSDNSMXc 

 
Calculations (​Examples): 

IMA = Din/Dout  AMA = Fout/Fin  Efficiency = Wout/Win * 100 
IMA = 300/70  AMA = 12/4  Eff = 840/1,200 x 100 
IMA = 4.29  AMA = 3  Eff = 70 

IMA = Din/Dout  AMA = Fout/Fin  Efficiency = Wout/Win * 100 
IMA = 100/70  AMA = 12/8  Eff = 840/800 x 100 
IMA = 1.43  AMA = 1.5  Eff = 105 

Data Table: (​Located on Google Classroom) 
 
 

Trial  Output Force  Output Dist.  Output  Input  Input  Input  IMA  Efficien
(N)  (m)  Work (J)  Force  Dist.  Work  AMA  cy 

Angle =  12  70  840  4  300  1,200  4.29  3  70 
13 

Angle =  12  70  840  6  200  1,200  2.89  2  70 
20  105 

Angle =  12  70  840  8  100  800  1.43  1.5 
44 

 

 

Graph:​(​Angle and Mechanical Advantage)*Make sure you have Titles! 

*Only graph the Angle and Mechanical Advantage 

 

 

 

 

Conclusion: 

The goal of this experiment was to find the AMA, IMA, and Efficiency of an inclined 
plane, as well as deciding whether or not it was a possible or impossible machine. If the 
angle of the inclined plane decreases, the distance of the inclined plane will increase. 
Additionally, if the AMA is greater than the IMA, then the machine is impossible. The 
reason that a machine is impossible if the AMA is greater than the IMA is because the 
Ideal Mechanical Advantage (IMA) is the highest achievable mechanical advantage, so if 
the Actual Mechanical Advantage (AMA) is greater than the IMA, it is an impossible 
machine. For example if the IMA was 4.5 and the AMA was 2, the Efficiency would be 

over 100, making it an impossible machine. Efficiency is calculated by the work output/ 
work input * 100, so if the work input is smaller then the work output, the efficiency 
will be over 100. For example, on the data table, when the work output was 840 Joules 
and the work input was 1,200 Joules, the efficiency was 70, but when the work input 
was 800 Joules, which is below 840, the efficiency came out to 105. A machine is 
impossible when more kinetic energy is produced then what was stored as potential 
energy (nyu.edu). Newton's First Law Of Motion says that an object at rest stays at rest 
and an object in motion stays in motion unless acted upon by an unbalanced forces 
(physicsclassroom.com). This means that it will be easier to use an inclined plane to lift 
an object because it is in motion. If you were to try to lift something straight up, it is at 
rest, and will seem heavier. 
 
Option #1 Write a Conclusion. 

***Your conclusion must also address which machine would be impossible and why? 

1. Discuss purpose 
2. Restate hypothesis - angle and mechanical advantage 
3. Data to support hypothesis 
4. Is there a machine that is impossible? Explain using research on the Law of 

Conservation of Energy (Support with research - Use Explore Tool research - 
INLINE CITATIONS )1 
5. Use this source to explain the relationship of this machine to Newton’s First 
Law of Motion. 
 

Lab Rubric - Data Analysis Sections 
 

  1  2  3  4 

Data/  ____Data is poorly  ____Data is  ____Data is  ___Data is clearly 
represented in a table  represented in the  and accurately 
Observations   organized or missing  or graph, but it is  table or graph with  represented in a table 
incomplete or there  minor errors. More  or graph. 
altogether.  are major errors.  complete discussion  Observations include 
Some discussion of  of observations.  discussion of both 
No mention of observations  observations  qualitative and 
quantitative 
observations. 

Conclusion/  ____No conclusion is  ____Somewhat  ____Adequately  ____Clearly explains 

1 "Introduction to mechanical advantage (video) | Khan Academy."
https://www.khanacademy.org/science/physics/work-and-energy/mechanical-advantage/v/introduction-to-
mechanical-advantage.​ Accessed 9 Apr. 2018.