6. A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s2. If the cart has a
beginning speed of 2.0 m/s, what is its final speed?
7. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of
this helicopter?
a= 6 0 m/s - 25 m/s
5
8. As she climbs a hill, a cyclist slows down from 25 mi/hr to 6 mi/hr in 10 seconds. What is her
deceleration?
9. A motorcycle traveling at 25 m/s accelerates at a rate of 7.0 m/s2 for 6.0 seconds. What is the
final speed of the motorcycle?
10. A car starting from rest accelerates at a rate of 8.0 m/s/s. What is its final speed at the end of 4.0
seconds?
11. After traveling for 6.0 seconds, a runner reaches a speed of 10 m/s. What is the runner’s
acceleration?
a= v2 - v1
12. A cyclist accelerates at a rate of 7.0 m/s2. How long will it take the cyclist to reach a speed of 18
m/s?
13. A skateboarder traveling at 7.0 meters per second rolls to a stop at the top of a ramp in 3.0
seconds. What is the skateboarder’s acceleration?
Article Reflection:
https://www.sciencenews.org/article/gravity-waves-black-holes-verify-einsteins-prediction?tgt=n
r
Write a 5 sentence reflection related to the article. Use evidence from the article.
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?
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?
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?
4. Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his
yodel back from the canyon floor 5.9 s later. Assume that the speed of sound in air is 740.0
m/s. How deep is the canyon?
5. The horse travelled 2.59 miles in 384 seconds. What was the speed of the horse in:
a. Miles per second
b. Miles per hour
6. 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?
b. Draw a distance vs. time graph of the situation. (Assume constant speeds for each
hallway.)
7. 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?
8. What is the Acceleration of the Cart on the Ramp? Determine the Angle of the Ramp (A).
Angle Chart: h ttps://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSDNSMXc
Which Angle had the greatest Acceleration? Write a Conclusion based on your findings. Create
a Graph if you have time.
Height of
Ramp Velocity Velocity
2 Acceleration
(Opposite) Dist. 1 Time 1 1 Dist. 2 Time 2
50 m 45 m 9 sec. 45 m 3 sec.
50 m 60 m 15 sec. 60 m 10 sec.
Graph:
Conclusion:
Potential Energy Project
Due: Friday 3/17
Define and make note cards for the following words:
Energy - the strength Joules - a unit of Chemical Potential Law of Conservation
need to fulfill a energy Energy - a form of of Energy - energy
mental or physical potential energy that can not be created or
challenge can be absorbed or destroyed, it can only
released during a be transferred into
chemical reaction or another form
phase transition
Kinetic Energy - the Kilojoules - a unit of Elastic Potential Gravity - the force
energy that the body energy Energy - Potential that attracts a body
has in motion energy stored as a toward the center of
result of deformation the earth
Potential Energy - the Gravitational Mechanical Energy -
maximum amount of Potential Energy - the sum of kinetic
energy something GPE = mgh and potential energy
can have in an object that is
used to do work
Resource: h ttp://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy
Videos: http://www.youtube.com/watch?v=x5JeLiSBqQY
*Video shows you how to use the GPE equation.
Gravitational Potential Energy
GPE = mgh
Determine the Gravitational Potential Energy (GPE) of 3 different masses (g) at 3 different
heights.
3 objects: You, gallon of milk, television (research the masses)
* 2.2 lbs = 1 kg
* h = 10 m, 20 m, 30m
● Milk
○ M = 3.9 kg, g = 9.8 m/s2 , h = 10 m
■ GPE = mgh
GPE = (3.9 kg)(9.8 m/s2 )(10 m)
GPE = 382.2 joules
○ M = 3.9 kg, g = 9.8 m/s2 , h = 20 m
■ GPE = mgh
GPE = (3.9 kg)(9.8 m/s2 ) (20 m)
GPE = 764.4 joules
○ M = 3.9 kg, g = 9.8 m/s2, h = 30 m
■ GPE = mgh
GPE = (3.9 kg)(9.8 m/s2 )(30 m)
GPE = 1146.6 joules
● Television
○ M = 31.6 kg, g = 9.8 m/s2, h = 10 m
■ GPE = mgh
GPE = (31.6 kg)(9.8 m/s2) (10 m)
GPE = 3096.8 joules
○ M = 31.6 kg, g = 9.8 m/s2 , h = 20 m
■ GPE = mgh
GPE = (31.6 kg)(9.8 m/s2)(20 m)
GPE = 6193.6 joules
○ M = 31.6 kg, g = 9.8 m/s2 , h = 30 m
■ GPE = mgh
GPE = (31.6 kg)(9.8 m/s2)(30 m)
GPE = 9290.4 joules
● Me (Brad Krutz)
○ M = 47.6 kg, g = 9.8 m/s2, h = 10 m
■ GPE = mgh
GPE = (47.6 kg)(9.8 m/s2) (10 m)
GPE = 4664.8 joules
○ M = 47.6 kg, g = 9.8 m/s2 , h = 20 m
■ GPE = mgh
GPE = (47.6 kg)(9.8 m/s2 )(20 m)
GPE = 9329.6 joules
○ M = 47.6 kg, g = 9.8 m/s2, h = 30 m
■ GPE = mgh
GPE = (47.6 kg)(9.8 m/s2)(30 m)
GPE = 13994.4 joules
Data Table:
Your data table will need: Object, mass, gravity, height, GPE
Object Mass (kg) Gravity (m/s2) Height (10 m) Height (20 m)
Me (Brad 47.6 9.8 4664.8 9329.6
Krutz)
Milk Carton 3.9 9.8 382.2 764.4
Television 31.6 9.8 3096.8 6193.6
Determine the GPE of one of the masses on the following planets:
Milk Carton
● “Planet Goffinian” - 17% greater than Earth’s Gravity
○ 9.8 m/s2 x 0.17 = 1.666 m/s2
1.666 m/s2 + 9.8 m/s2 = 11.466 m/s2
○ M = 3.9 kg, g = 11.466 m/s2 , h = 10 m
○ GPE = mgh
GPE = (3.9 kg)(11.466 m/s2 ) (10 m)
GPE = 447.174 joules
● “Planet Cabrerian” - 39% less than Earth’s Gravity
○ 9.8 m/s2 x 0.39 = 3.528 m/s2
9.8 m/s2 - 3.528 m/s2 = 6.272 m/s2
○ M = 3.9 kg, g = 6.272 m/s2 , h = 10 m
○ GPE = mgh
GPE = (3.9 kg)(6.272 m/s2)(10 m)
GPE = 244.647 joules
● “Planet Biondi” - 82% greater than Earth’s Gravity
○ 9.8 m/s2 x 0.82 = 8.036 m/s2
9.8 m/s2 + 8.036 m/s2 = 17.836 m/s2
○ M = 3.9 kg, g = 17.836 m/s2, h = 10 m
○ GPE = mgh
GPE = (3.9 kg)(17.836 m/s2)(10 m)
GPE = 695.604 joules
● “Planet Guralnick” - 63% less than Earth’s Gravity
○ 9.8 m/s2 x 0.63 = 6.174 m/s2
9.8 m/s2 - 6.174 m/s2 = 3.626 m/s2
○ M = 3.9 kg, g = 3.626 m/s2, h = 10 m
○ GPE = mgh
GPE = (3.9 kg)(3.626 m/s2)(10 m)
GPE = 141.414 joules
Data Table:
Mass (kg) Gravity Height (m) GPE (joules)
(m/s2)
Planet Goffinian 3.9 11.466 10 447.174
Planet 3.9 6.272 10 244.647
Cabrerian
Planet Biondi 3.9 17.836 10 695.604
Planet 3.9 3.626 10 141.414
Guralnick
Graph:
Critical Thinking Questions:
1. What factors affect Gravitational Potential Energy?
Some things that factor into GPE are weight, height, and gravity (if on a different planet).
2. Why did the GPE change on the other planets?
Because the gravity is less or more
3. Which planet would you be able to hit a golf ball further? Explain using data.
On Planet Guralnick, you would be able to hit a golf ball much further than on Earth. This is
because on Planet Guralnick g= 3.626 m/s2 and on Earth g= 9.8 m/s2
4. How does GPE relate to Chemical Potential Energy?
They are both certain types of energy stored in matter
5. How do Energy companies use GPE to generate Electrical Energy? Give an example
Energy companies use GPE to generate electrical energy by movement. For example, falling
water possesses energy. When water fall downwards, it’s GPE is converted into kinetic energy.
This kinetic energy is then transferred to a water wheel and the wheel rotates. If the water wheel
is connected to a generator, energy will be produced.
6. What happens to the GPE when the object falls to the ground? Describe the Energy
transformations along the way. Use a diagram.
As an object’s height off the ground decreases, the GPE of the object also decreases. The
object will fall faster and faster as the GPE decreases and this GPE will convert into kinetic
energy.
Worksheet 1:
http://glencoe.mheducation.com/sites/0078600510/student_view0/unit1/chapter4/math_practice
_2.html
Worksheet 2: h ttp://go.hrw.com/resources/go_sc/ssp/HK1MSW65.PDF
1. The world record for pole vaulting is 6.15 m. If the pole vaulter’s gravitational potential is 4942
J, what is his mass?
GPE = mgh
4942 j = m(9.8 m/s2)(6.15 m)
4942 j = 60.27m
60.27 60.27
81.99 kg = m
2. One of the tallest radio towers is in Fargo, North Dakota. The tower is 629 m tall, or about 44
percent taller than the Sears Tower in Chicago. If a bird lands on top of the tower, so that the
gravitational potential energy associated with the bird is 2033 J, what is its mass?
GPE = mgh
2033 j = m(9.8 m/s2 ) (629 m)
2033 j = 6164.2m
6164.2 6164.2
0.33 kg = m
3. One of the largest planes ever to fly, and the largest to fly frequently, is the Ukrainianbuilt
Antonov An-124 Ruslan. Its wingspan is 73.2 m, and its length is 69.2 m. The gravitational
potential energy associated with the plane at an altitude of 1.45 km is 3.36 × 109 J. What is the
airplane’s mass?
1.45 km = 1450 m
3.36 × 109 = 366.24 j
GPE = mgh
366.24 j = (1450 m)(9.8 m/s2)m
366.24 j = 1 4210m
14210 14210
0.03 kg = m
4. In 1993, Cuban athlete Javier Sotomayor set the world record for the high jump. The
gravitational potential energy associated with Sotomayor’s jump was 1970 J. Sotomayor’s mass
was 82.0 kg. How high did Sotomayor jump?
GPE = mgh
1970 j = (82 kg)(9.8 m/s2 )h
1970 j = 803.6h
803.6 803.6
2.45 m = h
5. An 1750 kg weather satellite moves in a circular orbit with a gravitational potential energy of
1.69 × 1010 J. At its location, free-fall acceleration is only 6.44 m/s2 . How high above Earth’s
surface is the satellite?
1.69 × 1010 = 1706.9 j
GPE = mgh
1706.9 j = (1750 kg)(6.44 m/s2 )h
1706.9 j = 11270h
11270 11270
0.15 m = h
10. The most massive piece of equipment ever carried by a plane was a 1.24 × 105 kg
generator built in Germany in 1993. How far above the ground was the generator when the
potential energy associated with it was 9.17 × 108 J?
9.17 × 108 = 990.36 j
1.24 × 105 = 130.2 kg
GPE = mgh
990.36 j = (130.2 kg)(9.8 m/s2 )h
990.36 j = 1 275.96h
1275.96 1275.96
0.78 m = h
Kinetic Energy Project
Objective: 7 .1.b. Energy can be stored in many forms and can be transformed
into the energy of motion.
Problem Statement:
1. Design an experiment to test how changing the angle of a ramp affects Kinetic Energy?
2. What is the velocity of a roller coaster at the bottom of the hill?
Hypothesis:
If the car is at the top of the roller coaster, the ve locity will be much greater than at the top of the roller
coaster.
Independent Variable:
Angle
Dependent Variable:
Final Velocity
*Use the following angles: 8, 18, 28
Example: S uppose you want to make a ramp with a 23 degree angle. Look up 23 degrees on
the Angle Chart and find the sine (decimal).
Sin 23 = 0.39
Substitute Sin 23 with 0.39
0.39 = opposite
hypotenuse
0.39 = opposite (height of ramp)
180 cm
solve for opposite (height of ramp)
*A ngle Chart
*Include diagrams of the 3 Angles
*Include math examples for determining the angles and KE.
M = 37.2 g
Hyp = 1.2 m
G = 9.8 m/s2
Sine 8 = opp/hyp
(1.2) 0.13917 = x/1.2m (1.2)
0.167004 = x
Opp.= 0.167004
GPE = KE
Mgh = 0.5ms2
(37.2 g)(9.8 m/s2 ) (0.167004 m) = (0.5)(37.2)v2
60.88 = 18.6v2
18.6 18.6
√3 .27 = √ v 2
1.81 = vf
T = 1.11
D/T=V
1.2 m /1.11 sec = 1.08 m/s
Sine 18 = opp/hyp
(1.2) 0.30902 = x/1.2m (1.2)
0.370824 = x
Opp.= 0.370824
GPE = KE
Mgh = 0.5ms2
(37.2 g)(9.8 m/s2) (0.370824 m) = (0.5)(37.2)v2
135.187597 = 1 8.6v2
18.6 18.6
√7.26815 = √ v 2
2.69595 = vf
T = 0.64
D/T=V
1.2 m / 0.64 sec = 1.875 m/s
Sine 28 = opp/hyp
(1.2) 0.46947 = x/1.2m (1.2)
0.563364 = x
Opp.= 0.563364
GPE = KE
Mgh = 0.5ms2
(37.2 g)(9.8 m/s2 ) (0.563364 m) = (0.5)(37.2)v2
205.37998 = 1 8.6v2
18.6 18.6
√11.04 = √v2
3.32 = vf
T = 0.53
D/T = V
1.2 m / 0.53 sec = 2.26 m/s
Angle of the Ramp The Velocity of the Car at the Average Velocity
Bottom of the Ramp
8 Degrees 1.81 1.08
18 Degrees 1.875
28 Degrees 2.69595 2.26
3.32
Video Resources:
1. How to solve KE problems: h ttps://www.youtube.com/watch?v=tryiwu4RhSM
2. PE/KE: h ttps://qwww.youtube.com/watch?v=Je8nT93dxGg
3. PE/KE: https://www.youtube.com/watch?v=BSWl_Zj-CZs
4. PE/KE: h ttps://www.youtube.com/watch?v=7K4V0NvUxRg
Data Analysis - W rite your data analysis paragraph here
In conclusion, our hypothesis, which was if the car is at the top of the roller
coaster, the velocity will be much greater than at the top of the roller coaster, was
correct. We know this because for all three angles the final velocity was much
greater than the average velocity, and the starting velocity is bringing the average
down because it is so low. The main trend was that the higher the angle was, the
greater the velocity was. One error that could be contained in our experiment is
that our measurements and times could be slightly off.
Data Analysis Rubric (Self Evaluate) 3 4
Lab Rubric - Data Analysis Sections
12
Data/ ____Data is poorly ____Data is ____Data is ___Data is clearly
Observation organized or missing represented in a represented in the and accurately
s altogether. table or graph, but it table or graph with represented in a
No mention of is incomplete or minor errors. More table or graph.
observations there are major complete discussion Observations
errors. Some of observations. include discussion
discussion of of both qualitative
observations and quantitative
observations.
Conclusion/ ____No conclusion is ____Somewhat ____Adequately ____Clearly
Analysis written in this report or it explains whether or explains whether or explains whether or
is very brief. No data is not the hypothesis not the hypothesis not the hypothesis
cited. was supported. was supported. Data was supported. Data
____No analysis is ____ Possible is cited to support was cited to support
included or it is extremely sources of error are hypothesis. the hypothesis.
brief no sources of error somewhat ____Possible ____Possible
are explained. explained. sources of error are sources of error are
____No discussion of ____ No discussion adequately clearly explained.
patterns or trends in the of patterns or trends explained.
data ____Some ____Trends and
discussion of Patterns in the data
patterns or trend in are clearly
the data discussed.
Self Evaluate Self Evaluate Score (1-4)
Category 3
Scientific Method 4
-Hypothesis 3
-Identify the variables
3
Math Examples
-Angle steps shown
-KE steps shown
Graph
-Accurate
-Informative
Data Analysis
-Hypothesis correct?
-Support for hypothesis
-Transition words
Reading
Comprehension
-Article questions
Article: Everyday Energy
Read the article and answer the questions.
\
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:
GPEtop = KEbottom
1. Cyclone - Coney Island
Height of largest hill -
Mass of Coaster/number of riders -
Velocity at Bottom of Hill in m/s -
2. Pick your own coaster
Height of largest hill
Mass of Coaster/number of riders
Velocity at Bottom of Hill in m/s -
*Write about your results in a paragraph.
Article: Everyday Energy
Read the article and answer the questions.
1) A roller coaster car at the top of hill, an archer preparing to release an arrow, and a lake
that sits above a dam are all examples of what kind of energy?
a) potential energy
b) kinetic energy
c) gravitational energy
d) consumption of energy
2) What does the author describe in the passage?
a) the history of human energy use in the United States
b) the ways in which potential energy is converted to kinetic energy
c) the best reasons to build new dams in the American Southwest
d) the consequences of drought for people who rely on dams
3) The conservation of stored potential energy into kinetic energy can also be harnessed to
power homes, factoring and entire cities. Which example from the text supports this
conclusion?
a) the softball pitcher
b) the slingshotting comet
c) the archer
d) the hoover dam
4) Which of the following conclusion is supported by the text?
a) nuclear power is the most efficient kind of energy for powering cities
b) professional athletes should study the science of energy to play better
c) dams power cities by converting stored potential energy into kinetic energy
d) drought is a serious problem for farmers in the American Southwest
5) What is this passage mainly about?
a) the movement of comets through our solar system
b) the scientific forces behind our favorite roller-coasters
c) the unusual properties of water molecules in rivers
d) the conversion of potential energy into kinetic energy
6) Read the following sentences: “The Arizona and Nevada spillways are two means by
which the waters of Lake Mead can escape the dam. As the lake water tumbles over the
walls into a spillway, potentially energy is instantly converted into kinetic energy.”
a) a place where water flows over the top of a dam, creating energy
b) a place where water accidentally spills, causing problems for engineers
c) a place where water flows underground, into tunnels
d) a place where water flows into nearby farms, watering crops
7) Choose the answer that best completes the sentence below.
“The conversion of stored potential energy into kinetic energy can also be harnessed to power
homes, factoring and entire cities. _____, the Hoover Dam provides power to California,
Nevada, and Arizona.”
a) even though
b) initially
c) for instance
d) however
8) How does the Hoover Dam provide power to California, Nevada, and Arizona?
The Hoover Dam provides power to California, Nevada, and Arizona. It does this by harnessing
the converted potential energy of Lake Mead.
9) What two factors determine the energy production of the Hoover Dam?
How much water is required downriver from the dam and the water levels of Lake Mead
determine the energy production of the Hoover Dam.
10) Explain why the prolonged period of drought ( a time where there is little rain, and little
water flowing into rivers and lakes) would cause the Hoover Dam to generate much less
energy since 2009. Use evidence from the text to support your answer.
If Lake Mead has less water, then there will be less potential energy stored in Lake Mead. If
there is less potential energy, then there will be less kinetic energy created by water flowing
through the Hoover Dam. There would also be less lake water to tumble over the walls into a
spillway and move through four intake towers into the powerhouse and hydroelectric generators.
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:
GPEt op = KEbottom
1. Cyclone - Coney Island
Height of largest hill - 26m
Mass of Coaster/number of riders - 907.185 kg (1 ton)
Velocity at Bottom of Hill in m/s - 60 m/h
GPE=KE
GPE=mgh
GPE=(907.185 kg)(9.8 m/s2 )(26 m)
GPE=231150.74 J
231150.74=0.5mv2
231150.74=0.5(907.185)v2
√509.6=√v2
22.57=v
2. Pick your own coaster (Superman - Six Flags New England)
Height of largest hill - 63 m
Mass of Coaster/number of riders - 2700 kg
Velocity at Bottom of Hill in m/s - 77m/h
GPE=KE
GPE=mgh
GPE=(2700 kg)(9.8 m/s2 ) (63 m)
GPE=1666980
1666980=0.5mv2
1666980=0.5(2700)(v)2
1666980=1350v2
√1234.8=√v 2
35.14=v
*Write about your results in a paragraph.
As we can tell from the data, the average velocity of the ride superman at Six Flags New
England is 35.14 meters per second. This is with the cart weighing 2700 Kg, including
people. The only variable in this is the mass of the cart. We cannot control this because
we do not know how much people weigh or how many people are on the ride.
More resources:
http://www.youtube.com/watch?v=BSWl_Zj-CZs
Kinetic and Potential Energy
http://www.youtube.com/watch?v=7K4V0NvUxRg
Kinetic and Potential Energy
http://www.youtube.com/watch?v=btLU2lb3-xs
Bill Nye
http://www.youtube.com/watch?v=-dpBVtAbKJU
Roller Coasters
http://www.youtube.com/watch?v=iYEWIuQBVyg
Inclined Plane Project
Due: April 19, 2017
1. Define the following vocabulary: Use pgs. 124 - 153
Simple M achine - Mechanical Work - using a Input F orce - work
any of the basic Advantage - the force to move an input of a machine
mechanical devices ratio of the force object a distance is equal to the effort
for applying a force, produced by a (when both the force times the
such as an inclined machine to the force and the distance over which
plane, wedge, or force applied to it, motion of the object the effort force is
lever. used in assessing are in the same exerted.
the performance of direction)
a machine.
Compound Ideal M echanical Power - Power is Output D istance -
Machine - A Advantage - is a the rate (energy number of times
machine consisting measure of the amount per time that a machine
of two or more period) at which increases an input
simple machines force amplification work is done or force.
operating together, energy converted
as a wheelbarrow achieved by using a
tool,mechanical
device or machine
consisting of a system
lever, axle, and
wheel.
Efficiency - The Actual Mechanical Input D istance - Output Force -
ratio of the energy Advantage - is the device that number of times
delivered (or work force that a changes a force, that a machine
done) by a machine make work easier, increases an input
to the energy machine can by changing size of force
needed (or work force needed, the
required) in multiply while direction of a force,
operating the or distance over
machine subtracting losses which a force acts
from the machine
having to overcome
friction
First Class Lever - Second Class Third Class Lever Energy - the ability
Fulcrum in the Lever The effort is - has its applied to do work
middle: the effort is applied to the force situated
applied on one side handles, the axle of between the load
of the fulcrum and the wheel acts as and fulcrum
the resistance (or the fulcrum or pivot
load) on the other point, and the load
side, for example, a is found in the
seesaw, a crowbar middle.
or a pair of
scissors.
Block a nd T ackle Fixed Pulley - Movable Pulley - a
Pulley - is a system changes the pulley that is free to
of two or more direction of the move up and down,
force on a rope or and is attached to a
pulleys with a rope belt that moves ceiling or other
along its object by two
or cable threaded circumference lengths of the same
rope
between them,
usually used to lift
or pull heavy loads
2. Experiment: How does the angle of an inclined plane affect:
A. Ideal Mechanical Advantage
B. Actual Mechanical Advantage
C. Efficiency
*Think about the scientific Method
DATA TABLE
***Why is the Actual Mechanical Advantage always less than the Ideal Mechanical
Advantage
Conclusion:
In conclusion, the data proved that the IMA is always more than the AMA in all
three angles. This is because the distance has to be larger than the force used. Our
data table had Angle A with a IMA of 2.3 and a AMA of 1.67. Angle B had an IMA is
1.92 and a AMA of 1.42. Finally, Angle C has a IMA of 1.19 and an AMA of 1.11. The
output force, distance, and work stayed constant for the all three angles. To find the
work, we had to multiply force by distance. The output work was 520 for all three
angles. Angle A had an input force of 720, Angle B had an input force of 700, and Angle
C had an input force off 558. Lastly, we had to find the efficiency for all three angles.
The efficiency for Angle A was 72%, Angle B was 74%, and Angle C was 93%. So, this
experiment proved that the IMA is always more than the AMA.
3. Critical Thinking (Include in Presentation):
A. How much WORK would be done to lift a 350 kg Piano to the top of the Empire State
Building using a ramp with an angle of 35 degrees?
1. What is the length of the ramp to the top of the Empire State Building?
Sin-35 = 443.2 meters/x
X = 836.35 meters
2. Suppose the Ideal Mechanical Advantage is 3.2
a2+ b2= c2
443.22 + b2 = 836.322
196,426.24 + b2 = 699,431.1424
b2 = 503,004.9024
b = 709.2 meters
3. The Actual Mechanical Advantage (AMA) is 2.5
2.5 = 3432
x
3,432/2.5 = x
1,372.8 = x
Force output is 1,372.8 newtons * distance 443.2 m = 608,424.96 joules
Force input is 3,432 newtons * distance 836.35 m = 2,870,353.2 joules
4. What is the Efficiency of this Machine?
608,424.96 joules/2,870,353.2 joules = 21%
5. Provide a diagram of this example.
4. Explain how the Ideal Mechanical Advantage and Actual Mechanical Advantage
is determined for the following simple machines:
A. Inclined Plane - IMA is determined by the input force and input distance. AMA is the
output force and output distance.
B. Lever - to find the IMA use the effort distance from fulcrum and the resistance
distance from the fulcrum. AMA is the resistance force and effort force.
C. Pulleys - to find the IMA use force of object and the number of ropes.
D. Wheel and Axle - IMA is radius of wheel and radius of axle or diameter of wheel and
diameter of axle.
5. Complete the Following Worksheet:
Worksheet 2
Effort Force = Input Force
Resistance Force = Output Force
4a. 24 m/5 m = 4.8 m
4b. 18 m/4 m = 4.5
5b. 325 N/20 N = 16.25 joules
6a. AMA = 783 N/150 N = 5.22 joules
IMA = 12 m/2 m = 6
Efficiency = 5.22 N/6 = 87%
7b. 24 m/30 m = 0.8
7c. 15 m/7 m = 2.14
8a. 597 N/75 N = 7.96 joules
8b. 128 N/55 N = 2.3 joules
6. Group: Video 1 Trial of the Lab that demonstrates the experiment and the
calculations
* Attach link to video here
https://drive.google.com/open?id=0B2H_r6ykX_pwOFBIczY1ZTNrLVk
Resources to Help:
QUIZ: Inclined Plane
Directions: A nalyze 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?
Hypothesis: ( Use proper form!)
If the angle of the inclined plane is greater, than the M echanical Advantage will be
greater.
Diagrams of Inclined Planes: (Label Diagrams)
Angle Chart: https://drive.google.com/open?id=0B4RmhXJlHvo1YXZhcDNMSDNSMXc
Calculations ( Examples):
Angle 1 : 12o Angle 2 : 19o Angle 3 : 37o
IMA IMA IMA
Din / Dout = IMA Din / Dout = IMA Din / Dout = IMA
150 / 30 = IMA 90 / 30 = IMA 50 / 30 = IMA
5 = IMA 3 = IMA 1.67 = IMA
AMA AMA AMA
Fout / Fin = AMA Fout / Fin = AMA Fout / Fin = AMA
7 / 2 = AMA 7 / 3 = AMA 7 / 4 = AMA
3.5 = AMA 2.33 = AMA 1.75 = AMA
Efficiency Efficiency Efficiency
Wout / Win x 100 = Eff. Wout / Win x 100 = Eff. Wout / Win x 100 = Eff.
210 / 300 x 100 = Eff. 210 / 270 x 100 = Eff. 210 / 200 x 100 = Eff.
70% = Eff. 77.78% = Eff. 105% = Eff.
Graph: ( Angle and Mechanical Advantage)
Conclusion:
Option #1 Write a Conclusion.
***Your conclusion must also address which machine would be impossible
and why?
Option #2 Building
Compare 2 famous buildings based on the following Inclined Plane Data.
A builder wanted to get a 6 0 kg bag of concrete to the top of the 2
buildings.
1. What would the length of the ramp be if the machine has:
IMA - 5.9
AMA - 3.7
Empire State Building - Dout = 443.2 m
IMA = Din / Dout
(443.2) 5.9 = Din / 443.2 (443.2)
2614.88 = Din
Space Needle - Dout = 184 m
IMA = Din / Dout
(184) 5.9 = Din / 184 (184)
1085.6 = Din
2. What are the angles of the ramps?
Empire State Building
Sin = opp. / hyp.
Sin = 443.2 / 2614.88
Sin = 0.16949152542
Sin = 10o
Space Needle
Sin = opp. / hyp.
Sin = 184 / 1085.6
Sin = 0.16949152542
Sin = 10o
3. Using Work Input and Output, what is the efficiency of the machines?
60 kg = 588.4 N = Fout
Empire State Building
AMA = Fout / Fin
(60) 3.7 = 60 / Fin (60)
222 = Fin
Wout = Fout x Dout
Wout = 588.4 x 443.2
Wout = 260778.88
Win = Fin x Din
Win = 222 x 2614.88
Win = 580503.36
Eff. = Wout / Win X 100
Eff. = 260778.88 / 580503.36 x 100
Eff. = 50%
Space Needle
AMA = Fout / Fin
(60) 3.7 = 60 / Fin (60)
222 = Fin
Wout = Fout x Dout
Wout = 588.4 x 184
Wout = 108265.6
Win = Fin x Din
Win = 222 x 1085.6
Win = 241003.2
Eff. = Wout / Win X 100
Eff. = 108265.6 / 241003.2 x 100
Eff. = 50%
Rubric
Lab Rubric - Data Analysis Sections
1 234
Data/ ____Data is poorly ____Data is ____Data is ___Data is clearly
Observations organized or missing represented in a represented in the and accurately
altogether. table or graph, but table or graph with represented in a
No mention of it is incomplete or minor errors. More table or graph.
observations there are major complete discussion Observations
errors. Some of observations. include discussion
discussion of of both qualitative
observations and quantitative
observations.
Conclusion/ ____No conclusion is ____Somewhat ____Adequately ____Clearly explains
Analysis written in this report or it explains whether or explains whether or whether or not the
is very brief. No data is not the hypothesis not the hypothesis hypothesis was
cited. was supported. was supported. supported. Data
____No analysis is ____ Possible Data is cited to was cited to support
included or it is extremely sources of error are support hypothesis. the hypothesis.
brief no sources of error somewhat ____Possible ____Possible
are explained. explained. sources of error are sources of error are
____No discussion of ____ No discussion adequately clearly explained.
patterns or trends in the of patterns or explained.
data trends ____Some ____Trends and
discussion of Patterns in the data
patterns or trend in are clearly
the data discussed.
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