Download GRAVITY The Universe`s Crazy Glue

GRAVITY
The Universe’s Crazy Glue
Kristina Atia
Torrance Elementary School
The instructional materials were developed as part of the BEST Science Project,
funded by Northrop Grumman Space Technology.
TABLE OF CONTENTS
Topic of Module
1
Targeted Grade Level
1
California Science Content Standards
1
Student Learning Outcomes
1
Time Needed
2
Science Content
2
Pre-Requisite Skills and Knowledge
11
Glossary
11
The Leaning Tower of Pisa – Part One
13
The Leaning Tower of Pisa – Part Two
17
The Leaning Tower of Pisa – Part Three
20
Resources and References
23
APPENDIX A – A Brief Biography of Galileo Galilei
24
APPENDIX B – The Leaning Tower of Pisa Worksheets – Student Edition
26
APPENDIX C – The Leaning Tower of Pisa Worksheets – Teacher Edition
39
DESCRIPTION OF THE INSTRUCTIONAL MATERIALS
GRAVITY: The Universe’s Crazy Glue
Gravity: The Universe’s Crazy Glue is a module, which takes students through Galileo
Galilei’s famous Leaning Tower of Pisa experiments. Student will replicate his
experiments by dropping various objects of various masses from a height and take part
in the inquiry process to develop their own conclusions about gravity and its effect on
the objects around us.
TARGETED GRADE LEVEL
This module is designed for fifth grade students. This module can also be adapted to
the fourth grade level.
CALIFORNIA SCIENCE CONTENT STANDARDS
California Science Standards for Grade Five
Earth Sciences
5c. Students know the path of a planet around the Sun is due to the gravitational
attraction between the Sun and the planet.
Investigation and Experimentation
6d. Identify the dependent and controlled variables in an investigation.
6e. Identify a single independent variable in a scientific investigation and explain
how this variable can be used to collect information to answer a question
about the results of the experiment.
California Science Standards for Grade Four
Investigation and Experimentation
6c. Formulate and justify predictions based on cause-and-effect relationships.
6d. Conduct multiple trials to test a prediction and draw conclusions about the
relationships between predictions and results.
STUDENT LEARNING OUTCOMES
1. Students will be able to describe the effect of gravity on everyday objects by
replicating Galileo Galilei’s Leaning Tower of Pisa experiments.
2. Students will be able to explain how everyday objects don’t appear to reach the
ground at the same time (but in theory should) by analyzing their experiment
results.
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TIME NEEDED
The expected timeline for this module is one hour a day for 3 days.
SCIENCE CONTENT
MAJOR PLAYERS IN THE ATTEMPT TO DEFINE GRAVITY
Aristotle 384 B.C. – 322 B.C.
Aristotle was born in Athens, Greece. He
was a teacher of art, literature, philosophy,
and the laws of nature.
Contribution To The Understanding Of Gravity
Aristotle’s theory stated that all bodies move towards their natural place. For some
objects, Aristotle claimed the natural place to be the center of the earth, wherefore they
fall towards it. For other objects, the natural place is the heavenly spheres, wherefore
gases, steam for example, move away from the center of the earth and towards heaven
and to the moon. The speed of this motion was thought to be proportional to the mass
of the object.
At his time, this may have been an acceptable explanation for gravity and why objects
behave the way they do, but his theory still leaves much to be explained.
In Aristotle’s theory the rock
will fall to Earth much more
quickly than the leaf because
the stone is made of Earth
and Earth wants it back.
The leaf is from a tree and the
Earth has no interest in the
leaf, so it falls slowly and lazily
until it rests on Earth.
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Galileo Galilei 1564-1642
Galileo Galilei was born in Pisa, Italy and
is considered one of the most important
scientists in our understanding of gravity.
(A biography of Galileo is in Appendix A.)
Contributions To The Understanding Of Gravity
Galileo conducted the famous experiment of dropping objects off of the Leaning Tower
of Pisa. In his experiment, he dropped two cannon balls, one 10 times the mass of the
other, at exactly the same time to determine which cannon ball would drop first. The
question is: Which cannon ball did reach the ground first? Answer: They both reached
the ground at the same time! Through his experiments, Galileo discovered that gravity
accelerates all objects at the same rate!
Regardless of their mass, both cannon balls will
reach the ground at the same time!
Galileo also believed that the speed of free falling objects increases in proportion to the
time of the fall, meaning that they accelerate uniformly. Since there were not
stopwatches in Galileo’s time and free fall was much too fast to record, Galileo decided
to test his theory with the use of an inclined plane and a ball. He assumed that the
speed of the ball rolling down the inclined plane would also accelerate uniformly, just at
a slower rate.
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Once the ball starts on its path down the plane the effect of gravity is uniform or
constant and the ball will continue to move in a straight line. Each second the ball
travels down the plane the acceleration of the ball increases as well as the amount of
distance the ball covers. These experiments helped Galileo to figure out that the total
distance covered is proportional to the time squared (d~t2).
d = the distance traveled
t = the time it takes to travel the distance
d = t2
Real Life Application
Let’s assume that it is winter and you are at the top of a very large, snow covered hill.
You are ready to fly down that hill on your sled, feel the wind in your hair, and the
exhilaration of the speed. Just as you are about to push off your college science
professor pops into your head and hear “the total distance an object covers it
proportional to the time it takes to travel that distance, squared”. As you push off, you
start your stopwatch just for fun to see how long it takes you to get to the bottom.
Whoosh! You’re off! 10.8 seconds! That’s a record! You decide to see what distance
you actually traveled down that hill.
(distance traveled down the hill)= (time it took to go down the hill)2
(distance traveled down the hill)= (10.8 seconds) 2
(distance traveled down the hill)= 116.64 m/s2
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Isaac Newton 1642-1727
Issac Newton was born in Lincolnshire, England.
He was a mathematician and a scientist.
Contributions To The Understanding Of Gravity
In order to fully understand Newton’s theory of gravity, one must know Newton’s Laws of
Motion.
Newton’s First Law of Motion
Every object will remain at rest or in uniform motion in a straight line unless compelled
to change its state by the action of an external force. This is normally taken as the
definition of inertia. A simpler way to state this law is to say: Objects tend to keep on
doing whatever they're doing unless acted on by a force.
Real Life Application
You and your dog Bud are riding in the car traveling 35 mph. You slam on the brakes
to avoid hitting the squirrel that ran out into the street to chase a acorn. Next thing you
know Bud, who was in the back, is now giving you a wet, sloppy kiss. What happened?
You and Bud are traveling at 35 mph, when you hit the brakes, friction (a force) between
the tires and the road changes the motion of the car from moving to not moving. You
stay pretty much where you are because your seatbelt exerts a force on you and
changes your motion from moving to not moving. Bud, on the other hand has nothing
to exert a force on him to stop him from not moving, so he continues to travel at 35
mph.
35 mph
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Newton’s Second Law of Motion
Newton’s Second Law explains the relationship between the force on an object and its
acceleration. The acceleration is how fast the velocity (or the speed of an object) is
changing. The law states that if the mass of an object stays the same, the force on an
object is proportional to its acceleration. If the force on an object increases, the
acceleration will also increase. If the force on an object decreases, the acceleration will
also decrease. Simply stated: Newton’s Second Law of Motion explains the relationship
between an object’s force, mass, and acceleration. You write it as F = ma.
F = force
m = mass
a = acceleration
F = ma
Real Life Application:
Let’s say you are playing a game of pool. You are one shot away from winning the
game and you have to hit the ball with just enough force to sink it in the hole. Let say
that you hit the ball with a force of 10 N (Newtons) and that the mass of the billiard ball
is 2 kg. How much acceleration does that billiard ball have on the way to the hole?
(Force acting on the billiard ball) = (Mass of the billiard ball)(Acceleration of the billiard
ball)
10 N = 2 kg x (acceleration of the billiard ball)
10 N / 2 kg = 5 m/s2
Therefore, your billiard ball has an acceleration of 5 m/s2.
Mass = 2 kg
Force = 10 N
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Newton’s Third Law of Motion
For every action (force) in nature there is an equal and opposite reaction (force). Simply
stated: If object A exerts a force on object B, then object B also exerts an equal force
on object A.
Real Life Application
It’s winter and you and your friend decide to go ice-skating (whoo hoo!). In several
hours, you and your friend are getting tired and are ready to call it a day. Your friend,
who is a little over dramatic, exclaims, “I cannot go on any longer! Push me home!”
You roll your eyes, then decide you are going to push her so hard that she will go flying
across the ice. You get in position and give your friend’s shoulders a hard push. Wait!!
What is happening? The push you gave your friend sent her forward on the ice but you
notice that you are now going backwards on the ice. The force you exerted on your
friend’s shoulders (pushing her forward) is the same force that her shoulders exerted on
you, pushing you backwards.
Oh… I’ll push
you home…he,
he, he, he…
Push me home! I
cannot bear it any
longer!
force = force
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The Universal Law Of Gravitation
Now that we are familiar with Newton’s Laws of Motion we can now take a look at how
Newton came up with The Universal Law of Gravitation. We have all heard of the story
of Newton sitting under a tree and the apple that fell on his head. But what does this
story have to do with the Universal Law of Gravitation? A lot!! The apple falling from
the tree sparked a thought in Newton about the force that caused the apple to fall from
the tree and if that force extends beyond our Earth.
The event that sparked the beginning of
Newton’s understanding of gravity.
Newton thought that if the force of gravity is present in the highest tree, then why not to
the Moon? This gravitational force could then explain the orbit of the Moon around the
Earth. The thought experiment below illustrates Newton’s idea.
Imagine we fire a cannon horizontally from a high mountain. The cannon ball will
eventually fall to Earth, as indicated by the shortest trajectory (path) in the figure,
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because of the gravitational force acting on the cannon ball, which is directed toward the
center of the Earth and the associated acceleration of the cannon ball towards Earth.
(Recall that acceleration is a change in velocity and that velocity is a vector, which has
both a magnitude and a direction. Acceleration occurs if either or both the magnitude
and the direction of the velocity change.) Simply stated, once we fire the cannon, the
cannon ball will begin its path back down to Earth due to gravity. If we increase the
velocity for our imaginary cannon, the projectile of the cannon ball will travel further and
further before returning to Earth. Newton reasoned that if the cannon projected the
cannon ball with exactly the right velocity, the projectile of the cannon ball would travel
completely around the Earth, always falling in the gravitational field but never reaching
the Earth. In this situation, the velocity that the cannon ball travels is equal to the rate
that the cannon ball is falling. The cannon ball would travel around the Earth and never
reach the ground. We would say that the cannon ball is “orbiting the Earth”. That is, the
cannon ball would have been put into orbit around the Earth. Newton concluded that
the orbit of the Moon was of exactly the same nature: the Moon continuously "fell" in its
path around the Earth because of the acceleration due to gravity, thus producing its
orbit.
By such reasoning, Newton came to the conclusion that any two objects in the Universe
exert gravitational attraction on each other, with the force having a universal form, or a
law that applies to all objects.
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Albert Einstein 1879-1955
Albert Einstein was born in Ulm, Germany.
He was a scientist and mathematician.
Contributions To The Understanding Of Gravity
The General Theory of Relativity
The General Theory of Relativity proposed by Einstein contributed greatly to the
understanding of gravity’s effect on objects of large masses such as planets and stars.
The key idea of general relativity, called the equivalence principle, is that gravity pulling
in one direction is completely equivalent to an acceleration in the opposite direction. An
example of this is evident when we ride an elevator. As the elevator accelerates upwards
it feels just like gravity pushing you into the floor.
Weight Vs. Mass
Is there really a difference between weight and mass? YES!! Weight and mass are not
interchangeable words! When we talk about weight, we are talking about a measure of
how strongly Earth’s gravity “pulls” on us.
Mass is the quantity of matter in an object. A measure of how much matter an object
contains. Basically, mass is how much “stuff” something has.
The mass of an object will stay consistent but the weight of an object can change. For
example, the mass of an astronaut is the “stuff” he or she is composed of. On Earth,
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the astronaut weighs 120 pounds. When the astronaut is outside of Earth’s gravitational
pull, traveling in the space shuttle toward the moon, the astronaut will still have exactly
the same mass, but his/her weight will change. In particular, we may say that the
astronaut is weightless while traveling in the space shuttle. Once the astronaut reaches
the moon, his/her weight will be 1/6 of that on Earth because the moon has 1/6 the
amount of gravity on Earth. The 120 pound astronaut on Earth weighs only 20 pounds
on the moon, but still has the same mass (“stuff”).
PRE-REQUISITE SKILLS AND KNOWLEDGE
Prior to teaching Gravity: The Glue of the Universe there are no pre-requisite skills or
knowledge needed to successfully complete this module.
GLOSSARY
The following words and their definitions should be addressed before the completion of
the module.
Acceleration – any change in motion of an object over time.
Air resistance – force from surrounding air that tends to oppose motion.
Constant – factor not changed in an experiment.
Control – standard for comparison in an experiment.
Controlled Variable – the variable in an experiment that does not change.
Dependent variable – the variable that is being observed, which changes in response to
the independent variable.
Force – a push, pull, whack, or bump that can change a state of motion.
Free fall – an object is said to be in free fall when it is falling toward the Earth without
slowing down due to the presence of air.
Friction – the force between two objects when they rub together.
g – a symbol for the acceleration due to gravity of everything that’s freely falling near the
surface of the Earth; g = 32 ft/sec2 or 9.8 meters/sec2
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G – The universal gravitational constant equal to 6.67 x 10-11 m3/kg-sec2. This number
is used in the formula for the gravitational force between two objects.
Gravity - The attractive effect that any massive object has on all other massive objects.
The greater the mass of the object, the stronger its gravitational pull.
Independent variable – the variable in the experiment that you purposely manipulate or
change.
Inertia – the tendency of an object to keep doing whatever it is doing. The inertia of an
object is also an object’s resistance to change. The inertia of an object is measured by
its mass.
Infinite – immeasurable and without end.
Light-year – the distance that light travels in empty space in one year (5.8 trillion miles).
Mass – the quantity of matter in an object. A measure of how much matter an object
contains.
Speed – how fast something is going, measured by the distance traveled and by the
time to travel that distance.
Variable – a factor or condition that is subject to change.
Vector – a quantity that has both magnitude and direction. Force, velocity, and
acceleration are all vectors.
Velocity – the speed and direction something is moving. Velocity is a vector.
Weight – a measure of how strongly Earth’s gravity “pulls” an object.
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The Leaning Tower of Pisa – Part One
Different Masses
Description of Activity
In this activity, students will replicate Galileo’s famous Leaning Tower of Pisa
experiments. Students will drop objects of different masses and record the length of time
it takes each object to fall. Students determine their dependent, independent, and
controlled variables and will try to get an object of light mass (a leaf) and an object of
heavy mass (a rock) to reach the ground at the same time.
Objectives for The Leaning Tower of Pisa - Part One
Students will be able to:
1) State the accomplishments that Galilei contributed to the understanding of gravity.
2) Describe the difference between mass and weight.
3) Identify the dependent, independent, and controlled variables of an experiment.
Materials Needed
2 Stopwatches per group
5-6 Leaves or pieces of 4in. x 4in. paper
5-6 Rocks, approximately the size of a half dollar
1 Pair of safety goggles for each student
1 Pencil for each student
1 Yardstick per group
1 Chair for each group
1 Leaning Tower of Pisa Worksheet – Part One for each student
Procedure
1.
Read the brief biography on Galileo Galilei to the class describing who he was
and contributions he made to further our understanding of gravity.
2.
Explain to students that a scientist’s experiments cannot be taken as truth just
because one person was able to achieve results. Scientific ideas and theories
can only be said to be truths when a multitude of different scientists are able to
perform the same experiment and achieve the same results.
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3.
Tell students that today they will be reenacting Galileo’s famous Leaning Tower
of Pisa experiment to see how their data compares to the results of Galileo.
4.
Assign students in groups of 4 students. Assign each student in every group a
number. Student #1 will be the dropper, Student #2 will be in charge of
measuring, and Student #3 and Student #4 will be timekeepers.
5.
Provide each group with a leaf, a rock, 2 stopwatches, safety goggles, and the
Leaning Tower of Pisa Worksheet – Part One. Tell students to record their
group information on their Leaning Tower of Pisa Worksheet – Part One.
6.
The teacher explains that in every experiment there are variables, or factors or
conditions that can be changed within an experiment. Write the definition of
variables on the board and have the students copy the definition on the Leaning
Tower of Pisa Worksheet – Part One notes section, located at the end of the
worksheet.
7.
Explain to students that there are three different types of variables that an
experiment can have and have them write down the definitions on the Leaning
Tower of Pisa Worksheet – Part One notes section, located at the end of the
worksheet. The first type of variable is a dependent variable, the variable that is
being observed, which changes in response to the independent variable. The
second type of variable is an independent variable, the variable in the
experiment that you purposely manipulate (change). The third type of variable
is a controlled variable, the variable in an experiment that does not change.
8.
The teacher demonstrates the experiment using different objects than the ones
students will use. The teacher mentions that he/she has already found the
mass of the objects. For example, a ball with a mass of 10 grams and a book
with a mass of 16 grams. The teacher holds one object in each hand with
his/her arms held out straight. If the classroom clock has a second hand, the
class can record the time it takes each object to fall. If the classroom does
not have a second hand, ask one student to be the timekeeper for each object
and record the time it takes each object to fall.
9.
Explain to the students that the distance from the teacher’s arms to the ground
is the controlled variable because it will not change throughout the experiment.
10.
Explain to the students that the objects being dropped are both independent
variables because these objects will change throughout each experiment.
11.
Explain to the students that the time it takes each object to drop is the
dependent variable because the time is what they are observing and the time
will change depending upon the objects (independent variables) used in each
experiment.
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12.
Have each group measure the mass (in grams) of their objects using scales in
the classroom. If scales are not available, the teacher can give students the
mass of each object.
13.
Ask students to record the mass (in grams) of the leaf and the rock by
completing questions 1-2 on the Leaning Tower of Pisa Worksheet – Part One.
14.
When students have completed questions 1-2 on the Leaning Tower of Pisa
Worksheet – Part One send them outside to set up their experiments in their
groups.
15.
Ask students to put on their safety goggles and wear them throughout the
experiment.
16.
Student #1 (Dropper) stands on the chair with the light mass object (leaf) in one
hand and the heavy mass object (rock) in the other hand, held at the same
height.
17.
Student #2 (Measurer) measures the distance between Student #1 hands and
the floor. This distance is a constant variable. All students record the distance
by completing question 3 on the Leaning Tower of Pisa Worksheet – Part One.
18.
Student #3 (Timekeeper) is the timekeeper for one object and Student #4
(Timekeeper) is the timekeeper for the other object. Student #3 and Student
#4 will stand on each side of Student #1 who is on the chair ready to drop the
objects.
19.
When Student #2 says “go!” Student #1 lets go of both objects at the same
time while Student #3 and Student #4 will simultaneously start their
stopwatches.
20. Student #3 and Student #4 stop the stopwatch when the object that they are
watching reaches the ground.
21.
All students will record this information by completing questions 4-5 on their
Leaning Tower of Pisa Worksheet – Part One.
22. Ask students to repeat the experiment two more times. Students may practice a
couple of times before recording their results on the Leaning Tower of Pisa
Worksheet – Part One by completing questions 6-9.
23. Ask students to decide what the variables were in their experiment by
completing questions 10-11 on the Leaning Tower of Pisa Worksheet – Part
One.
24. Ask students to make a prediction about why their objects did not reach the
ground at the same time and have them hypothesize by completing questions
12-13 on the Leaning Tower of Pisa Worksheet – Part One.
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25. Once students have tackled with the idea have them reach a conclusion about
objects of different masses and gravity and their experiment by completing
questions 14-18 on the Leaning Tower of Pisa Worksheet – Part One.
26. Once students are back in the classroom, ask the groups to share their results
and hypothesizes with the entire class.
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The Leaning Tower of Pisa – Part Two
Same Masses, Different Forms
Description of Activity
In this activity, students will replicate Galileo’s famous Leaning Tower of Pisa experiments
by dropping objects of the same mass but in different forms and timing how long it
takes each object to fall. Students will determine how the shape of an object impacts
the effect of gravity on the objects they dropped.
Objectives for The Leaning Tower of Pisa - Part Two
Students will be able to:
1) Identify the dependent, independent, and controlled variables of their experiment.
2) Recognize different variables and how they affect the outcome of an experiment.
3) Identify the importance of the form of an object and how different forms react
differently to gravity.
Materials Needed
2 Stopwatches per group
5-6 Pieces of 4in. x 4in. paper
5-6 Pieces of 4in. x 4in. paper, crumpled in a ball
1 Pair of safety goggles for each student
1 Pencil for each student
1 Yardstick per group
1 Chair for each group
1 Leaning Tower of Pisa Worksheet – Part Two for each student
Procedure
1.
Tell students that today they will be conducting the second part of their
experiment.
2.
Tell students to get in their assigned groups from Part One.
3.
Provide each group with 2 pieces of 4in. x 4in. paper, 2 stopwatches, goggles,
a yardstick, a chair, and the Leaning Tower of Pisa Worksheet - Part Two.
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4.
Give students the mass of the 4in. x 4in. paper and have them record this
information by completing questions 19-20 on the Leaning Tower of Pisa
Worksheet - Part Two.
5.
Tell students to take one piece of 4in. x 4in. paper and crumple it in a tight
ball.
6.
Inform students that they will be using the flat 4in. x 4in. piece of paper and
the 4in. x 4in. crumpled ball as their objects for the day’s experiment.
7.
When students have completed questions 19-20 on the Leaning Tower of Pisa
Worksheet - Part Two send them outside to set up their experiments in their
groups.
8.
Ask students to put on their safety goggles and wear them throughout the
experiment.
9.
Student #1 (Dropper) stands on the chair with the flat, 4in. x 4in. paper in one
hand and the crumpled 4in. x 4in. ball in the other hand, held at the same
height.
10.
Student #2 (Measurer) measures the distance between Student #1 hands and
the floor. This distance is a constant variable. All students record the distance
by completing question 21 on the Leaning Tower of Pisa Worksheet - Part Two.
11.
Student #3 (Timekeeper) is the timekeeper for one object and Student #4
(Timekeeper) is the timekeeper for the other object. Student #3 and Student
#4 will stand on each side of Student #1 who is on the chair ready to drop the
objects.
12.
When Student #2 says “go!” Student #1 lets go of both objects at the same
time while Student #3 and Student #4 will simultaneously start their
stopwatches.
13.
Student #3 and Student #4 stop the stopwatch when the object that they are
watching reaches the ground.
14.
All students will record this information by completing questions 22-23 on their
Leaning Tower of Pisa Worksheet - Part Two.
15.
Ask students to repeat the experiment two more times. Students may practice a
couple of times before recording their results on the Leaning Tower of Pisa
Worksheet - Part Two by completing questions 24-27.
16.
Ask students to decide what the variables were in their experiment by
completing questions 28-29 on the Leaning Tower of Pisa Worksheet - Part
Two.
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17.
Ask students to make a prediction about why their objects did not reach the
ground at the same time and have them hypothesize by completing questions
30-31 on the Leaning Tower of Pisa Worksheet - Part Two.
18.
Once students have tackled with the idea have them reach a conclusion about
objects of same masses but different forms, gravity, and their experiment by
completing questions 32-37 on the Leaning Tower of Pisa Worksheet - Part
Two.
19.
Once students are back in the classroom, ask the groups to share their results
and hypothesizes with the entire class.
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The Leaning Tower of Pisa – Part Three
Different Masses, Different Forms
Description of Activity
In this activity, students will replicate Galileo’s famous Leaning Tower of Pisa experiments
by dropping objects of different masses and different forms timing how long it takes
each object to fall. Students will determine the dependent, independent, and controlled
variables for the experiment and experiment to get their objects to reach the ground at
the same time.
Objectives for The Leaning Tower of Pisa - Part Three
Students will be able to:
1) Identify the dependent, independent, and controlled variables of their experiment.
2) Draw conclusions about the mass and form of an object and the effect of gravity
on such objects.
3) Compare their results of all three experiments and draw a conclusion based on
their collected data.
Materials Needed:
2 Stopwatches per group
2-3 medium size erasers
2-3 markers
1 Pair of safety goggles for each student
1 Pencil for each student
1 Yardstick per group
1 Chair for each group
1 Leaning Tower of Pisa Worksheet – Part Three for each student
Procedure
1.
Tell students that today they will be conducting the third and final part of their
experiment.
2.
Tell students to get in their assigned groups from Part One.
3.
Provide each group with 1 eraser, 2 stopwatches, goggles, a yardstick, a chair,
and the Leaning Tower of Pisa Worksheet - Part Three.
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4.
Have each group measure the mass of their objects using scales in the
classroom. If scales are not available, the teacher can give students the mass
of each object.
5.
Ask students to record the mass of the eraser and the marker by completing
questions 38-39 on the Leaning Tower of Pisa Worksheet - Part Three.
6.
When students have completed questions 38-39 on the Leaning Tower of Pisa
Worksheet - Part Three send them outside to set up their experiments in their
groups.
7.
Ask students to put on their safety goggles and wear them throughout the
experiment.
8.
Student #1 (Dropper) stands on the chair with the eraser in one hand and the
marker in the other hand, held at the same height.
9.
Student #2 (Measurer) measures the distance between Student #1 hands and
the floor. This distance is a constant variable. All students record the distance
by completing question 40 on the Leaning Tower of Pisa Worksheet - Part
Three.
10.
Student #3 (Timekeeper) is the timekeeper for one object and Student #4
(Timekeeper) is the timekeeper for the other object. Student #3 and Student
#4 will stand on each side of Student #1 who is on the chair ready to drop the
objects.
11.
When Student #2 says “go!” Student #1 lets go of both objects at the same
time while Student #3 and Student #4 will simultaneously start their
stopwatches.
12.
Student #3 and Student #4 stop the stopwatch when the object that they are
watching reaches the ground.
13.
All students will record this information by completing questions 41-42 on the
Leaning Tower of Pisa Worksheet - Part Three.
14.
Ask students to repeat the experiment two more times. Students may practice a
couple of times before recording their results on the Leaning Tower of Pisa
Worksheet - Part Three by completing questions 43-46.
15.
Ask students to decide what the variables were in their experiment by
completing questions 47-48 on the Leaning Tower of Pisa Worksheet - Part
Three.
16.
Ask students to make a prediction about why their objects did not reach the
ground at the same time and have them hypothesize by completing questions
49-50 on the Leaning Tower of Pisa Worksheet - Part Three.
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17.
Once students have tackled with the idea have them reach a conclusion about
objects of different masses and different forms, gravity, and their experiment by
completing questions 51-56 on the Leaning Tower of Pisa Worksheet - Part
Three.
18.
Once students are back in the classroom, ask the groups to share their results
and hypothesizes with the entire class.
19.
As a class, write a summary about the Leaning Tower of Pisa experiments by
completing question 57 on the Leaning Tower of Pisa Worksheet – Part Three.
22
RESOURCES AND REFERENCES
The following books and websites were very helpful in the development of this module.
They are also very useful resources in presenting additional material to students. Many
of the websites are interactive and offer many ideas for additional activities to present to
students.
BOOKS
Gilbert, Harry, Smith, G. Diana, Gravity: The Glue of the Universe 1997, Teacher Ideas
Press
Robertson C., William Stop Faking It! Force and Motion 2002, National Science
Teachers Association
WEBSITES
National Science Teachers Association (NSTA) – www.nsta.org
National Aeronautics and Space Administration (NASA) – www.nasa.gov
Star Child - http://starchild.gsfc.nasa.gov/docs/StarChild/whos_who_level2/galileo.html
ACKNOWLEDGEMENTS
I would like give special thanks to my two fifth grade students who graciously provided
some of the artwork for this module. Thank you to Megan Schumann for her picture on
page 7 and thank you to Allan Costa-Block for his picture on page 5.
23
Appendix A
A Brief Biography Of Galileo Galilei
24
A Brief Biography of Galileo Galilei
Galileo Galilei was an Italian physicist and astronomer. He was born in Pisa on February
15, 1564. Galileo's father, Vincenzo Galilei, was a well-known musician. Vincenzo decided
that his son should become a doctor.
In 1581, Galileo was sent to the University of Pisa to study medicine. While a student at
the university, Galileo discovered that he had a talent for mathematics. He was able to
persuade his father to allow him to leave the university to become a tutor in
mathematics. He later became a professor of mathematics.
In 1609, Galileo heard about the invention of the spyglass, a device which made distant
objects appear closer. Galileo used his mathematics knowledge and technical skills to
improve upon the spyglass and build a telescope. Later that same year, he became the
first person to look at the Moon through a telescope and make his first astronomy
discovery. He found that the Moon was not smooth, but mountainous and pitted - just
like the Earth! He subsequently used his newly invented telescope to discover four of the
moons circling Jupiter, to study Saturn, to observe the phases of Venus, and to study
sunspots on the Sun.
Galileo's observations strengthened his belief in Copernicus' theory that Earth and all
other planets revolve around the Sun. Most people in Galileo's time believed that the
Earth was the center of the Universe and that the Sun and planets revolved around it.
The Catholic Church, which was very powerful and influential in Galileo's day, strongly
supported the theory of a geocentric, or Earth-centered, Universe. After Galileo began
publishing papers about his astronomy discoveries and his belief in a heliocentric, or
Sun-centered, Universe, he was called to Rome to answer charges brought against him
by the Inquisition (the legal body of the Catholic Church). Early in 1616, Galileo was
accused of being a heretic, a person who opposed Church teachings. Heresy was a
crime for which people were sometimes sentenced to death. Galileo was cleared of
charges of heresy, but was told that he should no longer publicly state his belief that
Earth moved around the Sun. Galileo continued his study of astronomy and became
more and more convinced that all planets revolved around the Sun. In 1632, he
published a book that stated, among other things, that the heliocentric theory of
Copernicus was correct. Galileo was once again called before the Inquisition and this
time was found guilty of heresy. Galileo was sentenced to life imprisonment in 1633.
Because of his age and poor health, he was allowed to serve his imprisonment under
house arrest. Galileo died on January 8, 1642.
25
Appendix B
The Leaning Tower of Pisa Worksheets –
Part One, Part Two, and Part Three
Student Edition
26
The Leaning Tower of Pisa Worksheet Part One
My group members are _______________________________________________________________
Student #1 _____________________________ Dropper
Student #2 ____________________________ Measurement
Student #3 ____________________________ Timekeeper
Student #4 ____________________________ Timekeeper
OBJECT
1.
Leaf
2.
Rock
MASS (g)
3. Distance between Student #1’s hands and the ground = _______________________________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
4.
5.
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
6.
7.
1
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
8.
9.
10.
11. What variable in your experiment was the hardest to control? Why?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
12. Why do you think your objects did not reach the ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
13. What can you hypothesize about your experiment?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
2
14. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
______________________________________________________________________________________
______________________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
15. What were the results of your experiment?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
16. What conclusion can you make about your experiment?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
17. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
18. Did you get the same results that Galileo did when he conducted this experiment? Why or why not?
__________________________________________________________________________
__________________________________________________________________________
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__________________________________________________________________________
3
NOTES
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4
The Leaning Tower of Pisa Worksheet Part Two
OBJECT
MASS (g)
19.
4in. x 4in. paper (flat)
20.
4in. x 4in. paper (crumpled)
21. Distance between Student #1’s hands and the ground = _______________________________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
22.
23.
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
24.
25.
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
26.
27.
5
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
28.
29. What variable in your experiment was the hardest to control? Why?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
30. Why do you think your objects did not reach the ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
31. What can you hypothesize about your experiment and the different forms that your objects had?
______________________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
______________________________________________________________________________________
32. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
6
33. What were the results of your experiment?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
34. What conclusion can you make about your experiment relating to the different forms of objects that
have the same mass?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
35. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
36. How do your results from this experiment compare to the results of your first experiment? Are there
any similarities or differences between your first and second experiments?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
37. Did you get the same results that Galileo did when he conducted this experiment? Why or why
not?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
7
NOTES
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8
The Leaning Tower of Pisa Worksheet Part Three
OBJECT
38.
Eraser
39.
Marker
MASS (g)
40. Distance between Student #1’s hands and the ground = _______________________________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
41.
42.
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
43.
44.
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
45.
46.
9
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
47.
48. What variable in your experiment was the hardest to control? Why?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
49. Why do you think your objects did not reach the ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
50. What can you hypothesize about your experiment and the different objects that you had?
______________________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
______________________________________________________________________________________
51. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
10
52. What were the results of your experiment?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
53. What conclusion can you reach about your experiment relating to the different forms and different
masses of objects?
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
54. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
55. How do your results from this experiment compare to the results of your second experiment? Are
there any similarities or differences between your second and third experiments?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
56. Did you get the same results that Galileo did when he conducted his experiment? Why or why not?
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
__________________________________________________________________________
57. Write a summary of the Leaning Tower of Pisa experiments on a separate piece of paper.
11
NOTES
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12
Appendix C
The Leaning Tower of Pisa Worksheets –
Part One, Part Two, and Part Three
Teacher Edition
39
The Leaning Tower of Pisa Worksheet Part One
My group members are _______________________________________________________________
Student #1 _____________________________ Dropper
Student #2 ____________________________ Measurement
Student #3 ____________________________ Timekeeper
Student #4 ____________________________ Timekeeper
OBJECT
MASS (g)
1.
Leaf
0. 7 grams (answers will vary)
2.
Rock
1.2 grams (answers will vary)
3. Distance between Student #1’s hands and the ground = ______1 meter (answers will vary)________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
4.
Medium size leaf
1.2 seconds (answers will vary)
5.
Half-dollar size rock
0.7 seconds (answers will vary)
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
6.
Medium size leaf
1.5 seconds (answers will vary)
7.
Half-dollar size rock
0.5 seconds (answers will vary)
1
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
8.
Medium size leaf
1.6 seconds (answers will vary)
9.
Half-dollar size rock
0.8 seconds (answers will vary)
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
distance from the ground
controlled
leaf
independent
rock
independent
time
dependent
10.
11. What variable in your experiment was the hardest to control? Why?
The variable in our experiment that was the hardest to control was the distance from the ground because
it was hard for Student #1 to keep their hands up in the same position for each of the three test drops.
(Answers will vary).
12. Why do you think your objects did not reach the ground at the same time?
I think that our objects did not reach the ground at the same time because of the amount of air
resistance that the leaf encountered. (Answers will vary).
13. What can you hypothesize about your experiment?
I hypothesize that the objects in our experiment did not reach the ground at the same time because of
air resistance. (Answers will vary).
14. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
My group members and I had some trouble accurately recording the time for our objects dropping
because one timekeeper would stop the stopwatch too early and one timekeeper would stop the
stopwatch too late. I think that affected the results of our experiment. (Answers will vary).
2
15. What were the results of your experiment?
In our first test drop, the rock reached the ground first at 0.7 seconds, while the leaf reached the ground
at 1.2 seconds. In our second test drop, the rock reached the ground first at 0.5 seconds, while the leaf
reached the ground at 1.5 seconds. In our third test drop, the rock reached the ground first at 0.8
seconds, while the leaf reached the ground at 1.6 seconds. (Answers will vary depending on experiment
results).
16. What conclusion can you make about your experiment?
In all three test drops, the rock reached the ground before the leaf even though the times were not the
same for every test drop. My conclusion is that the rock will reach the ground first because it is less
susceptible to air resistance. (Answers will vary depending on experiment results).
17. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
No, my group was not able to get the objects to reach the ground at the same time. My group was not
able to figure out how to get the leaf to reach the ground at the same time as the rock. We were not
able to eliminate the air resistance that the leaf encountered. (Answers will vary depending on
experiment results).
18. Did you get the same results that Galileo did when he conducted this experiment? Why or why not?
No, we were not able to get the same results that Galileo did when he conducted this experiment.
Galileo was able to eliminate air resistance as a factor in his experiment but my group was not able to
do so. (Answers will vary depending on experiment results).
3
NOTES
Notes can be taken about results, conclusions, questions, or comments students have while conducting
their experiments.
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4
The Leaning Tower of Pisa Worksheet Part Two
OBJECT
MASS (g)
19.
4in. x 4in. paper (flat)
0.6 grams (answers will vary)
20.
4in. x 4in. paper (crumpled)
0.6 grams (answers will vary)
21. Distance between Student #1’s hands and the ground = _____1 meter (answers will vary)________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
22.
Flat paper
2.4 seconds (answers will vary)
23.
Crumpled paper
1.5 seconds (answers will vary)
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
24.
Flat paper
2.7 seconds (answers will vary)
25.
Crumpled paper
1.6 seconds (answers will vary)
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
26.
Flat paper
2.3 seconds (answers will vary)
27.
Crumpled paper
1.4 seconds (answers will vary)
5
28.
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
distance from the ground
controlled
flat paper
independent
crumpled paper
independent
time
dependent
29. What variable in your experiment was the hardest to control? Why?
The variable in our experiment that was the hardest to control was the time. It was difficult to get an
accurate measurement of time because the timekeepers would stop the time too soon or too late and
that gave us inaccurate results. (Answers will vary and may or may not be the same as Part One).
30. Why do you think your objects did not reach the ground at the same time?
Our objects did not reach the ground at the same time because it took a really long time for the flat
piece of paper to fall to the ground. (Answers will vary).
31. What can you hypothesize about your experiment and the different forms that your objects had?
I hypothesize that the different forms of the paper had a lot to do with which object reached the ground
first. The object with the more compact form, the crumpled piece of paper, always reached the ground
first because it was more compacted and had a smaller amount of air resistance than the flat piece of
paper. (Answers will vary).
32. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
My group members and I had some trouble accurately recording the time for our objects dropping
because one timekeeper would stop the stopwatch too early and one timekeeper would stop the
stopwatch too late. I think that affected the results of our experiment. (Answers will vary and may or
may not be the same as Part One).
33. What were the results of your experiment?
In our first test drop, the crumpled paper reached the ground first at 1.5 seconds, while the flat paper
reached the ground at 2.4 seconds. In the second test drop, the crumpled paper reached the ground
first at 1.6 seconds, while the flat paper reached the ground at 2.7 seconds. In the third test drop, the
crumpled paper reached the ground first at 1.4 seconds, while the flat paper reached the ground at 2.3
seconds. (Answers will vary depending on experiment results).
6
34. What conclusion can you make about your experiment relating to the different forms of objects that
have the same mass?
I can conclude that the mass of the objects in my experiment did not make a difference in the results
that I received. However, the form of the objects played a big role in the results of my experiment. The
more spread out the form is the longer it takes to reach the ground and the more air resistance the
object has. The more compact the form is the shorter it takes to reach the ground and the less air
resistance the object has. (Answers will vary depending on experiment results).
35. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
My group did figure out how to get the objects to reach the ground at the same time. In order to get
the objects to reach the ground at the same time we crumpled our previously flat piece of paper and
dropped it and the other crumpled paper at the same time. We were able to get relatively close to
having them reach the ground at the same time. We are aware that this changed the experiment but
were able to get the objects to reach the ground at the same time. (Answers will vary depending on
experiment results).
36. How do your results from this experiment compare to the results of your first experiment? Are there
any similarities or differences between your first and second experiments?
My results from Part Two were similar to my results in Part One. The heavier, more compact objects
were the objects to reach the ground first (the rock and the crumpled piece of paper). The lighter
objects, the objects that were more spread out (the leaf and the flat piece of paper) were the objects to
reach the ground second. (Answers will vary depending on experiment results).
37. Did you get the same results that Galileo did when he conducted this experiment? Why or why
not?
No, we were not able to get the same results that Galileo got when we first conducted our experiment in
Part Two. When we varied from the experiment and crumpled both pieces of paper we were able to get
both objects to reach the ground at relatively the same time. I think this happened because both
objects were similar in shape, size, and mass. (Answers will vary depending on experiment results).
7
NOTES
Notes can be taken about results, conclusions, questions, or comments students have while conducting
their experiments.
__________________________________________________________________________
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8
The Leaning Tower of Pisa Worksheet Part Three
OBJECT
MASS (g)
38.
Eraser
5 grams (answers will vary)
39.
Marker
3 grams (answers will vary)
40. Distance between Student #1’s hands and the ground = ______1 meter (answers will vary)________
FIRST TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
41.
Eraser
1.1 seconds (answers will vary)
42.
Marker
1.8 seconds (answers will vary)
SECOND TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
43.
Eraser
1 second (answers will vary)
44.
Marker
1.3 seconds (answers will vary)
THIRD TEST DROP
OBJECT
TIME TAKEN TO REACH THE GROUND
45.
Eraser
1.2 seconds (answers will vary)
46.
Marker
1.5 seconds (answers will vary)
9
47.
VARIABLE
DEPENDENT, INDEPENDENT, OR CONTROLLED?
Distance from the ground
controlled
Eraser
independent
Marker
independent
Time
dependent
48. What variable in your experiment was the hardest to control? Why?
The variable in our experiment that was the hardest to control was the time because the objects reached
the ground so fast that the timekeepers had a difficult time accurately stopping the stopwatches.
(Answers may vary and may or may not be the same as Part One and Part Two).
49. Why do you think your objects did not reach the ground at the same time?
I think that the objects did not reach the ground at the same time because the different forms of the
objects and how much air resistance each object had.
50. What can you hypothesize about your experiment and the different objects that you had?
I hypothesize that the different forms and different masses of our objects had an affect on the results of
our experiment. From the previous experiment, I can hypothesize that the form of the object had an
impact on how soon it reached the ground.
51. Were you and your group members able to accurately record the time for the objects dropping?
Why or why not?
My group members and I were not able to accurately record the time for the objects dropping because
they dropped so fast that the timekeepers had trouble accurately stopping the stopwatches. I believe that
the third test drop was the most accurate because the timekeepers had time to practice stopping the
stopwatches.
52. What were the results of your experiment?
In our first test drop, the eraser reached the ground first at 1.1 seconds, while the marker reached the
ground at 1.8 seconds. In our second test drop, the eraser reached the ground first at 1 second, while
the marker reached the ground at 1.3 seconds. In the third test drop, the eraser reached the ground first
at 1.2 seconds, while the marker reached the ground at 1.5 seconds. (Answers will vary depending on
experiment results).
10
53. What conclusion can you reach about your experiment relating to the different forms and different
masses of objects?
I can conclude that the forms of the objects had some bearing on which object reached the ground first.
The masses of the objects in this experiment were very close so I am not sure it made much of
difference in the results of the experiment. I can conclude though that the form of the objects
determined which reached the ground first because of the amount of air resistance each form of the
object had. (Answers will vary depending on experiment results and may or may not be the same as
Part One and Part Two).
54. Did your group figure out how to get the objects to reach the ground at the same time? If yes,
what did you do to make this happen? If no, why was your group unable to get the objects to reach the
ground at the same time?
My group was not able to figure out how to get the objects to reach the ground at the same time but
we came pretty close. We were not able to get them to reach the ground at the same time because we
could not figure out how to manipulate the items in order to get them to have approximately the same
amount of air resistance. (Answers will vary depending on experiment results and may or may not be the
same as Part One and Part Two).
55. How do your results from this experiment compare to the results of your second experiment? Are
there any similarities or differences between your second and third experiments?
My results from this experiment compare to the results of my second experiment in Part Two because
the objects were very close to reaching the ground at the same time. The object with the more compact
form reached the ground first in Part Two (the crumpled paper) and in Part Three (the eraser). (Answers
will vary depending on experiment results and may or may not be the same as Part One and Part Two).
56. Did you get the same results that Galileo did when he conducted his experiment? Why or why not?
I believe that my group and I were very close to achieving the same results Galileo achieved when
conducting his experiments. In Part Two and Part Three we were able to get the objects to reach the
ground approximately at the same time, being off by just a couple tenths of a second. I think we were
able to minimize the air resistance in our experiment in Part Two by being able to manipulate the form
of the objects, which allowed us to have the objects reach the ground at approximately the same time.
57. Write a summary of the Leaning Tower of Pisa experiments.
The Leaning Tower of Pisa experiments investigate how gravity impacts the time it takes an object to
reach the ground. Through a series of three experiments we investigate what factors affect the time it
takes different objects to reach the ground and why they reach the ground at different times when
science and math prove that all objects should reach the ground at the same time, according to Galileo
Galilei.
In the Leaning Tower of Pisa – Part One, we had to drop a leaf and a rock from the same
distance and record which object would reach the ground first. In our first test drop, the rock reached
the ground first at 0.7 seconds, while the leaf reached the ground at 1.2 seconds. In our second test
drop, the rock reached the ground first at 0.5 seconds, while the leaf reached the ground at 1.5 seconds.
In our third test drop, the rock reached the ground first at 0.8 seconds, while the leaf reached the
ground at 1.6 seconds. We concluded that the rock was able to reach the ground first because it had
more mass than the leaf and also that the rock had less air resistance than the leaf.
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In the Leaning Tower of Pisa – Part Two, we had to drop a flat piece of paper and a crumpled
piece of paper from the same distance and record which object would reach the ground first. In our first
test drop, the crumpled paper reached the ground first at 1.5 seconds, while the flat paper reached the
ground at 2.4 seconds. In the second test drop, the crumpled paper reached the ground first at 1.6
seconds, while the flat paper reached the ground at 2.7 seconds. In the third test drop, the crumpled
paper reached the ground first at 1.4 seconds, while the flat paper reached the ground at 2.3 seconds.
From Part Two, we concluded that the mass of the objects did not make a difference in our experiment.
We did figure out that the form of the object had a lot to do with the results of our experiment. We
learned that the more spread out the form is the more air resistance the object has causing it to take
longer to reach the ground. We varied our experiment so that both pieces of paper would have a
compact form (crumpled into a ball) and found that when the forms were the same and had the same
amount of air resistance, the objects reached the ground at relatively the same time.
In the Leaning Tower of Pisa – Part Three, we had to drop an eraser and a marker from the
same distance and record which object would reach the ground first. In our first test drop, the eraser
reached the ground first at 1.1 seconds, while the marker reached the ground at 1.8 seconds. In our
second test drop, the eraser reached the ground first at 1 second, while the marker reached the ground
at 1.3 seconds. In the third test drop, the eraser reached the ground first at 1.2 seconds, while the
marker reached the ground at 1.5 seconds. From Part Three, we concluded that form was still a big
factor in the objects reaching the ground at the same time. In this experiment we were unable to
manipulate the forms of the objects in order to get them to have the same amount of air resistance. As
a result, we could not get the two objects to reach the ground at the same, though we did come close
because they both had relatively compact forms. The overall conclusion that I reached for these
experiments is that all objects will fall at the same rate and reach the ground at the same time if there
were no air resistance. The reason that objects do appear to fall at different rates is air resistance.
Galileo Galilei was correct in his Leaning Tower of Pisa experiments when he stated that all objects
would fall at the same rate and hit the ground at the same time. (Answers will vary, but should include
results from all three parts).
NOTES
Notes can be taken about results, conclusions, questions, or comments students have while conducting
their experiments.
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