Roller Coaster
by Curt Wyman
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Curt Wyman PBI April 29, 2005 Roller Coaster Introduction I. Abstract: High
school physics starts with the laws of motion. This area covers about ten weeks of instruction and begins
early in the school year and includes widely divergent concepts that
include velocity, acceleration,
weight, friction, Newton’s 2nd Law (F=ma), potential energy,
kinetic energy, conservation of energy, momentum, and Newton’s 3rd
Law (inertia). A roller coaster project provides a good platform
to bring all of these concepts together. The material can be covered in the normal manner but with
all of the illustrative examples involving roller coasters. In addition, the students can be
assigned to build a small scale roller coaster either physically or with a
software model in order to give them hands on experience with the application
of the laws of motion. Our proposal is to assign a physical model to be
built to the specifications of
Paramount Great America Physics Day competition. They have a well defined project
format for a physically small model that is convenient for storage and
transport. A school wide
competition will be held among the schools three physics classes and one team
would be selected to travel to California for the Physics Day competition. Support is required for construction materials
and for travel expenses for the winning team. The materials for the roller coasters are basic and much
of it can be built with standard art supplies. However, the tracks and cars require precision and must be
purchased from a building supply company. We estimate a cost of $100 per project and eighteen
projects for the three classes or $1800 plus $800 to go toward travel
expenses for the winning team to go to California for the Paramount Great
America Physics Day competition. 2. Description:
Students will build a model roller coaster that will be fit into a space just 75cm long x
75 cm wide x 100 cm high. It
will be a gravity only model – no motors or magnets. The “cars” will be marbles or
ball bearings and the tracks will be plastic tubes that have been cut so that
they are open on the top so that the ball can fall off if the design is
faulty. The degree of
“open-ness” of the track is a factor in the grading. The
project will start during the first six-week grading period and will conclude
in the third six-week period.
One class period per week will be used for roller coaster design and
construction. It is expected that
the students will supplement this with additional time outside of class,
especially toward the end of the project. The
models with be judged based on the Paramount criteria: Technical features –
loops, hills, workmanship, and innovation, Theme – creativity and
marketability, and perceived rider enjoyment. The student teams will also be graded on their technical
explanation of the ride using the laws of motion. For example, how the potential energy at the beginning of
the ride is calculated and how it translates into velocity and gravitational
forces that contribute so much to the excitement of the ride. 3. Focus
Question: What makes a roller coaster exciting
and how would you design a roller coaster to maximize the excitement? How would you test
the design with a scale model?
You would need to first define the features of the roller coaster in
terms of the physical laws of motion, acceleration, velocity, energy,
etc. Then rate the various
features as to their excitement content. This will give you a good foundation for your
design. 4. Overall Goals of the project: In
this project, students will design and build a model roller coaster. A roller coaster makes a great
vehicle for studying the laws of motion. Building a model that will be judged on the basis of
perceived excitement will give the students hands-on experience with the laws
of motion and enable them to get a thorough understanding of how they
behave. Specifically, here are
the goals of the project:
5. Rationale:
Imagine you are in a roller coaster just starting down the highest,
very steep hill. As you begin
the decent, you release a tennis ball that you brought with you. As you fall, you are almost
weightless, and you watch the tennis ball magically float in front of you as
it slowly moves toward the back and floor of the car. High school Physics is often viewed as a
disconnected jumble of complex ideas.
Students can be intimidated and overwhelmed with the wide range of
concepts that need to be covered to meet the Texas TEKS. A bad experience in high school
physics can cause students to back away from technical majors in
college. This problem
causes American high tech companies to have to rely on graduates from non-US
universities in order to meet their engineering staffing requirements. The laws of motion are a good example of the
complexity of physics concepts.
Many students come into physics thinking that heavier objects will
fall faster than lighter objects.
They cannot connect the speed that a ball will develop rolling down a
ramp with the potential energy that the ball had at the top of the ramp. A roller coaster integrates virtually
all of the laws of motion into a cohesive system that can be understood as a
single model. Imagine the enthusiasm and confidence that come
from the ability to explain the floating tennis ball to your friends. The completion of a successful model
creates will foster an appreciation for the application of technical
concepts. Students will be
more likely to pursue technical degrees in college. We will be tracking seniors’ college plans in the
future as described in the Description section. 6. Background: A roller coaster is a
carnival ride in a car that starts at a high point on a track and ends
somewhat later at a lower point with lots of twists, turns, ups, downs, and
maybe loops in between. The car
does not get any additional energy after it is pulled up to the top of the
hill by a motor. All of the
motion comes from the conversion of the initial potential energy of the car
into kinetic energy and velocity as the car goes around the track. There are three key
excitement features to a roller coaster: Free fall, acceleration, and inversion. The primary cause for
excitement of the ride is acceleration.
Velocity is boring. As
Galileo taught us, and Einstein and Newton re-affirmed, you cannot feel a
constant velocity. As Newton’s
First Law states, an object at rest or in motion, does not change unless
acted on by an unbalanced force.
Acceleration causes force, F=ma.
You can feel and even measure acceleration as you ride a roller
coaster or any other vehicle. So the parts of the
roller coaster that are the most exciting are the parts that have the most
acceleration. We have linear
acceleration downward due to the acceleration of gravity. The free fall of the car at the top
of the first hill produces an almost weightless condition that is very exciting. The deceleration at the bottom of the hill as riders are
pushed down into their seats is also thrilling. Another key thrill
factor in the roller coaster is angular acceleration that is felt when the
car makes sharp turns. The
riders’ bodies try to continue in a straight line and are pushed hard into
the side of the car as it turns sharply. Angular acceleration is a function of the radius of the
turn and the tangential velocity.
The harder the push into the side of the car, or into the person next
to you, the higher the excitement. The third thrill feature
is inversion – going upside down when the roller coaster car goes through a
loop. During this action,
the riders are dis-oriented by being upside down, and at the same time, they
again approach weightlessness as the angular acceleration pushing them “up”
into their seats is almost canceled by the force from gravity pulling them
“down.” So with a roller
coaster, we have a great example to give the students examples of the key
concepts of physical motion that they can see and feel. We also have the
integration of the various aspects of motion that determine if the roller
coaster will stay on the track, make it up the next hill, how fast it will
go, and whether or not it will make it around the track. The key element is the
conservation of energy back and forth between Potential and Kinetic energy
throughout the ride. The
translation from the initial potential energy to kinetic energy as the roller
coaster accelerates down the track, and decelerates up the next hill. One of the main
analytical tools that we will learn to use is the Free Body Diagram. Using this vector analysis technique
will enable students to resolve the various forces that are acting on the
roller coaster at any given point in time and determine the level of
excitement. This will involve
trigonometric translations of the forces into their x and y components. We will review this area for the
students and they will get plenty of practice with it during the
project. They will have a deep
understanding of this fundamental concept by the end of the project. 7. Standards Addressed: TEKS addressed: (A) generate and interpret graphs describing
motion including the use of real-time technology; (B) analyze examples of
uniform and accelerated motion including linear, projectile, and circular; (C) demonstrate the
effects of forces on the motion of objects; Snapshot 4 (A) •
Generate and interpret graphs of
velocity/time, position/time. Snapshot 4 (B) •
Design and illustrate an amusement park ride featuring
accelerated motion. Justify the safety and thrill components. Snapshot 4 (C) •
Design and conduct demonstrations illustrating Newton's
laws of motion, such as rolling motion from roller blade wheels, pulling a
tablecloth out from under dishes on a table, and the stopping distance of a
car. Snapshot 4 (D) •
Draw a free-body diagram for an
everyday situation such as the raising of a flag. Identify the forces present
and describe their effects on the motion of the object. Snapshot 4 (E) •
Describe and illustrate the motion of
a ball rolled across a merry-go-round from two frames of reference: on the
merry-go-round and off the merry-go-round. 8. Assessment: Formative Assessment: Formative assessment
will consist mainly of asking good verbal questions in a logical sequence
that will enable the students to construct their own understanding of the
topic at hand. The questioning process will be utilized during labs, classwork, and
discussion periods. The time
when it is most effective is when a student comes to the teacher with a
question. The questioning strategy that will be used will be patterned after
the strategy presented by Penick, Crow and Bonnstatter in their article,
“Questions are the Answer,” that was published in the January, 1996 issue of The
Science Teacher.” Here are the key elements of the strategy: Which questions to ask? When to ask them? What order to ask them
in? Where to begin
questioning? How one question easily
leads to another? Where the questions are
leading? Clear, non-threatening
questions. Teaching strategy must
insure that student can answer the first pivotal question. One possible logical
order for categories of questions:
HRASE History
- Getting Students to talk is always one of your goals. What did they do, see? Relationships - Seeking patterns and
relationships Applications - Applying
knowledge is a true test of understanding. Speculation - Constants,
variables and evidence. Explanation - Hardest task in science: Communicate an idea to clarify the
nature of
the phenomenon and how it occurs. Avoid the ultimate and
threatening “WHY” questions. Teaching goal: To help students develop new, more
accurate conceptions to replace their old ones. Develop: Create an environment where a concept
is available for exploration, analysis and consideration. Language precedes
logic. As individuals learn to
verbalize about a phenomenon, they build logical structures and ways of thinking
about it. Students copy your
behavior. Demonstrate a logical
problem solving process. Summative Assessment: The summmative
assessment of the students work on this project consists of the grade plan
for the six weeks. The grades
during this period will be equally weighted between the standard classroom
activities like homework and tests and the project activities like the
milestone completions, the performance of the final model and the
presentation of the final paper.
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