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Partial design procedure
class Level: 7 (6 – 8) Time Required: 30 minutes topic Areas:
Physical science

NGSS power Expectations:


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Students discover the physics exploited by engineers in designing today"s roller coasters, consisting of potential and also kinetic energy, friction and gravity. First, they learn that every true roller coasters are completely driven by the pressure of gravity and that the conversion in between potential and kinetic energy is essential to all roller coasters. Second, they think about the duty of friction in slowing under cars in roller coasters. Finally, they study the acceleration that roller coaster cars together they travel roughly the track. Throughout the linked activity, college student design, build and also analyze design roller coasters castle make making use of foam tubing and also marbles (as the cars). This engineering curriculum to adjust to next Generation science Standards (NGSS).

As the dare drop, potential energy listed by the chain lift on the left is converted to kinetic energy.

Engineering link

Students check out the most simple physical ethics of roller coasters, i beg your pardon are an essential to the initial design process for engineers who develop roller coasters. Castle learn about the possibilities and limitations that roller coasters within the paper definition of energy conservation, frictional losses and other physics principles. ~ the lesson, students should be able to analyze the activity of any type of existing gravity-driven coaster and also design the basics of their own model roller coasters.

learning Objectives

After this activity, students must be able to:

Explain why the is crucial for engineers to know just how roller coasters work.Explain in physics terms exactly how a roller coaster works.Discuss the results of gravity and friction in the paper definition of their roller coaster designs.Use the principle of conservation of power to describe the layout the roller coasters.Identify point out in a roller coaster monitor at i beg your pardon a vehicle has preferably kinetic energy and also maximum potential energy.Identify clues in a roller coaster track whereby a car experiences much more or much less than 1 g-force.Identify point out in a roller coaster track wherein a car speeds up and decelerates.

Educational requirements

every lesson or task is correlated to one or much more K-12 science, technology, engineering or mathematics (STEM) educational standards.

every 100,000+ K-12 STEM standards covered in room collected, maintained and also packaged by the Achievement standards Network (ASN), a job of D2L (

In the ASN, standards space hierarchically structured: very first by source; e.g., through state; within source by type; e.g., scientific research or mathematics; within kind by subtype, climate by grade, etc.

NGSS: next Generation scientific research Standards - scientific research
NGSS power Expectation science & design Practices Disciplinary Core ideas Crosscutting ideas

MS-PS3-5. Construct, use, and present arguments to support the case that as soon as the kinetic power of an item changes, power is moved to or from the object. (Grades 6 - 8)

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This lesson focuses on the complying with three Dimensional Learning facets of NGSS:
Science expertise is based upon reasonable and theoretical connections between evidence and also explanations.

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When the motion power of an object changes, over there is inevitably some other readjust in power at the exact same time.

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Energy might take various forms (e.g. Power in fields, heat energy, energy of motion).

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center School task
Building Roller Coasters

Students develop their own small-scale version roller coasters using pipe insulation and marbles, and then analysis them making use of physics ethics learned in the associated lesson. They study conversions between kinetic and potential energy and also frictional effects to style roller coasters that are compl...

structure Roller Coasters

High institution Lesson
A tale of Friction

High college students find out how designers mathematically architecture roller coaster routes using the strategy that a curved path have the right to be approximated by a succession of many brief inclines. Lock apply straightforward calculus and the work-energy theorem because that non-conservative forces to quantify the friction follow me a curve...

A tale of Friction
center School great
Kinetic and also Potential power of Motion

Students are introduced to both potential energy and kinetic power as forms of mechanically energy. A hands-on task demonstrates exactly how potential power can readjust into kinetic power by swinging a pendulum, depicting the ide of conservation of energy.

Kinetic and also Potential power of movement
High School task
Mathematically making a frictional Roller Coaster

Build a tiny roller coaster prototype the end of foam pipeline wrap insulation and also marbles, but use calculus and physics in the design! This real-world engineering difficulty applies useful mathematics to check small-sized models top top a actual track.

Mathematically making a friction Roller Coaster

Pre-Req knowledge

An understanding of forces, an especially gravity and friction, and also some familiarity through kinetic and potential energy. An expertise of Newton"s second law of activity and an easy motion principles such as position, velocity and acceleration.


Today"s lesson is all around roller coasters and also the science and also engineering behind them. Prior to we start talking around physics, though, I"d like you come share some of your experiences through roller coasters. (Listen come a couple of students explain their favourite roller coasters. Allude out some of the distinctive features of each coaster, such as hills and loops, that relate come the lesson.)

Does anyone know how roller coasters work? You might think that the roller coaster cars have actually engines inside them that press them follow me the track favor automobiles. While that is true of a few roller coasters, most use gravity to move the cars follow me the track. Do any of friend remember talk a roller coaster that started out through a large hill? If girlfriend looked closely at the roller coaster track (on i beg your pardon the cars move), friend would see in the center of the monitor on that an initial hill, a chain. You can have also have felt it "catch" come the cars. That chain hooks to the bottom that the cars and also pulls them come the height of that first hill, i m sorry is constantly the highest point on a roller coaster. As soon as the cars space at the height of the hill, they room released native the chain and also coast with the rest of the track, i beg your pardon is where the name roller coaster comes from.

Figure 1. Example setup for rapid lesson demo.

What do you think would take place if a roller coaster had actually a hill in the center of the track the was taller 보다 the first hill the the roller coaster? would certainly the cars be able to make it up this larger hill using just gravity? (Conduct a short demonstration to prove the point. Take a piece of foam pipeline insulation reduced in half lengthwise and also shape it right into a roller coaster by taping it to classroom objects such together a desktop and a textbook, as presented in figure 1. Then, making use of marbles to represent the cars, show students that the first hill that a roller coaster need to be the tallest allude or the cars will not reach the finish of the track. Describe the structure Roller Coasters task for extr instructions.)

(Next, pat off various other students" roller coaster experience to relocate the great forward, covering the material noted in the lesson Background and Vocabulary sections. Because that example, talk around the suggest in the roller coaster whereby you travel the fastest, how cars endure loops and also corkscrews, and also what causes passengers to feeling weightless or an extremely heavy at certain points in the roller coaster. The stimulate in which you teach these points, and possibly more, is not crucial to the lesson. Also, it may be more engaging because that the students come ask questions based upon their experiences v roller coasters and also let those concerns lead the lesson from one point to the next. All of these points deserve to be demonstrated making use of the foam tubing and marbles, so use them often to show the great concepts.)

lesson Background and Concepts for Teachers

The underlying principle of every roller coasters is the regulation of preservation of energy, which defines how energy can neither be lost nor created; energy is only transferred native one form to another. In roller coasters, the two creates of energy that room most necessary are gravitational potential energy and kinetic energy. Gravitational potential power is the power that an object has because of that is height and also is same to the object"s mass multiplied by its elevation multiplied by the gravitational continuous (PE = mgh). Gravitational potential energy is greatest at the highest point of a roller coaster and least at the shortest point. Kinetic power is energy things has since of that is motion and is equal to one-half multiplied by the mass of things multiplied through its velocity squared (KE = 1/2 mv2). Kinetic energy is biggest at the lowest point of a roller coaster and least in ~ the highest point. Potential and also kinetic energy can it is in exchanged for one another, so at specific points the dare of a roller coaster may have just potential power (at the height of the an initial hill), simply kinetic energy (at the lowest point) or some mix of kinetic and also potential energy (at all various other points).

The an initial hill of a roller coaster is always the highest suggest of the roller coaster because friction and also drag immediately begin robbing the vehicle of energy. In ~ the height of the an initial hill, a car"s power is almost entirely gravitational potential power (because that velocity is zero or virtually zero). This is the maximum power that the automobile will ever have throughout the ride. That energy can end up being kinetic power (which that does in ~ the bottom that this hill when the auto is relocating fast) or a combination of potential and kinetic energy (like in ~ the top of smaller sized hills), however the full energy that the auto cannot be much more than it to be at the height of the an initial hill. If a taller hill were placed in the center of the roller coaster, it would represent more gravitational potential power than the very first hill, so a auto would not have the ability to ascend to the optimal of the higher hill.

Cars in roller coasters constantly move the fastest at the bottom of hills. This is pertained to the first concept in that at the bottom that hills every one of the potential energy has to be converted come kinetic energy, which method more speed. Likewise, cars constantly move the slowest in ~ their highest point, i m sorry is the height of the very first hill.

A web-based simulation demonstrating the relationship between vertical position and also the rate of a automobile in a roller coaster miscellaneous shapes is provided at the MyPhysicsLab Roller Coaster Physics Simulation. This website offers numerical data for simulated roller coaster of assorted shapes.

Friction exist in every roller coasters, and it takes away from the beneficial energy detailed by roller coaster. Friction is caused in roller coasters through the rubbing the the car wheels top top the track and by the rubbing of wait (and occasionally water!) against the cars. Friction turns the helpful energy the the roller coaster (gravitational potential energy and also kinetic energy) into warmth energy, which offer no purpose associated with propelling cars follow me the track. Friction is the reason roller coasters cannot go on forever, for this reason minimizing friction is just one of the biggest obstacles for roller coaster engineers. Friction is additionally the factor that roller coasters can never regain their maximum height after the initial hill uneven a 2nd chain lift is integrated somewhere on the track.

Cars deserve to only endure loops if lock have sufficient speed in ~ the height of the loop. This minimum speed is described as the an important velocity, and is equal the square source of the radius that the loop multiply by the gravitational constant (vc = (rg)1/2). While this calculation is too complicated for the vast bulk of saturday graders, they will certainly intuitively understand that if a car is not moving fast enough at the top of a loop it will certainly fall. Because that safety, most roller coasters have wheels top top both political parties of the track to stop cars native falling.

Most roller coaster loops are not perfectly circular in shape, however have a teardrop shape dubbed a clothoid. Roller coaster designers discovered that if a loop is circular, the rider experiences the greatest pressure at the bottom the the loop once the cars are moving fastest. After many riders sustained neck injuries, the looping roller coaster was abandoned in 1901 and restored only in 1976 once Revolution at six Flags Magic Mountain came to be the very first modern looping roller coaster using a clothoid shape. In a clothoid, the radius that curvature the the loop is widest at the bottom, reduce the force on the riders when the cars move fastest, and also smallest in ~ the top once the cars space moving relatively slowly. This enabled for a smoother, more secure ride and also the teardrop form is now in use in roller coasters around the world.

Riders may experience weightlessness at the tops of hills (negative g-forces) and feel hefty at the bottom of hills (positive g-forces). This feeling is caused by the adjust in direction of the roller coaster. At the optimal of a roller coaster, the vehicle goes from relocating upward to flat to moving downward. This readjust in direction is known as acceleration and also the acceleration provides riders feel as if a pressure is exhilaration on them, pulling them the end of their seats. Similarly, in ~ the bottom of hills, riders go from relocating downward to flat to moving upward, and also thus feel as if a pressure is pushing them down right into their seats. These forces can be referred to in terms of gravity and also are referred to as gravitational forces, or g-forces. One "g" is the force applied by gravity while was standing on earth at sea level. The human being body is used to present in a 1 g environment. If the acceleration of a roller coaster in ~ the bottom of a hill is same to the acceleration of gravity (9.81 m/s2), another g-force is created and, when included to the typical 1 g, we get 2gs. If the acceleration in ~ the bottom of the hill is double the acceleration of gravity, the overall force is 3 gs. If this acceleration acts rather at the peak of a hill, it is subtracted from the standard 1 g. In this way, it can be less than 1 g, and it can even be negative. If the acceleration at the peak of a hill were same to the acceleration of gravity, the as whole force would be zero gs. If the acceleration at the optimal of the hill were double the acceleration the gravity, the resulting all at once force would be an adverse 1 g. At zero gs, a driver feels fully weightless and at negative gs, they feel as though a pressure is lifting them out of the seat. This principle may it is in too advanced for students, yet they should understand the simple principles and where g-forces higher than or much less than 1 g deserve to occur, also if castle cannot completely relate them come the acceleration the the roller coaster.

Associated activities


acceleration: how quickly an item speeds up, slows down or changes direction. Is equal to change in velocity divided by time.

an essential velocity: The speed required at the top of a loop for a automobile to endure the loop without falling turn off the track.

force: any kind of push or pull.

friction: A pressure caused through a rubbing motion in between two objects.

g-force: quick for gravitational force. The pressure exerted on an item by the Earth's gravity at sea level.

gravitational constant: The acceleration brought about by Earth's gravity at sea level. Is equal to 9.81 m/sec^2 (32.2 ft/sec^2).

gravity: A pressure that draws any kind of two objects toward one another.

kinetic energy: The energy of an item in motion, i m sorry is straight related to its velocity and also its mass.

potential energy: The power stored by things ready to be used. (In this lesson, we usage gravitational potential energy, i beg your pardon is directly related to the height of things and that mass.)

speed: just how fast an item moves. The distance that object travels separated by the moment it takes.

velocity: A combination of speed and the direction in which an object travels.


Pre-Lesson Assessment

Before the lesson, make certain students have actually a firm manage on gravity, friction, potential and kinetic energy, and the basics that motion. This can be done in the kind of a quick quiz, a warm-up practice or a short discussion. Instance questions:

What causes gravity?What is friction?How perform potential and kinetic power differ?What is the difference between speed and velocity?How is acceleration regarded velocity?

Lesson an introduction Assessment

Show college student a photo of a roller coaster that consists of a hill and also a loop. Suppose them to have the ability to identify:

Points of best potential and kinetic energy.Points of maximum and minimum velocity.Points where g-forces better or much less than 1 room experienced.

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Ask college student to design their very own roller coasters or discover an existing roller coaster ~ above the Internet and identify its qualities in terms of the physics concepts learned in the lesson. This assignment additionally serves as an advent to the linked activity, structure a Roller Coaster.