MS-PS3-5

### Quick watch

Partial design process
power
grade Level: 7 (6 – 8) Time Required: 30 minute subject Areas:
 Physical science Physics

NGSS power Expectations:

 MS-PS3-5

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You are watching: A roller coaster reaches its maximum kinetic energy when it

note that no all class and tasks will exist under a unit, and instead might exist as "standalone" curriculum.

### summary

Students check out the physics exploited by designers in creating today"s roller coasters, consisting of potential and also kinetic energy, friction and also gravity. First, they find out that every true roller coasters are completely driven by the pressure of gravity and that the conversion between potential and also kinetic power is vital to every roller coasters. Second, they consider the duty of friction in slowing down cars in roller coasters. Finally, they examine the acceleration of roller coaster cars together they travel approximately the track. Throughout the associated activity, students design, build and analyze design roller coasters castle make using foam tubing and marbles (as the cars). This design curriculum set to following Generation scientific research Standards (NGSS).

As the cars drop, potential energy listed by the chain background on the left is convert to kinetic energy.

Students check out the most an easy physical principles of roller coasters, i m sorry are an essential to the initial design procedure for engineers who develop roller coasters. They learn around the possibilities and also limitations that roller coasters in ~ the context of energy conservation, friction losses and also other physical principles. After the lesson, student should be able to analyze the activity of any type of existing gravity-driven coaster and also design the basics of your own model roller coasters.

### finding out Objectives

After this activity, students have to be able to:

Explain why the is crucial for designers to know just how roller coasters work.Explain in physics terms how a roller coaster works.Discuss the impacts of gravity and friction in the context of their roller coaster designs.Use the principle of preservation of power to define the layout the roller coasters.Identify clues in a roller coaster monitor at i beg your pardon a automobile has preferably kinetic energy and maximum potential energy.Identify points in a roller coaster track whereby a car experiences an ext or much less than 1 g-force.Identify point out in a roller coaster track wherein a car speeds up and decelerates.

### Educational standards each cg-tower.com lesson or activity is associated to one or much more K-12 science, technology, engineering or math (STEM) education standards. all 100,000+ K-12 STEM standards extended in cg-tower.com room collected, maintained and also packaged by the Achievement requirements Network (ASN), a task of D2L (www.achievementstandards.org). In the ASN, standards room hierarchically structured: very first by source; e.g., by state; within source by type; e.g., science or mathematics; within kind by subtype, then by grade, etc.

NGSS: next Generation scientific research Standards - science
NGSS performance Expectation science & engineering Practices Disciplinary Core principles Crosscutting principles

MS-PS3-5. Construct, use, and present debates to support the claim that as soon as the kinetic power of an object changes, power is transferred to or indigenous the object. (Grades 6 - 8)

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This lesson concentrates on the adhering to 3 Dimensional Learning elements of NGSS:
Science knowledge is based upon reasonable and theoretical connections in between evidence and also explanations.

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When the motion energy of things changes, there is inevitably some other change in power at the exact same time.

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

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International an innovation and design Educators association - modern technology
State standards
phibìc Carolina - scientific research
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### much more Curriculum prefer This

Building Roller Coasters

Students develop their very own small-scale version roller coasters making use of pipe insulation and also marbles, and then analyze them making use of physics values learned in the associated lesson. They research conversions between kinetic and also potential energy and frictional effects to design roller coasters that room compl...

structure Roller Coasters

High school Lesson
A tale of Friction

High school students discover how engineers mathematically architecture roller coaster paths using the approach that a curved path can be approximated by a succession of many short inclines. Castle apply basic calculus and the work-energy theorem because that non-conservative forces to quantify the friction along a curve...

A story of Friction
middle School class
Kinetic and also Potential energy of Motion

Students are introduced to both potential energy and also kinetic power as forms of mechanical energy. A hands-on activity demonstrates how potential energy can readjust into kinetic energy by swinging a pendulum, showing the ide of preservation of energy.

Kinetic and Potential power of motion
Mathematically designing a frictional Roller Coaster

Build a tiny roller coaster prototype out of foam pipe wrap insulation and marbles, but apply calculus and physics in the design! This real-world engineering challenge applies valuable mathematics to check small-sized models on a real track.

Mathematically creating a friction Roller Coaster

### Pre-Req understanding

An knowledge of forces, particularly gravity and friction, and some familiarity through kinetic and also potential energy. An knowledge of Newton"s 2nd law of motion and basic motion principles such as position, velocity and acceleration.

### Introduction/Motivation

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

Does everyone know exactly how roller coasters work? You might think the the roller coaster cars have engines within them that press them along the track choose automobiles. While that is true the a few roller coasters, most use heaviness to relocate the cars follow me the track. Do any kind of of girlfriend remember speak a roller coaster that started out v a huge hill? If you looked closely at the roller coaster track (on i beg your pardon the car move), friend would watch in the center of the track on that an initial hill, a chain. You could have also have felt that "catch" to the cars. The chain hooks to the bottom of the cars and pulls them come the height of that first hill, which is constantly the highest allude on a roller coaster. When the cars room at the top of that hill, they space released indigenous the chain and coast through the rest of the track, i beg your pardon is where the surname roller coaster come from.

Figure 1. Example setup for quick lesson demo.

What perform you think would happen if a roller coaster had a hill in the center of the track that was taller than the an initial hill the the roller coaster? would certainly the cars be able to make it up this larger hill using just gravity? (Conduct a quick demonstration to prove the point. Take a piece of foam pipeline insulation reduced in fifty percent lengthwise and also shape it into a roller coaster through taping it come classroom objects such as a desktop and a textbook, as shown in figure 1. Then, using marbles to represent the cars, present students the the an initial hill that a roller coaster should be the tallest suggest or the cars will not with the finish of the track. Refer to the structure Roller Coasters activity for additional instructions.)

(Next, play off various other students" roller coaster experience to move the class forward, extending the material provided in the class Background and Vocabulary sections. For example, talk about the point in the roller coaster wherein you take trip the fastest, how cars endure loops and also corkscrews, and also what causes passengers to feeling weightless or really heavy at specific points in the roller coaster. The stimulate in which girlfriend teach these points, and possibly more, is not crucial to the lesson. Also, it may be an ext engaging because that the students to ask questions based on their experiences through roller coasters and let those concerns lead the lesson from one point to the next. Every one of these points have the right to be demonstrated making use of the foam tubing and also marbles, so usage them regularly to illustrate the class concepts.)

### lesson Background and also Concepts for Teachers

The underlying rule of every roller coasters is the law of conservation of energy, which describes how power can no be lost nor created; energy is just transferred from one kind to another. In roller coasters, the two creates of power that space most necessary are gravitational potential energy and also kinetic energy. Gravitational potential power is the power that things has because of that is height and is equal to the object"s mass multiplied by its height multiplied through the gravitational consistent (PE = mgh). Gravitational potential energy is greatest at the highest suggest of a roller coaster and also least in ~ the shortest point. Kinetic energy is energy an item has because of its motion and is equal to one-half multiplied by the mass of an item multiplied by its velocity squared (KE = 1/2 mv2). Kinetic power is greatest at the lowest point of a roller coaster and least in ~ the highest possible point. Potential and also kinetic energy can it is in exchanged for one another, for this reason at details points the car of a roller coaster may have just potential energy (at the optimal of the first hill), just kinetic power (at the shortest point) or some mix of kinetic and also potential energy (at all other points).

The an initial hill that a roller coaster is always the highest suggest of the roller coaster since friction and drag automatically begin robbing the auto of energy. In ~ the optimal of the an initial hill, a car"s energy is practically entirely gravitational potential power (because that is velocity is zero or almost zero). This is the maximum power that the vehicle will ever have throughout the ride. That power can end up being kinetic energy (which that does in ~ the bottom of this hill as soon as the auto is relocating fast) or a mix of potential and also kinetic power (like at the tops of smaller hills), however the complete energy of the auto cannot be much more than it was at the height of the an initial hill. If a higher hill were put in the center of the roller coaster, it would certainly represent more gravitational potential energy than the an initial hill, for this reason a automobile would not be able to ascend to the height of the taller hill.

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

A web-based simulation demonstrating the relationship in between vertical position and the rate of a car in a roller coaster various shapes is detailed at the MyPhysicsLab Roller Coaster Physics Simulation. This website provides numerical data because that simulated roller coaster of various shapes.

Friction exists in all roller coasters, and it takes away from the useful energy noted by roller coaster. Friction is resulted in in roller coasters through the rubbing the the automobile wheels top top the track and by the rubbing of air (and periodically water!) against the cars. Friction turns the useful energy that the roller coaster (gravitational potential energy and also kinetic energy) into warm energy, which offer no purpose associated with propelling cars along the track. Friction is the reason roller coasters cannot walk on forever, for this reason minimizing friction is just one of the biggest difficulties for roller coaster engineers. Friction is additionally the reason that roller coasters can never restore their maximum height after the early stage hill uneven a 2nd chain lift is included somewhere top top the track.

Cars can only make it through loops if castle have sufficient speed at the top of the loop. This minimum speed is referred to as the critical velocity, and also is equal the square root of the radius the the loop multiply by the gravitational constant (vc = (rg)1/2). While this calculate is too complex for the vast majority of seventh graders, they will certainly intuitively recognize that if a car is not relocating fast sufficient at the top of a loop it will fall. Because that safety, most roller coasters have wheels ~ above both sides of the monitor to protect against cars from falling.

Most roller coaster loops room not perfectly circular in shape, but have a teardrop shape dubbed a clothoid. Roller coaster designers discovered the if a loop is circular, the rider experiences the greatest force at the bottom of the loop as soon as the car are moving fastest. After many riders continual neck injuries, the looping roller coaster was exit in 1901 and restored only in 1976 as soon as Revolution at six Flags Magic Mountain became the an initial modern looping roller coaster utilizing a clothoid shape. In a clothoid, the radius that curvature the the loop is widest at the bottom, to reduce the force on the riders as soon as the cars relocate fastest, and also smallest at the top as soon as the cars room moving reasonably slowly. This permitted for a smoother, much safer ride and also the teardrop form is now in usage in roller coasters about the world.

Riders might experience weightlessness in ~ the tops of hills (negative g-forces) and also feel heavy at the bottoms of hills (positive g-forces). This emotion is resulted in by the readjust in direction that the roller coaster. In ~ the optimal of a roller coaster, the auto goes from moving upward to level to moving downward. This adjust in direction is well-known as acceleration and the acceleration makes riders feel as if a pressure is acting on them, pulling them the end of their seats. Similarly, at the bottom that hills, riders go from relocating downward to flat to relocating upward, and also thus feel together if a force is advertise them down right into their seats. These pressures can be referred to in terms of gravity and also are dubbed gravitational forces, or g-forces. One "g" is the force applied by gravity while stand on planet at sea level. The person body is offered to existing 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), one more g-force is produced and, when added to the traditional 1 g, we obtain 2gs. If the acceleration at the bottom of the hill is double the acceleration the gravity, the in its entirety force is 3 gs. If this acceleration acts instead at the height of a hill, it is subtracted native the standard 1 g. In this way, it can be much less than 1 g, and it can also be negative. If the acceleration at the peak of a hill were equal to the acceleration that gravity, the overall force would be zero gs. If the acceleration at the peak of the hill were double the acceleration the gravity, the resulting all at once force would certainly be an adverse 1 g. At zero gs, a rider feels totally weightless and at an adverse gs, castle feel together though a force is lifting them the end of the seat. This principle may be too advanced for students, but they should understand the simple principles and also where g-forces higher than or less than 1 g can occur, even if castle cannot fully relate them come the acceleration the the roller coaster.

### Vocabulary/Definitions

acceleration: how quickly an object speeds up, slows down or alters direction. Is equal to change in velocity separated by time.

an important velocity: The speed essential at the peak of a loop for a vehicle to endure the loop there is no 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: brief for gravitational force. The pressure exerted on an object by the Earth's gravity at sea level.

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

gravity: A force that draws any two objects toward one another.

kinetic energy: The power of an item in motion, i beg your pardon is directly related come its velocity and also its mass.

potential energy: The power stored by an item ready to be used. (In this lesson, we use gravitational potential energy, which is directly related come the height of an item and the mass.)

speed: exactly how fast things moves. The distance that thing travels divided by the moment it takes.

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

### assessment

Pre-Lesson Assessment

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

What causes gravity?What is friction?How execute potential and also kinetic energy differ?What is the difference between speed and velocity?How is acceleration pertained to velocity?

Lesson an overview Assessment

Show students a photograph of a roller coaster that includes a hill and also a loop. Expect them to have the ability to identify:

Points of best potential and also kinetic energy.Points of maximum and also minimum velocity.Points whereby g-forces higher or less than 1 space experienced.

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Homework

Ask college student to architecture their very own roller coasters or discover an existing roller coaster on the Internet and identify its attributes in terms of the physics concepts learned in the lesson. This assignment also serves as an arrival to the connected activity, structure a Roller Coaster.