0. Introduction to Coaster Physics
Coaster Engineers & Energy
Riders sat in a giant ice cube and slid down an 0.1 Mission Impossible ? iced over wooden ramp. The first US coaster appeared in 1884 at Coney Island. The coaster Your team’s mission is to create the "ultimate" had a top speed of 10 mph. Before the Great roller coaster. Your thrill machine will include Americas and six flags, there existed thousands loops, bumps, turns, and maybe even advanced of small local parks across the country. Most features like banked turns, camel backs, or went bankrupt during the Great Depression. Ask pretzel double loops. Instead of designing a an older Chicagoan (parents?) if they rode the coaster, you might have the choice of building Comet or the Bob at the famous Riverview Park your own kind of thrill ride. The final product before it closed in 1967. A man named Walt should conform to all project rules, be physics Disney helped create a new surge in theme parks. accurate, and should have a death-defying Advances in computer modeling and steel thrilling, yet safe appeal. So let's start coasting! technology promoted the rapid rise of steel structure coasters. These new thrill machines Is RAGING BULL the ultimate coaster? travel through twisted loops at speeds approaching 100 mph and at g-forces usually Probably not. Each only experienced by astronauts. Great America year amusement parks opened in 1976 with the Demon and Whizzer try to make the ultimate rides. The park added the Tidal Wave (no longer ride, only to be foiled exists!) in 1978, then American Eagle in 1981, the next year by a followed by Shockwave (1988), Iron Wolf competing park. What (1990), Batman (1992), and the Raging Bull would it take to make (1999). Where else can you free fall over 100 the most thrilling feet all day for only a few bucks? If you want to coaster? Certainly you find the latest scoop on the best parks, check out can’t do it by yourself. these certifiably awesome web sites: It takes teams in the real world to make great things happen. Certainly if you knew the physics behind it all, you could probably invent some cool new rides that might even be safe. Web sites to wet your appetite: Yes, I want to build the ultimate coaster park! This text will help you and your teammates to master everything you need to know. In addition, www.rcdb.com - over 600 coaster previewed it will hopefully offer interesting insights and www.ultimaterollercoaster.com – news & rides cool “did you know” sorts of information about www.discovery.com/exp/rollercoasters/ - build it the world of coasters. Of course you also have http://www.sixflags.com/greatamerica/rides/ to do all the labs and homework to build your www.learner.org/exhibits/parkphysics/coaster.html knowledge. (You knew there was a catch). http://www.district86.k12.il.us/central/faculty/j-Remember to consult your book and your vetrone/coasterphysics.html - our class web site! teacher whenever you hit a roadblock. Don’t www.coasterquest.com – how they work forget to teach your teammates along the way www.thrillride.com – who builds them and share your own experiences:) www.fmcg.com/jmiller – famous coaster builder www.ridezone.com – other rides, old & virtual 0.2 Theme Parks: Amusement parks have thrilled the young and old for many years. One of the first coasters was thbuilt in St.Petersburg during the 15 century. 0.3 Coaster ENGINEERS (you!)
4. How much power will it take to lift the To achieve the delicate balance between “death riders up the first hill?
defying excitement” and “absolute safety”, an
engineer must fully understand the laws of 5. How do I make the track exactly the right physics and know which materials to use in length so the ride slows to a stop without building a new ride. He must also consider cost, using brakes? (a tough calculation?) safety, rider appeal, and environmental issues.
Of all these, safety cannot be compromised. 6. What material should I make the ride out of Theme parks are designed to prevent accidents, so it’s strong, not too heavy, and will last?
but unfortunately no park is 100% safe.
7. How do I ensure the riders won’t get hurt?
On April 18, 1998, 15 (you can’t make money if the rider gets maimed
people were stuck upside or too sick so he never returns to your park)
down for 3 hours on the
Demon ride at Great 8. How do banks, rolls, & turns add thrill?
America. No one got hurt,
but many complained of Add some of your own; Now! reoccurring nightmares and headaches. Recently they 9. were awarded together a sum of about $450,000 as compensation. The accident was blamed on a wheel pin, which 10. vibrated loose and jammed the coaster. Top 5 qualities you’ll need as a ride engineer 11. 5. Know when and how to listen to others 4. Stay focused on your goals 12. 3. Support and encourage team members 2. Speak up when you know you’re right 1. Know what you’re talking about 13. You should try to polish these skills whenever 14. working with your team members, and especially whenever the class does team-building events. 15. 0.4 Brainstorming Questions Here are some questions an engineer must try to 16. answer in designing the ultimate coaster. Continue to reflect and talk to your teammates. Write comments in the margin as you go along. 17 There are no wrong questions. Just remember to stay focused on your mission and not get lost in all the details of cool rides.
Project hint: 1. What determines a ride’s maximum speed?
2. How much will friction slow down the cars? " your team should ask and answer questions like
these as you design your ride! " 3. Does friction cause any electrical problems?
0.5 Outline of Roller coaster Course
You could explain most of how a roller coaster works using only two principles: gravity and the law of conservation of energy. But to actually know the velocity, acceleration, and forces on a coaster at any point,
a coaster engineer must know many more physics concepts. Here's an outline of what we will learn!
Coaster Questions Physics Concepts Math Equations
What is the coaster project? Coaster Background Info
How can I determine the speed? Energy (KE,PE) KE = 1/2 mv2 PE = mgh,
PE + KE = PE + KE
What does it take to start & stop? Work (forces, power, friction) Work= F*d
Power = Work/time
Weight = m*(g)
Why I feel pushed into my chair? Horizontal G-Forces F = ma
2Why don't I fall out on turns? Turns a = v/r
(centripetal force, inertia, loops & turns)
Why do I feel sick on loops & bumps? Vertical G-Forces g’s (top) = a/-9.8 - 1
(projectiles, free body diagrams) g’s (bottom) = a/9.8 + 1
0.6 Review Questions
Roller Coaster History:
1. In what country is St.Petersburg, site of the
first recorded coaster in the 1400’s?
16. Which coaster at G.A. is known for its 2. The first US coaster was when & where? continuous spiral of banked turns? 3. This Chicago coaster park closed in 1967 17. How many stories do you fall on Giant Drop? 4. Which ride at Great America is older, Shock 18. How many times have you already asked Wave or the Demon? when are we going to Great America? (answer – too many! - mid May ) Mission Possible
5. Besides making awesome rides, what other
considerations are there in designing a ride?
6. How much cash did each person receive for
hanging upside down for 3 hours on the
Demon ride?(assume same amount for each)
7. What safety devices exist on roller coasters?
8. Suggest 4 categories for the types of rides
typically found at an amusement park
9. Which qualities of a good engineer do you
feel match your work habits?
10. Which qualities will you personally try to
work on to develop this quarter ?
11. In what town is Great America located?
12. This ride at G.A. is often called spin & barf!
13. How many vertical & corkscrew loops are in
the Demon roller coaster?
14. Which roller coaster has 7 loops and the first
ever banked curve on the first drop?
15. Which coaster(s) at G.A. are made mostly of
1. Running Roller Coasters
energy (screeches) and light energy (sparks). 1.1 What makes the fastest coaster? During a collision, the car may bounce so it has spring or elastic energy. If the car were jolted Thrill parks attract visitors in part by having a off the ground, it would have potential energy. variety of rides. Some roller coasters use Any time you lift an object, you increase its wooden tracks with lots of hills and turns but no potential energy. There also exists nuclear loops. Steel coasters often flip the riders in energy inside the atoms making up the car, as multiple loops and banked turns. Much of the well as chemical energy between those same thrill of any coaster is going fast. Compare the atoms. Finally, if the car receives any permanent speeds of these coasters at Great America. damage (a dent or scratch), the car has deformation energy. ； Finally, if you add all the types of energy an object has at any Fastest rides at Great America particular moment, the sum is called the total energy Coaster Top Speed (mph) Raging Bull 72 1.3 Conservation of Energy Eagle 66 Shockwave 65 The exciting part of energy is changing from one
type to another. As the bumper car moves Iron Wolf 55
electrical energy (electricity) is converted to Vipor 50 kinetic energy (motion). As a coaster goes down Whizzer 42 a hill it gives up potential energy (height), and gains kinetic energy (speed). Unfortunately, energy can not be entirely converted to another. What is the key to designing a coaster to make it run very fast? The answer lies ahead! Efficiency is the percent of energy retained (i.e. still available) after an energy conversion. Did you know a typical car is 30% efficient? Only 1.2 Energy - #1 physics concept? 30% of the chemical energy in gasoline is converted to kinetic energy that moves the car. Where did the rest go? Heat! Whenever energy Energy is a term often used to describe people or is changed into another type, heat is also objects. It's also a powerful physics concept. produced. Most of the time heat is undesirable, Energy can be defined as the ability to do work. and it can never be fully converted back to more The more energy present in you or any object, useful energies. Even so, if you include heat the more likely something can be made to with all other energies present, you will find the happen or change. Amusement park rides total energy of any completely described possess many kinds of energy. Imagine a situation is constant. That’s a powerful law bumper car. It is energized by electricity so it called conservation of energy. has electrical energy. All objects in motion have kinetic energy. When the bumper car goes Energies are not lost or created; they are just forward or backward, it has kinetic energy. A converted from one type to another. Think of an car that is stopped has no kinetic energy. After a object's energy as a shirt having many pockets while the car wheels warm up due to friction for different types of energy. An object, for with the ground. Energy associated with heat is example a marble, can lose or gain certain types called thermal energy. The electrical rod of energy by switching pockets, but the total touching the ceiling creates examples of sound energy stays the same. There is an old saying -
"what you get out of something is what you put
into it". Does what you just read support this
statement? Weight = m*g So also
1.4 PE stands for Potential Energy
PE = Weight * height
Gravity is a force that must be overcome to lift
an object. Since energy is put into an object to
raise it, that object gains height energy called
gravitational potential energy ("PE"). How about Great America on the moon?
Potential energy depends on three factors: On the moon, the acceleration of gravity is only 2mass, height, and gravity. . All objects have the same mass, but 1.6 m/s weight about six times less! . A moon ride would The higher an object, the more work it took to take much less work to lift up to the first hill, but get there, and hence the more PE possessed by it would also have much less potential energy. In the object. A coaster has the most PE at the top summary, potential energy depends only on of the heighest hill. It should also makes weight and vertical height. common sense that more massive objects will have more potential energy than lighter ones. The PE of a coaster is higher if more people are on board since it takes more work to lift a heavier coaster. Finally, PE depends on gravity Hints: since gravity determines the weight of a coaster. 1. Don’t confuse mass (in kilograms) with Gravity or more accurately, the acceleration of weight (measured in newtons) gravity is given the symbol “g”, and has a value 2. Mass is in kilograms (1000 grams = kg) 2of about 9.8 m/s on earth. 3. Energy is in Joules (sounds like jewels) En garde, I have a sharp equation for you! Calculating Potential Energies
1. How much more PE does a 1.0 kg banana have after raising it higher by 3.0 meters? (BTW, that’s a 2 1/4 pound fruit!)
PE = m*g*h
Answer PE = mgh = 1kg * 9.8 * 3 m = 29 Joules (J) PE = potential energy in joules (J) m = object’s mass in kilograms (kg) 2. What is the PE of a cheeseburger in your mouth? h = height of object in meters (m) (assume burger weights 1N, mouth is 1.5 m high) 2 g = gravity (about 9.8 m/s on Earth)
PE = Weight * height = 1N * 1.5m = 1.5 Joules (J)
The above equation can be used to find the potential energy anywhere along a roller coaster
along as the coaster’s mass and vertical height
are known. The weight of an object is simply its
mass multiplied by the acceleration of gravity.
Can perpetual motion machines exist? 1.5 Who is Rube Goldberg? Theoretically it is possible to have perpetual Reuben Lucius Goldberg was a cartoonist who motion. The total energy must stay the same so poked fun at and designed silly gadgets such as
the conservation of energy law is not an automatic back scratcher, a self-operating
violated. However, technically it has been napkin, and a 20-step method to turn off the
room lights. His cartoons live on and have impossible to make or even design on paper such inspired many people to invent very complicated a device. Ultimately some additional energy gadgets to do very simple things. Some have from outside the machine is needed or the device
requires heat to travel from cold to hot, which it appeared in movies such as Flubber, Goonies,
can’t. For more info, check out Back to the Future, and the Nutty Professor.
http://prisoner.soe.bcit.bc.ca/rjw/pmm Rube Goldberg- like gadgets are the essence of
the Mousetrap board game. There also exist
annual contests to create the most excessive
gadget to do the simplest task. A competition is 1.7 Kinetic Energy (KE) held each year for high school students in Chicago. More information can be found out at: Kinetic energy is the energy of motion. It takes http://www.anl.gov/OPA/rube/ energy to make things move, so moving object have kinetic energy. . Students walking to class Years ago, engineering fraternities at Purdue have KE, while those simply standing in the University sought to win the contest by setting hallway have no KE. A roller coaster has its another fraternity’s house on fire. The college greatest KE which it has its greatest speed. quickly smothered that competition! Likewise it takes more energy to move more massive objects. If two students fall at the same speed on the Giant Drop ride, the heavier student Why should we care about Rube Goldberg? will have more kinetic energy. You may be assigned to create a poster or So, kinetic energy depends only on two variables, working model of your own Rube Goldberg mass and speed: design. You will be expected to describe all the changes in energy that would occur in your I’m back!!! Goldberg machine. Who knows? Your machine might win in a real contest or even be sold on 2KE = ? m * v those late night TV ads. Someone invented the
first electric toothbrush; it could have been you!
KE = kinetic energy in joules (J) m = mass in kilograms (kg) 1.6 Perpetual Motion Machines v = velocity in meters/ second (m/s) The United States Patent Office still has an open application for a perpetual motion machine- some gadget that does something forever. Such Note velocity is speed in a certain direction. For a gadget would convert between energy types energy calculations, direction is not needed. forever without changing any energy into heat. If heat were created, it would have to be converted back 100% into a practical form of energy. If such a device existed its owners would Calculating kinetic be very rich. Imagine a car that never needs
Energies refueling! Somehow gas fumes and heat would
have to be collected and reused over and over. a. What is the KE of a 2 kg bowling ball at rest? b. What is KE if the same ball is rolling at 6 m/s?
Hence, one can solve for one of the velocities if Answer the other velocity and two heights are known. a. KE = 0 since at rest!
This method can be used anywhere on the track, 2not just at the top and bottom of hills. b. KE = ? * 2kg * 6 = 36 Joules (J) Coaster
So which property explains why one
1. A 2000. kg coaster is moving at 4.00 m/sec roller coaster is faster than another? at the top of a hill having a 20.0 m drop. What is the coaster's speed at the bottom of The fastest coaster will have the most kinetic the drop? energy. Where did that energy come from? KE was converted from the potential energy of the Answer first hill. So the fastest coaster has the biggest drop. You knew that already, but now you the Find energy at top: physic reasons for it. (we ignored air resistance and friction for now). But what about mass? A PE = mgh = 2000*9.8*20 = 392,000 J more massive coaster will have more potential 22 = 1/2*2000*4 = 16,000 J KE = 1/2mvenergy at the same height. Be prepared to Total Energy = PE + KE = 408,000 J explain why the coaster's speed doesn't depend on its mass! Find energy at bottom: PE = mgh = 2000 *9.8 * 0 = 0 (at bottom!) KE = don't know yet 1.8 Coaster Problems Total Energy = 408,000 J (same as above) There is a simple way to find the speed of a So, KE at bottom = Total energy at top 2coaster at any height along the ride as long as 1/2*2000*v = 408,000 J one knows another speed at a different height. v = 20.2 m/sec (about 44 mph) Consider two points “A” and “B” on a roller coaster. We can calculate the total energy at 2. Your are traveling at 2.0m/sec at the top of a each point by assuming the coaster has only 20. m high hill. What is your coaster's speed potential and kinetic energy. Minor errors due to when you are at the top of the next hill (10. effects of friction will be ignored for now. m high)? Mass of coaster is 2000 kg Answer A B stFind energy at 1 hill: h h AB PE = mgh = 2000*9.8*20 = 392,000 J 22 KE = 1/2mv = 1/2*2000*2 = 4,000 J Total Energy = PE + KE = 396,000 J At point A: At point B: PE = mg h PE = mg h ABndFind energy at 2 hill: 22KE = ? mv KE = 1/2mv AB PE = mgh = 2000 *9.8 *10 = 196,000 J KE = don't know yet We can now invoke the conservation of energy. Total Energy = 396,000 J (same as above) The total energy at either point is the same. stSo, 196,000 + KE = Total energy on 1 hill 196,000 + 1/2mv2 = 396,000 J 2KE + PE (height A) = KE + PE ( height B) 1/2*2000*v = 200,000 J v = 14 m/s
Simple Roller Coaster Equation
Assumes only force is gravity Conservation of total energy So no friction or external work done (super important!) You can’t make or destroy energy, only change it to another type of KE + PE (height A) = KE + PE ( height B) energy!
Efficiency (% not lost to heat)
Eff =(Energy out/ Energy in )*100
Unit Conversions 1 m/sec = 2.24 mph. Potential energy (height energy)
1 kg = 2.22 lbs
PE = m*g*h 1 mile = 1610 m -doubles if double mass 1 ft = 0.305 m -doubles if double height
1 hr = 3600 sec Also note: Weight = m*g
Kinetic Energy (motion energy)
2 KE = ? m * v
-doubles if double mass
-quadruples if double speed
1.10 Review Questions
Energy Potential energy 1. Name 3 differences between the older 17. What does the symbol g stand for? coaster ride Eagle, and the new Raging Bull 18. How could a bowling ball and tennis ball 2. What in your opinion is the most important have the same potential energy? question to answer when creating a new ride? 19. When is your PE higher, when in social 3. Define energy in your own words studies on the second floor or math on the first floor? 4. Give an example of kinetic energy 20. What is the weight of a 70 kg student? 5. You may have heard the phrase: you have a lot of potential! Explain using physics 21. What is the potential energy of a 1/2 pound hamburger in your mouth (assume your 6. What type of energy is associated with the standing so your mouth is 1.5m high above bonding between atoms to form molecules? the ground)? 7. Why would you want sport shoes to have 22. How much energy must you expend to raise stored elastic energy? yourself another 2.0 m while on a ladder? Assume your mass is 55kg 8. The fission or breaking apart of atoms is an example of __________ energy being used. 23. You stand at the top of a staircase which is 4 meters tall (about 12 feet). All of a sudden 9. A toaster or hair dryer needs ________ you trip and fall all the way down, plowing energy to provide __________ energy. into an unwary freshman at the bottom. If you have 80 kg of mass, how much energy 10. If a brittle object is dropped on the floor, it do you give the unlucky freshman? may suffer _____________ energy. 24. Tricky one! How much energy would a 60 11. Which energy types are often maximized at kg person have if he hiked up a 20 meter rock concerts? crater on the moon, where gravity is only 1/6 as strong as it is on the Earth? 12. Which energy allows you to read this page, pick up radio signals, or microwave food?: 25. What is the hidden source of energy in those perpetual motion balancing toys that seem to 13. List the types of energy in the order you rock back and forth forever? used them to get to school today:
Kinetic Energy Conservation of Energy 26. Calculate the kinetic energy of a100 kg 14. Which energy (PE,KE, or total) is constant? student walking at 0.8 m/sec to class 15. How is energy conservation like recycling? 27. What happens to an object’s kinetic energy if its velocity is doubled? Tripled? 16. Why is heat energy often called the graveyard for energy conversions? 28. What happens to an object’s kinetic energy if its mass is doubled? Tripled?