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# coasterdoc - Hinsdale Township High School District 86

By Russell Walker,2014-01-29 00:12
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coasterdoc - Hinsdale Township High School District 86High,high,HIGH

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0. Introduction to Coaster Physics

Coaster Engineers & Energy

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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,

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

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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

(gravity,Newton's laws)

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

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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

10. Which qualities will you personally try to

work on to develop this quarter ?

Coaster Trivia

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

wood?

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1. Running Roller Coasters

Energy

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 -

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"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.

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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?

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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

Problems

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

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1.9 Summary

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

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1.10 Review Questions