Rolling into Math (Using Formula) Ms. C. Turner Math.
-
Upload
alison-maxwell -
Category
Documents
-
view
225 -
download
0
Transcript of Rolling into Math (Using Formula) Ms. C. Turner Math.
![Page 1: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/1.jpg)
Rolling into Math(Using Formula)
Ms. C. TurnerMath
![Page 2: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/2.jpg)
Roller Coaster
Small fast cars on light railroad tracks with many tight turns, steep slopes, and/or loops.
Found in amusement parks and modern theme parks.
LaMarcus Adna Thompson patented the first roller coast on January 20, 1885.
There are two types: wooden and steel
![Page 3: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/3.jpg)
Wooden Roller Coasters
Nonlooping Not very tall Slower speed Not very steep hills Shorter track/ride More sway
![Page 4: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/4.jpg)
Steel Roller Coasters
Looping Taller Faster speed Steeper hills Longer track/ride Greater drops and
rolls
![Page 5: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/5.jpg)
The Roller Coaster's Journey
• A roller coast has no engine or motor to give it power.
• It uses external energy from a lift motor to get to the top of the first hill.
• After it is pulled to the top of the first hill, the conversion of potential energy to kinetic energy is what drives the roller coaster the rest of the journey.
• The unit for energy is joule (j).
• The roller coaster has three kinds of wheels to guide it around the tracks and compressed air brakes to stop it at the end of its journey.
![Page 6: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/6.jpg)
How does the roller coaster move?
• It depends on potential energy (Ep), it gets
from being pulled to the top of the first hill, to complete its journey.
– Ep = mgh
• m – mass of the object (kg)
• g – the acceleration due to gravity (9.8 m/s^2)
• h – the height the object will reach (m)
![Page 7: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/7.jpg)
Your Turn
• Find the potential energy of a 800 kg roller coast postion at 80 meters off the ground.
• Ep = mgh
• Ep = 800 kg(9.8 m/s^2)(80 m)
• Ep
= 627200 j
![Page 8: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/8.jpg)
How does the roller coaster move?
• As the roller coaster move down the first hill, the potential energy changes into kinetic energy (E
k).
– Ek = mv2/2
• m – mass of the object (kg)• v – speed and direction in which the
object moves– v = d/t; unit m/s
![Page 9: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/9.jpg)
Your Turn
• The same roller exits the first hill. Calculate its kinetic energy at the speed of 39.6 m/s.
• Ek = mv2/2
• Ek = 800 kg (39.6 m/s)2/2
• Ek = 627264 j
![Page 10: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/10.jpg)
How does the roller coaster move?
• More hills are added at the highest, safest level to keep the feeling of speed and weightlessness.
• When adding loops the following two issues must be consider:
– the speed it will need to make it safely around the loop
– the gravitational pull the riders will feel going around the perimeter.
![Page 11: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/11.jpg)
Free-Falling
• Roller coasters are intended to give off of a sense of weightlessness, where the rider feels no external force; instead the force is solely due to gravity.
• This sense of weightlessness happens during free-falls.
• Free-fall costs an acceleration, increase in speed.
• How to find speed for a Free-fall:
– v = g(ᐃt)2/2• g = 9.8 m/s2
• t = final time – initial timeᐃ
![Page 12: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/12.jpg)
Your Turn
• You are riding Superman the Escape. It raises you up 41 story. Then you experience a 6.5 second backward drop. How fast was the roller coaster traveling?
• v = g(ᐃt)2/2
• v = 9.8 m/s2 (6.5 s)2/2
• v = 207.025 m/s
![Page 13: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/13.jpg)
The Tallest Roller Coaster
• Kingda Ka at Six Flags Great Adventure in Jackson, New Jersey
• Open in 2005
• 456 ft Tall
• Click to take a virtual ride!
![Page 14: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/14.jpg)
The Longest Roller
• Steel Dragon 2000 at Nagashima Spa Land in Mia, Japan
• Open in 2000
• 8,133 ft Long
![Page 15: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/15.jpg)
The Fastest Roller Coaster
• Kingda Ka at Six Flags Great Adventure in Jackson, New Jersey
• Open in 2005
• 128 mph
Click here to read how the Kingda Ka gets its speed.
![Page 16: Rolling into Math (Using Formula) Ms. C. Turner Math.](https://reader036.fdocuments.in/reader036/viewer/2022062304/56649e435503460f94b35f9b/html5/thumbnails/16.jpg)
References
Annenberg Media. (Designer). (1997). Amusement park physics. [Web]. Retrieved from http://www.learner.org/interactives/parkphysics/
Google videos. (2006). Virtual rollercoaster ride!. Retrieved from http://video.google.com/videoplay?docid=-4120582391209730459&hl=en&emb=1#
Levine, A. (2002). Theme parks. Retrieved from http://themeparks.about.com/