Rolling into Math(Using Formula)

Ms. C. TurnerMath

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

Wooden Roller Coasters

Nonlooping Not very tall Slower speed Not very steep hills Shorter track/ride More sway

Steel Roller Coasters

Looping Taller Faster speed Steeper hills Longer track/ride Greater drops and

rolls

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.

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)

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

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

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

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.

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

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

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!

The Longest Roller

• Steel Dragon 2000 at Nagashima Spa Land in Mia, Japan

• Open in 2000

• 8,133 ft Long

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.

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/