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Aneri & Saba

ROLLER COASTERS. Aneri & Saba. Roller coasters are all about acceleration experienced within loops, hills, dips, etc. Loop Hill . Dip. Clothoid Loops. Centripetal acceleration occurs within Clothoid Loops

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Aneri & Saba

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  1. ROLLER COASTERS Aneri & Saba

  2. Roller coasters are all about acceleration experienced within loops, hills, dips, etc. Loop Hill Dip

  3. Clothoid Loops • Centripetal acceleration occurs within Clothoid Loops • Clothoid refers to the teardrop shape of the loop (radius is constantly changing) • Radius is much larger at the bottom than at the top • As a rider travels through a clothoid loop, he/she experiences an acceleration due to change in speed and change in direction

  4. SAMPLE PROBLEM 1: Wario is riding the Toadster Coasterand goes through a loop with radius 4.0 m at the top and radius 17.3 m at the bottom. He travels at a speed of 8.2 m/s at the top and a speed of 20.1 m/s at the bottom. What is the normal force acting on him (at the top and bottom of the loop) if his mass is 90 kg? Givens: TOPBOTTOMv top = 8.2 m/s v bottom = 20.1 m/sr top = 4.0 m r bottom = 17.3 mm = 90 kg

  5. FREE BODY DIAGRAMS: Top Bottom y FN y FN Fg Fg

  6. CALCULATIONS:Topa = vtop2 / r = (8.2 m/s)2 / 4.0 m = 16.81 m/s2 FR = Fg + FNma = mg + FNFN = (90)(16.81) – (90)(9.81)FN = 630.0 N [down] Therefore, the normal force acting on Wario is 630.0 N [up] at the top of the loop.

  7. CALCULATIONS:Bottoma = vbottom2 / r = (20.1 m/s)2 / 17.3 m = 23.35 m/s2 FR = Fg + FNma = mg + FNFN = (90)(23.35) – (90)(9.81)FN = 1219 N [up] Therefore, the normal force acting on Wario is 1219 N [up] at the bottom of the loop.

  8. Fa Fg SAMPLE PROBLEM 2: Aneri and Saba are riding Moors’ Monster Mayhem on Fizzix Island. Their speed is 19.2 m/s while at the top of the hill that has a radius of 13.1 m. What is the applied force of the track pulling down on their car, which has a mass of 636 kg.Givens:FBD v = 19.2 m/s r = 13.1 m m = 636 kg

  9. CALCULATIONS:a = v2 / r a = (19.2 m/s)2 / 13.1 ma = 28.14 m/s2 FR = Fg + Fama = mg + FaFa = (636 kg)(28.14 m/s2) – (636 kg)(9.81 m/s2)Fa = 1.166 x 104 N [down] Therefore, the applied force is 1.166 x 104 N [down]

  10. Moors' Monster Mayhem

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