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Physics of Amusement Park Rides

Physics of Amusement Park Rides. The Carousel Ferris Wheel Loop-the-Loop The Rotor. The Carousel: An Example of Uniform Circular Motion. Turning about axis O w/ Constant Angular Speed . Axis O. . Draw the Forces on the Rider. What is the nature of the net force on

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Physics of Amusement Park Rides

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  1. Physics of Amusement Park Rides • The Carousel • Ferris Wheel • Loop-the-Loop • The Rotor

  2. The Carousel: An Example of Uniform Circular Motion Turning about axis O w/ Constant Angular Speed  Axis O

  3. Draw the Forces on the Rider What is the nature of the net force on the rider ? Where is this pointing ? Central force pointing to O What provides the net force on him ? The normal support force of the back of the seat What kind of net force along the y-axis ? Is there motion along y ? y: stationary uniform motion What is the sensation he feels ? Pressed against the chair (or alternatively, chair pressing against his back) How can this be enhanced ? Increase  O y N’ = mg N = mv2/R x mg

  4. The Ferris Wheel “Weightless” Feeling at the top ‘Heavy’ feeling at the bottom

  5. Draw the Forces on the Rider constant  2 N What is the nature of the net force on the rider ? Where is this pointing ? a central force mg At 2: mg - N = mv2/R or N = mg - mv2/R ‘feels lighter’ 1 At 1: N - mg = mv2/R or N = mg + mv2/R ‘feels heavier’ 3 N What is the sensation he feels At locations 2 and 4 ? 4 mg What happens if the rotational speed is increased beyond (gR)1/2? He flies off upon reaching position 2

  6. The Roller Coaster SLOW FAST Weightless Sensation Heavy Sensation

  7. How is Energy conserved in the roller coasterride ? Potential Energy = mgh Kinetic Energy= 0 A. C Vo = 0 h R B. KE = (1/2) mv2 PE = 0 To clear the top of the loop, h  2R. In fact, ignoring friction, minimum h = 2.5 R

  8. Draw the Forces on the Rider constant  What is the nature of the net force on the rider ? Where is this pointing ? A central force towards O 2 v Radius R At 2: N + mg = mv2/R or N = mv2/R - mg N mg 1 O At 1: N - mg = mv2/R or N = mg + mv2/R N 3 What is the sensation he feels at locations 2 and 4 ? Heavier at 4, lighter at 2 4 mg What happens if the speed v is decreased below (gR)1/2? Rider falls out of car at 2, if not wearing harness.

  9. The Rotor Radius R • A large cylinder spins. • You are thrown and pinned against the wall. • The floor then slides out. • Yet you do not fall.

  10. Draw the forces on the rider ‘pinned’ to the rotor’s wall: Friction f = N N= Fc = mv2/R rotor wall Floor pulled out mg The central force Fc is provided by the normal or support force N from the rotor’s walls. For a minimum rotor speed, the normal force is large enough that the friction f is enough to overcome the weight mg, keeping the man pinned to the wall. The critical minimum speed is solved from mg = N =mv2/R or v = (gR/)1/2

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