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Physics of Amusement Park Rides 1.The Carousel 2.Ferris Wheel 3.Loop-the-Loop 4.The Rotor.

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Presentation on theme: "Physics of Amusement Park Rides 1.The Carousel 2.Ferris Wheel 3.Loop-the-Loop 4.The Rotor."— Presentation transcript:

1 Physics of Amusement Park Rides 1.The Carousel 2.Ferris Wheel 3.Loop-the-Loop 4.The Rotor

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

3 O 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 x y N = mv 2 /R N = mg mg

4 The Ferris Wheel Weightless Feeling at the top Heavy feeling at the bottom

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

6 SLOW FAST Weightless Sensation Heavy Sensation The Roller Coaster

7 R How is Energy conserved in the roller coaster ride ? A. B. KE = (1/2) mv 2 PE = 0 C Potential Energy = mgh Kinetic Energy= 0 V o = 0 h 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 What is the nature of the net force on the rider ? Where is this pointing ? A central force towards O What is the sensation he feels at locations 2 and 4 ? Heavier at 4, lighter at 2 What happens if the speed v is decreased below (gR) 1/2 ? Rider falls out of car at 2, if not wearing harness constant v mgN N At 2: N + mg = mv 2 /R or N = mv 2 /R - mg Radius R At 1:N - mg = mv 2 /R or N = mg + mv 2 /R O

9 The Rotor 1.A large cylinder spins. 2.You are thrown and pinned against the wall. 3.The floor then slides out. 4.Yet you do not fall. Radius R

10 mg Friction f = N N= Fc = mv 2 /R Draw the forces on the rider pinned to the rotors wall: The central force F c is provided by the normal or support force N from the rotors 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 = mv 2 /R or v = (gR/ ) 1/2 Floor pulled out rotor wall


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