13. A roller coaster at the Six Flags 2C Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each ver- tical loop, instead of being cir- cular, is shaped like a teardrop (Fig. P6.13). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 m high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car Figure P6.13 at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the cars have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops. Frank Cezus/Photogapher's Choice/Getty Images
13. A roller coaster at the Six Flags 2C Great America amusement park in Gurnee, Illinois, incorporates some clever design technology and some basic physics. Each ver- tical loop, instead of being cir- cular, is shaped like a teardrop (Fig. P6.13). The cars ride on the inside of the loop at the top, and the speeds are fast enough to ensure the cars remain on the track. The biggest loop is 40.0 m high. Suppose the speed at the top of the loop is 13.0 m/s and the corresponding centripetal acceleration of the riders is 2g. (a) What is the radius of the arc of the teardrop at the top? (b) If the total mass of a car plus the riders is M, what force does the rail exert on the car Figure P6.13 at the top? (c) Suppose the roller coaster had a circular loop of radius 20.0 m. If the cars have the same speed, 13.0 m/s at the top, what is the centripetal acceleration of the riders at the top? (d) Comment on the normal force at the top in the situation described in part (c) and on the advantages of having teardrop-shaped loops. Frank Cezus/Photogapher's Choice/Getty Images
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Transcribed Image Text:**Educational Text on Roller Coaster Physics**
The roller coaster at Six Flags Great America amusement park in Gurnee, Illinois, features innovative design technology and fundamental physics principles. Each vertical loop of the coaster is teardrop-shaped rather than circular (see Figure P6.13). The cars ride on the inner side of the loop at the top, traveling at speeds sufficient to keep them on track. The largest loop is 40.0 meters high. Assuming the speed at the top of the loop is 13.0 m/s with a corresponding centripetal acceleration of the riders at 2g, consider the following questions:
(a) What is the radius of the arc of the teardrop at the top?
(b) If the total mass of a car plus riders is \( M \), what force does the rail exert on the car at the top?
(c) Assuming the roller coaster had a circular loop of radius 20.0 m and the cars maintain a speed of 13.0 m/s at the top, what is the centripetal acceleration of the riders?
(d) Discuss the normal force at the top in the situation described in part (c) and the benefits of teardrop-shaped loops.
**Figure P6.13 Description:**
The image shows a roller coaster with a teardrop-shaped loop. This shape is designed to enhance the ride’s safety and performance by maintaining ride comfort and speed efficiency. The track construction ensures that cars ride smoothly on the inside edge as they move through the loop.
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