Banked Curve Worksheet

 
1. What must the curve's angle be for a roller coaster car to travel around a curve of radius 30 m at 20 ^m/s?
2. How many g's are felt by a rider as he travels around the banked curve in the previous problem?
3. A car is to make it around a banked curve. The radius is 15.35 m and the car will travel at 30 ^m/s. What is the optimum banking angle of the curve?
4. A car is to make it around a banked curve. The radius is 15.35 m and the car will travel at 30 m/s. This roller coaster is on the moon where the acceleration due to gravity is 1.67 ^m/s2. What is the optimum banking angle of the curve?
5. A rider is to make it around a curve of radius of 24.28 m so that the rider will feel 2.50 g's. What is the angle of the banked curve?
   
6. A rider is to make it around a curve of radius of 31.15 m so that the rider will feel 1.64 g's. How fast must the rider be traveling?
   
7. A rider is to make it around a curve of radius of 51.15 m so that the rider will feel 4.52 g's. How fast must the rider be traveling?
   

8 What is the banked angle of the bottom curve?

9 How many g's are felt by the rider along the bottom curve?

10 What is the optimum angle of the top banked curve after spiraling up 10 m?

11 What is the radius of the top curve?

































ANSWERS
1 53.68° 2 1.69 g's 3 80.51° 4 88.37°
5 66.42° 6 19.92 ^m/s (52.69°) 7 47.01 ^m/s (77.22°) 8 60.01°
9 2.000 g's 10 48.19° 11 13.11m (11.99 ^m/s at the top)