SUMMARY
The velocity of a roller coaster at the top of a loop with a radius of curvature of 12 m can be determined using the forces acting on a passenger. At the top of the loop, the normal force exerted by the seat is 0.4 mg, where m is the mass of the passenger. By applying Newton's second law (ƩF = Fnet = ma) and the centripetal acceleration formula (ac = v²/r), the speed can be calculated as v = √(rg(0.4 + 1)), leading to a definitive speed calculation based on gravitational force.
PREREQUISITES
- Understanding of Newton's second law (ƩF = Fnet = ma)
- Knowledge of centripetal acceleration (ac = v²/r)
- Familiarity with gravitational force (Fg = mg)
- Basic algebra for solving equations
NEXT STEPS
- Calculate the speed of the roller coaster using the derived formula v = √(rg(0.4 + 1))
- Explore the effects of different radii on roller coaster speed
- Investigate the role of gravitational force in circular motion
- Learn about safety factors in roller coaster design
USEFUL FOR
Physics students, engineering students, and anyone interested in the mechanics of roller coasters and circular motion dynamics.