Final answer:
Fractions are vital in the engineering design process of roller coasters, allowing designers to apply physics principles to ensure proper speeds and forces for a safe and exciting ride.
Step-by-step explanation:
Fractions play a crucial role when engineers apply physics principles to design roller coasters. When determining the necessary speed of a roller coaster at different points along the track, especially at the top of a loop, fractions could be used to calculate proportional changes in speed, radius of curvature, and other forces acting on the coaster and its riders. Imagine a scenario where the centripetal acceleration must exceed the force of gravity to prevent riders from losing contact with their seats; the use of fractions helps designers manipulate and apply these principles to ensure a thrilling, yet safe ride.
For instance, if the speed at the top of the loop and the radius of curvature are given, designers can use the fraction of the acceleration due to gravity (g) that this speed represents to determine if the ride will be safe. When considering energy conservation, potential energy at the highest point is converted into kinetic energy, and fractions again assist in determining what proportion of that energy is required for different parts of the ride. Overall, the application of fractions in the engineering design process of roller coasters helps ensure a smooth and safely engineered ride.