Mathematically Designing a Frictional Roller Coaster

Type of Resource



Students apply high school-level differential calculus and physics to the design of two-dimensional roller coasters in which the friction force is considered, as explained in the associated lesson. In a challenge the mirrors real-world engineering, the designed roller coaster paths must be made from at least five differentiable functions that are put together such that the resulting piecewise curving path is differentiable at all points. Once designed mathematically, teams build and test small-s

Performance Expectations

HS-PS3-3   Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

HS-ETS1-2   Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

HS-ETS1-3   Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.