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1-120-CircularRollerCoaster-ModelingScenario

Author(s): Kevin Huang

Centennial High School, Ellicott City MD USA

Keywords: population dynamics energy Fluid Mechanics m friction roller coaster integration by8 parts

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Abstract

Resource Image Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students

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Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

Consider a cart of mass m moving through a vertical circle of radius R. We will assume the size of the cart is much smaller than the circle and neglect the rotational inertia of the cart's wheels. The acceleration due to gravity is g.

Model to calculate the minimum initial velocity of the cart for it to stay on the track throughout the loop

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Authors

Author(s): Kevin Huang

Centennial High School, Ellicott City MD USA

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