Dropping a Particle Out of a Roller Coaster

Abstract

A rider in a roller coaster lets go of a particle such as a small marble. How far does the marble travel horizontally from the point of release before hitting the ground, assuming the speed of the roller coaster is determined by conservation of mechanical energy starting from the highest hill up which it was pulled? Where should the marble be released along the track if one wishes to maximize the range of the marble? These questions constitute interesting variations on conventional problems in two-dimensional kinematics, appropriate for an undergraduate course in classical mechanics. Exploration of various shapes of tracks could form interesting student projects for numerical or experimental investigation.

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Document Details

Document Type
Technical Report
Publication Date
Apr 24, 2014
Accession Number
ADA605104

Entities

People

  • Carl E. Mungan
  • Trevor C. Lipscombe

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Ball Bearings
  • Differential Equations
  • Electronic Mail
  • Energy
  • Equations
  • Geometry
  • Ground Level
  • Information Operations
  • Instructors
  • Kinetic Energy
  • Mathematical Programming
  • Particles
  • Physics
  • Quadratic Equations
  • Shape
  • Two Dimensional
  • United States Naval Academy

Readers

  • Aerosol Science/Aerosol Physics
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Tribology (the study of the boundary interaction between sliding surfaces, lubrication, wear and friction).