Abstract

Acceleration is at the heart of the experiences in an amusement park, as we move down drops, over hills, through helices and narrow curves of a roller coaster or round and round in carousels. The changing accelera- tions involve changing forces that can be experienced throughout the body. This chapter focuses on experiences, measurements and representations of accelerations in an interplay between mathematics and physics. Equations are complemented with graphs of authentic data, sequences of screen shots, simulations, as well as measurements with simple toys as well as electronic sensors, e.g in a smartphone. This chapter starts with a few simple examples of acceleration in one-dimensional motion: The horizontal acceleration of an airplane and launched roller coasters, is followed by examples of vertical acceleration in drop towers, as well as bouncing on a trampoline, where the results of mathematical modelling is compared to real data. Finally a few examples of acceleration in two dimensions are discussed: The horizontal acceleration in teacup and wave swinger rides, as well as the vertical acceleration over roller coaster ‘airtime’ hill.

Keywords: acceleration, force, multiple representations, measurement, modelling, calculus, smartphone, drop tower, trampoline, launch coaster

Excerpt 

Introduction + Physics or Math? Motion is relative, acceleration is absolute.

See also Images of acceleration.

The chapter also included examples (or variations of them) from several published papers, as listed below:

Table of content

• Experiencing acceleration:
  • Images of horizontal acceleration.
• Mathematical description:
  • Horizontal acceleration in launch coasters.
  • More general horizontal accelerations (Teacup rides, Wave Swinger, Kvasten roller coaster)
• Vertical acceleration:
  • Small drop towers
  • Acceleration and forces in large drop towers
  • ... with magnetic brakes
  • Falling faster than free fall
  • Complementary reporesentations of velocity and acceleration
  • A virtual Turbo Drop
• Force and acceleration on a trampoline
  • Phase portraits
  • Mathematics of trampoline bouncing
• Physics or Maths: Motion is relative, acceleration is absolute
  • Projectile motion in a roller coaster

Horizontal acceleration

• Classical physics experiments in the amusement park (2002)
• Acceleration in 1, 2, and 3 dimensions in launched roller coasters (2008)
• Rotating swings - a theme with variations (2016)
• Understanding acceleration: An interplay between different mathematics and physics representations (2019)