EJSS Circular Motion Ferris Wheel
Model http://weelookang.blogspot.sg/2014/05/ejss-circular-motion-ferris-wheel-model.html https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_ferrisWheelJSwee/ferrisWheelJSwee_Simulation.xhtml source: https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_src_ferrisWheelJSwee.zip authors: Mario Belloni, this version by lookang author of EJS 5: Paco. |
EJSS Circular Motion Ferris Wheel Model
this model uses the constant angular velocity to evolve the simulationOrdinary Differential Equation
Position of Ferris Wheel Mass
the coordinates of the mass are spaced out by usingwhere
because there are $ N_{1} =12 carriages
Newtonian Forces
the following equations are used to represent the forces such asWhere
By using the Newton's second law on the carriage in circular motion resolving to a general angle of
typical resolving in the
parallel and perpendicular to circular path,
where d2θdt2=0
constant angular
velocity motion
resolving into x and y
direction
The resultant is also resolve as
Conversion of radian to degree
The simple relationship is used to convert radian (used by
computer) to degree ( used by human and thus the sliders and
input fields)
General Description
This program simulates the effect of being on a Ferris Wheel. The simulation shows a wheel that can be varied in radius from 40 m (Ferris' original wheels) to 100 m, or about 10 meters larger than the current world record. In addition, the rotational speed of the wheel can be varied from -20 m/s to 20 m/s. By selecting the check-box, the free-body diagram can be shown.
This simulation is part of a collection of simulations related to amusement park physics. Additional simulations can be found on the OSP ComPADRE site.
Controls
Radius of the wheel (40 - 100 meters).
Speed: sets the speed of the Ferris wheel (-20 to 20 m/s).
Mario Belloni (mabelloni@davidson.edu) and now weelookang@gmail.com
Changes made by lookang include
- added velocity array to be display via check-box
- added theta to show
- added title
- made free body diagram to show weight and contact force while resultant force is a dotted line to illustrate the difference, actually FBD only has weight and contact force
- added values to aid numerical calculations
- made R = the outside hub to aid association of radius of circular motion made by carriage and man and woman
- made time step to allow exactly 0 , 90 , 180 , 270, 360 degrees, previously was dt =0.02