HTML_EDITOR Intro Page true true This is a simulation of a particle in a box with adjustable hardness walls. The idea here is to think about the behavior of the the particle as it enters the wall regions. The particle starts with starts with an initial velocity. As it enters the wall regions, the model makes use of a decelerating force, not unlike that of a rocket fired in order to decelerate. Here, the decelerating force brings the particle to a stop, it makes turn around, accelerates it, and brings it back to its original but opposite velocity, thus concerving energy. This model is made possible by solving Newton's law in differential form: d²x(x)/dt² =F(x) with boundary conditions such that F(x)= {-a1 if x >= L, or a1 if x <=0), where a1 is a constant and L is the size of the box. The model conserves energy as can be seen, since its kinetic energy (E=(1/2)*m*v ²) remains constant. This is easily seen also by noticing that the particle's speed inside the box is constant as well. The equation is solved by a Runge-Kutta solver using EJS. ]]> 25 false VARIABLE_EDITOR Var Table true true m1 double d1 double x1 double y1 double vx1 double t double L double a1 double double ODE_EDITOR Evol Page true true t 0.01 vx1 F(x1) RungeKutta LIBRARY_EDITOR force true true =L) return -a1/m1; return 0.0; } ]]> true Elements.Frame Frame true Frame border true 500,500 false Elements.Panel buttonspanel Frame south border:0,0 500,100 false Elements.Panel Panel1 buttonspanel north flow:left,0,0 500,50 Elements.Button Play Panel1 center Play _play() Elements.Button Pause Panel1 Pause _pause() Elements.Button reset Panel1 reset _reset() false Elements.Panel Panel2 buttonspanel south flow:left,0,0 500,50 Elements.Slider vx1 Panel2 vx1 -5.0 5.0 vx1= #0.00 150,50 Elements.Slider mass1 Panel2 m1 0.01 10.0 m1 = #0.00 150,50 Elements.Slider force1 Panel2 a1 0.0 25 a1 = #0.00 150,50 true Elements.Panel drawing Frame north border 300,300 true Elements.DrawingPanel DrawingPanel drawing center false false -5.0 L+5.0 -10.0 10.0 Elements.Particle Particle DrawingPanel x1 y1 0.5 0.5 1 1.8 FILLED_CIRCLE Elements.Arrow wall_left DrawingPanel 0.0 -1.0 0 2.0 SEGMENT Elements.Arrow wall_rigth DrawingPanel L -1.0 0 2.0 SEGMENT