A freely falling object is acted on by a constant downward gravitational force if we ignore air resistance. Because this gravitational force F is constant and because it is proportional to the mass of the falling object, all objects near Earth fall with the same constant downward acceleration g = 9.8 m/s2. In the Free Fall model, the ball's speed is reduced by a constant factor at every floor collision. All motion takes place in the vertical (y) direction to keep this first Ejs example as simple as possible.

References:

The Free Fall model is a designed to teach Ejs modeling. Right click within the simulation to examine this model in the Ejs modeling and authoring tool. See:

"Modeling Physics with Easy Java Simulations" by Wolfgang Christian and Francisco Esquembre, The Physics Teacher, November 2007, 45 (

, pp. 475-480.

The Easy Java Simulations (EJS) manual can be downloaded from the ComPADRE Open Source Physics collection and from the Ejs website.

Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. You can examine and modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu.

Information about Ejs is available at:

.

The Free Fall model uses 6 variables having their usual meaning. The variable g is the acceleration new Earth's surface due to gravity in m/s2. The coefficient of restitution is used to reduce the speed of the falling object at each bounce.

Numerical algorithms for solving second order differential equations, such as Newton's Second Law, usually require that the differential equation be rewritten as a system of first ordinary differential equations. This is a straightforward process if we introduce a variable for each velocity component. Because the ball's motion occurs only along the y (vertical) axis, we introduce the variable vy. For the simple Free Fall example the differential equations for vertical position y and velocity vy can be written as:

dy/dt = vy dvy/dt =-9.8 .

Differential equations for position y and the velocity vy are entered on the Ejs Evolution page.

Modeling the bounce requires an Ejs event that is triggered when the ball passes through the table top. An Ejs event occurs when the event's zero condition becomes negative. Because the table is located at y=0, we can use the y-position of the ball to trigger the event.

If the ball is below the floor and if the velocity is downward, the zero condition is negative and the event's action takes place. Note that Ejs automatically determines the time of the event (to within the given tolerance) before applying the action. The time evolution will then continue unless the Stop at event box is selected. In the Simple Free Fall model, the event's action diminishes the speed of the ball and causes the ball to move upward.

**My contributions are**

1. Event for ODE Evolution Page in EJS that is easier to modify

if (y<-0.5) return y; // change the value to check where to rebounce example y<1.0

else

return 1;

**2. panel for inputs of variables like vx and vy so that students can explore when if scenarios**

**source code**

download the *.jar for using the applet on standalone without internet connection.