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Ceiling Bounce Model

written by
Wolfgang Christian
supported by
the National Science Foundation

This simulation shows a ball launched by a spring-gun in a building with a very high ceiling. The student's task is to calculate an initial velocity so that the ball barely touches the 80-foot ceiling. Students can test their answers by setting the initial velocity on the simulation, then watch the ball's path. Graphs of position vs. time or velocity vs. time may be turned on to view the ball's motion as a function of time.

This item was created with Easy Java Simulations (EJS), a modeling tool that allows users without formal programming experience to generate computer models and simulations. To run the simulation, simply click the Java Archive file below. To modify or customize the model, See Related Materialsfor detailed instructions on installing and running the EJS Modeling and Authoring Tool.

Please note that this resource requires
at least version 1.5 of Java.

Editor's Note:This model is especially helpful for visualizing the relationship between the one-dimensional motion of this example and its graph, as it displays the ball continuously bouncing at constant velocity in a straight line from floor to ceiling. There is no horizontal displacement. For students who need help determining time of flight and peak height, SEE ANNOTATIONS for an editor-recommended tutorial.

Ceiling Bounce Model source code
The source code zip archive contains an XML representation of the Ceiling Bounce Model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 10kb .zip
Last Modified: June 2, 2014
previous versions

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

11. Common Themes

11B. Models

6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.

9-12: 11B/H3. The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that other models would not work equally well or better.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.4 Model with mathematics.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.^{?}

Building Functions (9-12)

F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

This editor-recommended resource provides a step-by-step tutorial in determining time of flight and peak height of a projectile, which will be needed to perform the calculations required in the Ceiling Bounce simulation.

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion Unit Title: Modeling Motion

In this model, a ball is launched by a spring-gun in a building with a very high ceiling. The task: calculate an initial velocity so that the ball barely touches the 80-foot ceiling. Students can test their answers by setting the initial velocity on the simulation, then watch the ball's path. Graphs of position vs. time or velocity vs. time can be turned on to view the ball's motion as a function of time.

W. Christian, Computer Program CEILING BOUNCE MODEL, Version 1.0 (2008), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926).

W. Christian, Computer Program CEILING BOUNCE MODEL, Version 1.0 (2008), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926>.

Christian, W. (2008). Ceiling Bounce Model (Version 1.0) [Computer software]. Retrieved February 22, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926

%A Wolfgang Christian %T Ceiling Bounce Model %D December 16, 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926 %O 1.0 %O application/java

%0 Computer Program %A Christian, Wolfgang %D December 16, 2008 %T Ceiling Bounce Model %7 1.0 %8 December 16, 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=8385&DocID=926

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