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# 12.2: Squeak

Difficulty Level: At Grade Created by: CK-12

## What is Squeak?

Squeak is a free, open-source, object-oriented, multimedia authoring environment that runs on many platforms and can be used to construct active learning environments for all ages. Programs can be written in the Squeak environment by novices using graphical programming tiles or by experts using Smalltalk. Developers around the world are continually adding functionality to the open-source Squeak image. In fact, Squeak is written in Squeak. Everything in the Squeak world is an object. Each object has properties and can send messages to other objects. The objects are like actors on a stage. Each object can be imbued with actions that create interactive experiences for learners and authoring is always on. Squeak is currently being rewritten from the ground up and is the basis for many new collaborative programming environments and exciting developments.

Two activities have been developed using Squeak. The first activity introduces students to the use of lasers to measure aerosol and cloud thickness. The second activity introduces students to Squeak programming through the study of motion in one dimension. These programs can be opened by following this link, http://www.pcs.cnu.edu/~rcaton/flexbook/flexbook.html.

## Using Lasers to Measure Aerosol and Cloud Thickness

In this activity, students will use a Squeak program to investigate how lasers are used to measure the thickness of aerosols and clouds. Students will investigate the mathematical relationship between aerosol/cloud thickness and laser signal attenuation. The Squeak program also contains a mathematics review book for student reference. This activity is divided into six parts:

1. Calibration
2. Challenge 1: determining the relationship between laser intensity and aerosol/cloud thickness
3. Challenge 2: determining the thickness of an aerosol and/or cloud
4. Challenge 3: developing the algebraic equation that relates laser intensity to thickness
5. Challenge 4: developing the exponential equation that relates laser intensity to thickness
6. Challenge 5: writing a Squeak script to make a fifth test cell.

### Directions and Questions to Accompany Laser Simulation

There are six parts to this activity. The directions for each activity can be found in the “book” on the left-hand side of the simulation. It will make more sense if you first read the directions then complete the activity. Each activity has one or more questions that are listed below. Be sure to answer the questions for one activity before moving on to the next activity. As part of the simulation, there is a mathematics review “book” for your reference.

1. Calibration

For both the aerosol and cloud calibrations, make a data table that includes number of cells (thickness) and laser intensity. Be sure to record laser intensity values as you take measurements.

2. Challenge 1

Make a graph of laser intensity vs. number of cells (thickness) for both the aerosol and cloud calibrations. Determine whether the relationship between intensity and thickness is directly proportional, inversely proportional, always decreases by the same factor, or none of these. Show work to support you answer.

3. Challenge 2

In the calibration activity, each cell was $1$ cm thick. In real life, clouds and aerosols can be meters or even kilometers thick. Scale the cell thicknesses to meters using the following information:

For aerosols, $1 \;\mathrm{cm} = 3500 \;\mathrm{m}$

For clouds, $1 \;\mathrm{cm} = 70 \;\mathrm{m}$

In the Squeak program, click on the “aerosol challenge” and “cloud challenge” buttons to measure the laser intensity as it passes through aerosols/clouds of various thicknesses. Record these intensities and determine the corresponding thickness in meters. Explain the method you used to determine the thickness in meters.

4. Challenge 3

Based on your graphs, write an algebraic equation for the relationship between laser intensity and thickness for both aerosols and clouds. Show work to support your answer.

5. Challenge 4

Plot the natural log (ln) of intensity vs. thickness for both the aerosol and cloud calibration data. Write an exponential equation for each relationship.

6. Challenge 5

Construct a fifth test cell using Squeak. Save the edited program and submit it to your teacher.

### Answer Key for Laser Simulation

Aerosol Calibration Data Table
Number of Test Cells Laser Intensity
1 $.500$
2 $.250$
3 $.125$
4 $.063$
Cloud Calibration Data Table
Number of Test Cells Laser Intensity
1 $.750$
2 $.563$
3 $.422$
4 $.316$

Challenge 1 The intensity decreases by the same factor every time the thickness increases by the same amount.

Challenge 2 Below is a sample calculation for aerosol and cloud thickness. Students’ answers will vary depending on the thickness of the aerosol or cloud they measure. They may also determine the thickness using the graph they created.

Aerosol

$\mathrm{Laser\ intensity\ reading} = .281$

From the data table above, a $1 \;\mathrm{cm}$ thickness gives a laser intensity reading of $.500$, so

$\frac{.500}{1} & = \frac{.281}{x}\\x & = .562 \ \text{cm}$

From the information provided in the simulation, $1 \;\mathrm{cm}$ in the simulation is $3500 \;\mathrm{m}$, so

$\frac{.3500}{1} & = \frac{x}{.562}\\x & = 19678 \ \text{m}$

Cloud

$\mathrm{Laser\ intensity\ reading} = .553$

From the data table above, a $1 \;\mathrm{cm}$ thickness gives a laser intensity reading of $.750$, so

$\frac{.750}{1} & = \frac{.553}{x}\\x & = .737 \ \text{cm}\\$

From the information provided in the simulation, $1 \;\mathrm{cm}$ in the simulation is $70 \;\mathrm{m}$, so

$\frac{70} {1} & = \frac{x} {.737}\\ x & = 51.6 \ \text{m}\\$

Challenge 3

Aerosol equation: $y = .50^x$

Cloud equation: $y = .75^x$

Challenge 4

Transformed Aerosol Calibration Data Table
Number of Test Cells ln (Laser Intensity)
1 $-.693$
2 $-1.38$
3 $-2.07$
4 $-2.76$

Equation: $ln(y) = -.144x + .594$ or $y = 1.81e^{-.144x}$

Cloud Calibration Data Table
Number of Test Cells ln (Laser Intensity)
1 $-.288$
2 $-.574$
3 $-.863$
4 $-1.15$

Equation: $ln(y) = -.144x + .874$ or $y = 2.40e^{-.144x}$

## Learning About Newton’s Second Law by Exploring One—Dimensional Motion

In this activity, students will explore one-dimensional motion and at the same time learn about programming in Squeak. The program explores the interrelationship between position, velocity, acceleration, force, mass, and time as well as touching on the relationship between force and energy. Students work through the program at their own pace and then are given a challenge to demonstrate their understanding of the physics concepts presented by being challenged to write their own Squeak program.

### Directions and Challenge for Newton’s Second Law

Click on the following link to access the Squeak program for Newton’s second law: http://www.pcs.cnu.edu/~rcaton/flexbook/flexbook.html.

You should read through the "book" and complete the activities described. There are no questions for you to answer; you are simply learning about motion and how to model it using Squeak. On the last page of the book, you will find the challenge to complete. The only item you need to turn in is the program you write for the challenge. The following is an overview of how to use the programming controls found in the book:

• Any value that can be changed is next to a blue box with a description of the value.
• Once you have changed the values, click and hold the “!” in the yellow circle to run the simulation.
• Click the yellow reset button to return to the original conditions.
• The scripts that are running the simulation are in the green boxes.

The challenge you are given is:

“Use Squeak to create a simulated microworld that shows how a body moves under the action of a force law of your choice. Illustrate the motion with graphs. Write an instruction manual for your project and be sure to include an explanation of how your project works. To be sure your instructions are clear, test your manual on others not familiar with your project to see if they can follow your instructions. As an additional challenge, explore the relationship between Newton’s second law $(F=ma)$ and energy in your microworld.”

Feb 23, 2012

Jan 30, 2016