1. If your students have learned the equations for constant acceleration, they could use those equations to calculate the velocity and height as the package falls and then calculate the kinetic and gravitational potential energies. They could explore how the results calculated from the equations compare to the results they got from the MAIL activity. You can find the equations for constant acceleration in many textbooks.

2. For this Squeak project, the motions of the sled and package are calculated by the computer in many small steps. It doesn't use equations. If you make a small enough change in time the velocity is approximately constant so you can calculate the new position by adding the product of the current velocity and time change (change in position equals velocity times the change in time if the velocity is constant). To get the new velocity add the acceleration times the time change. Then do it again and again and again ... The computer is very good at routine tasks like this. A problem may occur if they try to go too fast and make big time changes. The time change for each step is the "dt" at the bottom of the Control Center. Have your students try taking data with bigger "dt" values with all the other parameters the same (that's how they would control in an experiment). Then they should compare and find out when the computer's results aren't so reliable anymore.

Before trying Challenge 3 in either the PARK or MAIL activity, your students and you should read this section. You can take the activity apart, which is the power of Squeak. Click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 1024x768 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. Taking a project apart and even breaking it is a good way to learn. No matter how bad a mess they make, your students can always get back to the original activity by quiting Squeak and starting over, so don't worry.

3. PARK Challenge 3: It would be very helpful to download and print the Etoy Quick Start Guide for your students before they start. Have your more advanced students draw a garage door and place a spring (from the Springs flap) on the garage door so Norbert's sled collides with the spring when Norbert is unparking. They need to examine the scripts to see how they work by following the directions for Challenge 3 in the book in the activity. Once they figure out how the scripts work, they need to modify the script for the new spring and the scripts that control the action. Your students should submit their Squeak project for Challenge 3 to the NASA CONNECT web site. We will post all the good entries that we receive to acknowledge your student's good work and let others learn from their solution.

Other more advanced extensions you can attempt by modifying the PARK Squeak project:
• Add heating energy loss during the collision of the sled with the spring. Use a simple model and assume a constant amount of energy is lost during the collision or a more advanced model where the energy lost depends on the velocity of the sled as it approaches the spring. Use the principal of conservation of energy.
• Add heating energy loss during the compression of the spring. Use a simple model and assume a constant amount of energy is lost during the compression or a more advanced model where the energy lost depends on the compression of the spring. Use the principal of conservation of energy.
• Assume the spring has mass and consider the effect of the kinetic energy of the spring mass on the parking. You can look up models of springs with mass in textbooks.

4. MAIL Challenge 3: It would be very helpful to download and print the Etoy Quick Start Guide for your students before you start. Have your more advanced students place a second package (from the Packages flap) side by side with the first package. They should examine the scripts to see how they work by following the directions for Challenge 3 in the book in the activity. Once they figure out how the scripts work, they need to modify the script for the second package and the scripts that control the action. Have your students submit their Squeak project for Challenge 3 to the NASA CONNECT web site. We will post all the good entries that we receive to acknowledge your student's good work and let others learn from their solution.

Other more advanced extensions you can attempt by modifying the MAIL Squeak project:
• Instead of Zot releasing the package from rest, have Zot throw the package upward or downward. You have to modify the script so the velocity is not zero at the start, but some positive or negative constant. Compare the results for the same speed when the package is thrown upward and downward.
• Have the package follow a parabola as it is delivered to a moving magical mailbox. You can do this by adding the same constant velocity in the horizontal (x) direction to both the package and the mailbox. Create a similar and simplier script to do this following the script for falling. Since the acceleration is zero for constant velocity, you can just change x by a constant times dt.
• Include air drag in the simulation. Air drag produces an upward force that has to be subtracted from the downward force of gravity. The acceleration is no longer just g, but g minus a constant times the speed divided by the mass. Add this change to the script and try different constants.

5. Have your more advanced students try creating their own microworld that involves kinetic, elastic potential and gravitational potential energies.

6. You may think mathematics and art aren't related, but nothing could be farther from the truth. The sense of beauty you see in art is equally important in mathematics. Symmetry is part of beauty and it runs throughout art and mathematics. Theorems have a sense of beauty because they represent truth. Beauty gives you a sense of balance and well-being in your life. The Squeak project was organized on the page to be functional and that often leads to a kind of beauty. But beauty is in the eye of the beholder, so we challenge you to recreate the Squeak Exercise Challenge project in a way that leaves you with a sense of balance and beauty. With the tools in Squeak, you can make your own drawings. Any of the objects can be moved and resized and their colors can often be changed. Click on any object while holding down the alt key on a PC or the Apple key on a Mac and you will see the halo of handles. Click on the red handle at the upper left to explore many options for changing the object. Go to Squeakland for tutorials and more information on using Squeak. When you are done go to the NASA CONNECT web site to submit your version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open your project.