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# Introduction to Physics Problem Solving on the Internet

Interactive Examples

Many students, taking Physics I and II, Phy 143 and Phy 144, for the first time, sometimes find the problem solving overwhelming. In order to help these students, I have computerized every illustrative example in my textbook, " Physics for Science and Engineering Students", by Dr. Peter J. Nolan. These computerized Interactive Examples will allow you to solve the example problem in the textbook, with all the in-between steps, many times over but with different numbers placed in the problem.

Figure 1 shows an example from Chapter 2 of the textbook for solving a problem in Kinematics. It is a problem in kinematics in which a car, initially traveling at 30.0 km/hr, accelerates at the constant rate of 1.50 m/s2. The student is then asked how far will the car travel in 15.0 s? The example in the textbook shows all the steps and reasoning done in the solution of the problem.

Example 2.6

Using the kinematic equation for the displacement as a function of time. A car, initially traveling at 30.0 km/hr, accelerates at the constant rate of 1.50 m/s2. How far will the car travel in 15.0 s?

## Solution

To express the result in the proper units, km/hr is converted to m/s as

The displacement of the car, found from equation 2.14, is

x = v0t + 1/2 at2

= 125 m + 169 m

= 294 m

The first term in the answer, 125 m, represents the distance that the car would travel if there were no acceleration and the car continued to move at the velocity 8.33 m/s for 15.0 s. But there is an acceleration, and the second term shows how much farther the car moves because of that acceleration, namely 169 m. The total displacement of 294 m is the total distance that the car travels because of the two effects.

Figure 1 Example 2.6 in the textbook.

The interactive example for this same problem is shown in the spreadsheet in figure 2. When the student opens this particular spreadsheet, he or she sees the problem stated in the identical manner as in the textbook. Directly below the stated problem is a group of yellow-colored cells labeled Initial Conditions. Into

Figure 2 Interactive Example 2.6 in Microsoft Excel Spreadsheet.

these yellow cells are placed the numerical values associated with the particular problem. For this problem the initial conditions consist of the initial velocity v0 of the car, the acceleration a of the car, and the time t that the car is moving, as shown in figure 2. The problem is now solved in the identical way it is solved in the textbook. Words are used to describe the physical principles and then the equations are written down. Then the in-between steps of the calculation are shown in light green-colored cells, and the final result of the calculation is shown in a light blue-colored cell. The entire problem is solved in this manner, as shown in figure 2. If the student wishes to change the problem by using a different initial velocity or a different time or acceleration, he or she then changes these values in the yellow-colored cells of the initial conditions. When the initial conditions are changed the computer spreadsheet recalculates all the new in-between steps in the problem and all the new final answers to the problem. In this way the problem is completely interactive. It changes for every new set of initial conditions. The examples can be changed many times over to solve for all kinds of special cases.

These Interactive Examples are a very helpful tool to aid in the learning of physics if they are used properly. The student should try to solve the particular problem in the traditional way using paper and an electronic calculator. Then the student should open the spreadsheet, insert the appropriate data into the Initial Conditions cells and see how the computer solves the problem. Go through each step on the computer and compare it to the steps you made on paper. Does your answer agree? If not, check through all the in-between steps on the computer and your paper and find where your made a mistake. Repeat the problem using different Initial Conditions on the computer and your paper. Again check your answers and all the in-between steps. Once you are sure that you know how to solve the problem, try some special cases. What would happen if you changed an angle?, a weight?, a force? etc. In this way you can get a great deal of insight into the physics of the problem and also learn a great deal of physics in the process.

You must be very careful not to just plug numbers into the Initial Conditions and look at the answers without understanding the in-between steps and the actual physics of the problem. You will only be deceiving yourself. Be careful, these spreadsheets can be extremely helpful if they are used properly.

We should point out two differences in a text example and in a spreadsheet example. Powers of ten, that are used in scientific notation in the text, are written with the capital letter E in the spreadsheet. Hence, the number 5280, written in scientific notation as 5.280 % 103, will be written on the spreadsheet as 5.280E+3. Also, the square root symbol in the textbook is written as sqrt[ ] in a spreadsheet. Finally, we should note that the spreadsheets are "protected" by allowing you to enter data only in the designated light yellow-colored cells of the Initial Conditions area. Therefore, the student cannot damage the spreadsheets in any way, and they can be used over and over again.

The Interactive Examples are available for the personal computer, using Microsoft's Excel computer spreadsheet.

## Getting Started on the Computer

The Interactive Examples are written on Microsoft's Excel spreadsheet for Windows 95 or Windows 98. The windows environment is used because it is the easiest way to use a computer. It relies on the basic concepts of point and click. An electronic mouse is used to control the location of the pointer on the computer screen. By moving the mouse, you can place the pointer at any location on the screen. If you place the pointer at a menu item and click the left mouse button you activate that particular function of the menu. You must have Microsoft's Excel software on your computer to use these interactive examples.

Procedure for using the Interactive Examples.

1. Download thefile below that you are interested in, by double clicking on the file of your choice. The files are listed by chapter number. As an example, if you want to see the examples from Chapter 2, you will download the file Chapter 2 Examples.

2. You must have the Microsoft Excel 97 or higher software on your personal computer. When you double click on the desired chapter below, the file will be automatically downloaded to you and will be automatically opened in the Microsoft Excel spreadsheet and is ready for you to use. Depending on your Internet provider, the time of day, and your modem, downloading the file may be a little slow. Be patient, the file will come up.

3. The examples will start with example 1 and will continue to the last example covered in that chapter. Use the vertical scroll bar to the right of the screen to scroll to the example of your choice. The spreadsheet will have all the necessary data for the problem already in it. If you wish to change any data in the yellow-colored cells of the Initial Conditions, place the pointer at the particular cell in the spreadsheet and click the left mouse button. This will activate that particular cell of the spreadsheet and you can enter any numbers you wish into that cell. The problem will be resolved with your new set of numbers. You can save the file to your own computer by clicking on the file menu at the top left corner of the screen and then clicking on the save as command. The save window will open and you can save the file in your computer in any directory that you choose.

4. If you wish to open examples from another chapter, repeat steps 1 through 3. Good luck to you and have fun with these interactive examples.

Download each chapter's interactive examples:

 Chapter 1 Examples Chapter 2 Examples Chapter 3 Examples Chapter 4 Examples Chapter 5 Examples Chapter 6 Examples Chapter 7 Examples Chapter 8 Examples Chapter 9 Examples Chapter 10 Examples Chapter 11 Examples Chapter 12 Examples Chapter 13 Examples Chapter 14 Examples Chapter 15 Examples Chapter 16 Examples Chapter 17 Examples Chapter 18 Examples Chapter 19 Examples Chapter 20 Examples Chapter 21 Examples Chapter 22 Examples Chapter 23 Examples Chapter 24 Examples Chapter 25 Examples Chapter 26 Examples Chapter 27 Examples Chapter 28 Examples Chapter 29 Examples Chapter 30 Examples Chapter 31 Examples Chapter 32 Examples Chapter 33 Examples Chapter 34 Examples Chapter 35 Examples Chapter 36 Examples Chapter 37 Examples

## Computer Assisted Instruction

Interactive Tutorials

Besides the Interactive Examples in your text, I have also introduced a section called Interactive Tutorials at the end of the problem section in each chapter. These Interactive Tutorials are a series of physics problems, very much like the interactive examples, but are more detailed and more general. The Interactive Tutorials are available for the personal computer (PC), using Microsoft's Excel computer spreadsheet.

Figure 3 show a typical Interactive Tutorial for problem 29 in chapter 4 on kinematics in two dimensions. When the student opens this particular spreadsheet, he or she sees the problem stated in the usual manor. That is, this problem is an example of a projectile fired at a initial velocity vo = 53.0 m/s at an angle q = 50.00, and it is desired to find the maximum height of the projectile, the total time the projectile is in the air, and the range of the projectile. Directly below the stated problem is a group of yellow-colored cells labeled Initial Conditions.

Into these yellow cells are placed the numerical values associated with the particular problem. For this problem the initial conditions consist of the initial

velocity vo, the initial angle q, and the acceleration due to gravity g as shown in figure 3. The problem is now solved in the traditional way of a worked out example in the book. Words are used to describe the physical principles and then the equations are written down. Then the in-between steps of the calculation are shown in light green-colored cells, and the final result of the calculation is shown in a light blue-green-colored cell. The entire problem is solved in this manor as shown in

Figure 3. A typical Interactive Tutorial.

figure 3. If the student wishes to change the problem by using a different initial velocity or a different launch angle, he or she then changes these values in the yellowed-colored cells of the initial conditions. When the initial conditions are changed the computer spreadsheet recalculates all the new in-between steps in the problem and all the new final answers to the problem. In this way the problem is completely interactive. It changes for every new set of initial conditions. The tutorials can be changed many times over to solve for all kinds of special cases.

These Interactive Tutorials are a very helpful tool to aid in the learning of physics if they are used properly. The student should try to solve the particular problem in the traditional way using paper and an electronic calculator. Then the student should open the spreadsheet, insert the appropriate data into the Initial Conditions cells and see how the computer solves the problem. Go through each step on the computer and compare it to the steps you made on paper. Does your answer agree? If not, check through all the in-between steps on the computer and your paper and find where your made a mistake. Repeat the problem using different Initial Conditions on the computer and your paper. Again check your answers and all the in-between steps. Once you are sure that you know how to solve the problem, try some special cases. What would happen if you changed an angle?, a weight?, a force? etc. In this way you can get a great deal of insight into the physics of the problem and also learn a great deal of physics in the process.

You must be very careful not to just plug numbers into the Initial Conditions and look at the answers without understanding the in-between steps and the actual physics of the problem. You will only be deceiving yourself. Be careful, these spreadsheets can be extremely helpful if they are used properly.

## Getting Started on the Computer

The Interactive Tutorials are written on Microsoft's Excel spreadsheet for Windows 98. The windows environment is used because it is the easiest way to use a computer. It relies on the basic concepts of point and click. An electronic mouse is used to control the location of the pointer on the computer screen. By moving the mouse, you can place the pointer at any location on the screen. If you place the pointer at a menu item and click the left mouse button you activate that particular function of the menu. You must have Microsoft's Excel software on your computer to use these interactive tutorials.

### Procedure for using the Interactive Tutorials.

1. Download the interactive tutorial file below that you are interested in, by double clicking on the file of your choice. The files are listed by chapter number. As an example, if you want to see the tutorials from Chapter 2, you will download the file Chapter 2 Tutorials.

2. You must have the Microsoft Excel 97 or higher software on your personal computer. When you double click on the desired chapter below, the file will be automatically downloaded to you and will be automatically opened in the Microsoft Excel spreadsheet and is ready for you to use. Depending on your Internet provider, the time of day, and your modem, downloading the file may be a little slow. Be patient, the file will come up.

3. The tutorials will start with the first numbered tutorial for that chapter. As an example, if you are opening the tutorials for chapter 2 the first tutorial that opens will be for problem 55 from the second chapter of your textbook. At the bottom of the spreadsheet you will see the other tutorials of that chapter listed as Problem 56, Problem 57, and Problem 58. If you click on Problem 56, the spreadsheet for interactive tutorial problem 56 will open for you. Use the vertical scroll bar to the right of the screen to scroll through the tutorial. As you will see, it looks just like figure 3 above. The spreadsheet will have all the necessary data for the problem already in it. If you wish to change any data in the yellow-colored cells of the Initial Conditions, place the pointer at the particular cell in the spreadsheet and click the left mouse button. This will activate that particular cell of the spreadsheet and you can enter any numbers you wish into that cell. The problem will be resolved with your new set of numbers. You can save the file to your own computer by clicking on the file menu at the top left corner of the screen and then clicking on the save as command. The save window will open and you can save the file in your computer in any directory that you choose.

4. If you wish to open tutorials from another chapter, repeat steps 1 through 3. Good luck to you and have fun with these interactive tutorials.

Download each chapter's tutorials:

 Chapter 1 tutorials Chapter 2 tutorials Chapter 3 tutorials Chapter 4 tutorials Chapter 5 tutorials Chapter 6 tutorials Chapter 7 tutorials Chapter 8 tutorials Chapter 9 tutorials Chapter 10 tutorials Chapter 11 tutorials Chapter 12 tutorials Chapter 13 tutorials Chapter 14 tutorials Chapter 15 tutorials Chapter 16 tutorials Chapter 17 tutorials Chapter 18 tutorials Chapter 19 tutorials Chapter 20 tutorials Chapter 21 tutorials Chapter 22 tutorials Chapter 23 tutorials Chapter 24 tutorials Chapter 25 tutorials Chapter 26 tutorials Chapter 27 tutorials Chapter 28 tutorials Chapter 29 tutorials Chapter 30 tutorials Chapter 31 Examples Chapter 32 Examples Chapter 33 tutorials Chapter 31 Examples Chapter 35 Examples Chapter 36 tutorials Chapter 37 Examples
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