Preview - Charge Interactions Chem/Phys

Determining a mathematical model for the Electrical Interaction

Now that we have explored the simulation a little, let's take some time to construct a mathematical model to represent this electrical interaction between two charges.

We decided that our independent variables would be the amount of excess charge each particle has, and the separation between the charges.  The strength of the electrical interaction between charges is the value of the force.

We are going to use an automated graphing program (CODAP) to collect our data.  You will then be able to apply different fits to the data to obtain a linear relationship between all of the variables.  

In order to collect a data point, 1) Change the slider bars to the values you want.  2) Click on "Setup".  3) Click on "Compute".  4) Click on "Collect data point".  This will enter your data into the CODAP data table with all of the appropriate values. 

If you don't see a data table, click on "Tables" and then click on "Experiment Results".  If you don't see a graph, simply click on "Graph" then drag it to where you want.

IF you need to linearize data at some point:

  1. Decide what you have to do to the data to linearize.  Usually we think about doing stuff to the independent variables on the x-axis.
  2. In your data table, look for a little + sign that says "Add a new attribute to this table" when you hover your mouse over it.
  3. Click that + sign and then type in a name for this calculated variable. For example, if you decided to take the square root of charge_1, you might want to call this variable "charge_1^0.5" so you know what that column represents.
  4. Now after you hit enter, left-click on the new variable, then click on "edit formula". 
  5. Click on "insert value" then from the list select charge_1 (click on it).  It will now be in the formula box, and then just type " ^0.5 " which will take the square root of charge_1.  There is also an arithmetic function that does this but typing ^0.5 is easier.
  6. Click "Apply" and you will have a new data column.  Drag this column to the appropriate axis on your graph, and you should now have linearized data!
  7. Now you can click on the graph, then click on the ruler tool, then on the "least-squares line".  This will draw a best fit line through your (linear) data.  You can then write this in correct linearized form.  Remember to use variables, not x & y, and determine what the units must be for slope and intercept.  Write your mathematical model in the answer box.

Questions

Please answer the questions below.

Conduct and run an experiment to determine the relationship between the charge of the first particle, charge_1, and the force.  Collect data points using the "Collect data point" button when the simulation is running. Change your independent variable at least 8-10 times to collect different values of the dependent force. Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and charge_1?

Upload your graph that depicts the relationship between force and charge_1 by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete

Let's now find a mathematical relationship between charge_1 and force.  

Is this data linear? If so, we can click on the graph, then click on the ruler tool, then on the "least-squares line". This will draw a best fit line through your (linear) data. You can then write a mathematical model that describes the line. Remember to use the actual variables, not x & y, and to determine what the units must be for slope and intercept.  Write your mathematical model in the answer box.

If your original data was not linear, follow the procedure listed below the simulation to linearize your data with CODAP.

Conduct and run an experiment to determine the relationship between the charge of the second particle, charge_2, and the force.  Collect data points using the "Collect data point" button when the simulation is running.  Change your independent variable at least 8-10 times to collect different values of the dependent force.  Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and charge_2?

Upload your graph from the previous question by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete

Now use your simulation and CODAP to write a mathematical model that describes the relationship between charge_2 and force.  Use the same process as you did in question 2.3 above to linearize your data if necessary.  Write your mathematical model in the space below.

Conduct and run an experiment to determine the relationship between the separation of the two charges and the force. Collect data points using the "Collect data point" button when the simulation is running. Change your independent variable at least 8-10 times to collect different values of the dependent force. Then, drag these variables from where they appear in the table to the correct axes on the graph, and CODAP will create a graph for you.  

Note: It is not necessary to collect multiple trials of each data point.

What type of relationship do you observe between force and separation?

Upload your graph from the previous question by clicking on the camera icon to the right of the graph.

Upload files that are less than 5MB in size.
File Delete

Now use your simulation and CODAP to determine write a mathematical model that describes the relationship between force and separation. Use the same process as you did in 2.3 above to linearize your data if necessary. Write your mathematical model in the space below.

While you are waiting for other groups to finish this part of the lab, compare your mathematical models from questions 2.3, 2.6, & 2.9 with at least one other group.  Record any similarities or differences you notice.

Notes

These notes will appear on every page in this lesson so feel free to put anything here you'd like to keep track of.