AP Physics – Kowinsky – Linearization I Lab

Linearizing I Lab: Experimentally Determine Pi

Introduction:

There are many different ways to experimentally determine the value for Pi. In this experiment, we will use linearization techniques to experimentally determine Pi. This lab will allow you to become familiar with basic linearization techniques and hopefully allow you to see why the linearization of graphs are important in Science.

Materials:

Graph Paper

Compass

Ruler

Procedure:

(accuracy is the key to this lab)

1. Carefully and accurately measure the area inside 1 grid box on a piece of graph paper (use standard units).

2. You will need to draw 6 circles of different sizes on graph paper. Use a ruler to measure the radius of each circle. Count the number of grid squares that at inside each of the circles. Determine the size of 1 grid square and determine the area inside each of the circles. Write down each of the measurements (A and r) on a data table. Make sure you convert your units into meters.DO NOT CALCULATE THE AREAS; EXPERIMENTALLY DETERMINE IT BASED ON YOUR GRAPH PAPER.

3. Use your data table to make a graph of the Area vs Radius (A is along the Y axis, r is along the X axis). Label your graph with an appropriate title that is not —Graph #1“ but explains thevariables and the relationship between them.. Label the two axis with units. Make your graph fit an entire sheet of graph paper, do not squish the graph into a corner of the graph paper.DO NOT USE EXCEL (I know excel is much less tedious and much more accurate, but on the AP exam, you must hand draw your own graphs and cannot use Excel)

3. Once your data is plotted on the graph, Draw a line or curve of best fit that comes the closest to going through all the points. Determine what Graph Form this graph is.

4. On a separate sheet of graph paper, linearize the graph and draw a best fit line with a ruler.

4. From your linearized graph, determine the slope of the best fit line.

5. Show your calculation for the slope.

6. Write the equation of your line for your graph. Remember, for a straight line, Y = mX + b

In this case, Y = A , X = r, plug in your value of the slope for m, and your Y-intercept should be 0.

7. This equation should look familiar to you. You just experimentally derived the equation for the area of a circle. Write down the accepted equation for the area of a circle.

8. Your linearized slope should have been Pi. Estimate the percent error between your Pi value and the accepted Pi value.

Conclusion

In your conclusion, give an overview of the lab. For example was it successful, discuss your % error in this lab and discuss why you may have an error. Also discuss possible improvements to this lab to remove the error.

NAMES: ______

Lab Answer Sheet

For this 1st introductory lab, you do not have to do a lab report, simply fill in this sheet and attach your graph.

  1. Create your data table here with the Area and Radius:
  1. What graph form is the first graph? Write the equation for this graph. How do you linearize it?
  1. Your second graph should be the linearized graph. Write the equation of a line for this, using A and r, not X and Y.
  1. Write the equation for the area of a circle
  1. Write down your value of Pi (your slope of the linearized graph)
  1. Calculate the % error. Show all of your work.
  1. Discuss your Lab Conclusion in complete sentences