Honors Physical Science

Mr. Mahlum    

           

Measuring π

 

Background: 

The relationship between the area of a circle and its radius has interested mathematicians for many centuries.  In this activity you will measure the radius and the area of several different sized circles to determine an experimental value for the number π.  In doing so, you will make use of all the topics and techniques discussed in class including significant figures, conversion factors, graphing, linear transformation, slope, and graphical analysis. 

 

 

Materials:  Ruler, Cardboard, balance,

 

Part 1 – Determination of an area / mass conversion factor

  1. Obtain a square piece of cardboard measuring 10 cm by 10 cm
  2. Calculate the area of the square, and write this value on the data table.
  3. Mass the square using the electronic balance provided.  Record this value on the data table.
  4. Calculate the area/mass conversion factor for the cardboard using the measurements obtained.  Divide the area of the square by the mass of the square and record this value on your data sheet.  Be sure to round properly for significant digits.

 

Part 2 – Measurement of Circles

  1. Obtain a series of cardboard circles
  2. Determine the radii of the circles.  Each group will have a different set of circles with different radii.  If you are missing some circles cross off that radius on the data table.  You will not be able to obtain data for a circle you do not have.
  3. Use the electronic balance to mass the circles you have.  Record the mass on the data table.
  4. Use the conversion factor from part one to determine the area for each circle.  Do not calculate the area in any other method.

 

Part 3 – Graphs

  1. Plot a graph of Area vs. Radius using the data you collected.  Draw a best-fit curve using a plastic curve fitter.
  2. Square the radius by taking the radius times itself or using the x2 button on your calculator.
  3. Plot a graph of Area vs. Radius2 using the data you collected.  Draw a best-fit line using a ruler.
  4. Calculate the slope of the best-fit line for the area vs. Radius2 graph and write the slope on your graph.

 

Part 4 - Data Analysis

  1. Record your observed value for π (your slope) and the accepted value for π (3.14).  Calculate your experimental error and record the value on your data table.
  2. Record the observed values for π calculated by all groups performing the experiment and calculate the class mean and standard deviation.

 

Formal Lab Report Requirements

You will submit a formal lab report for this activity.  You report will include an introduction, methods, results, and discussion section.  The report will be word-processed and spell checked.

 

Questions – Answer in complete sentences at the end of your formal lab report.

 

  1. Why was it necessary to measure the mass and the area of the square piece of cardboard before measuring the circles?

 

  1. Why was it necessary to plot a second graph of Area vs. Radius2 for the circles?

 

  1. On the graph why did you draw a line instead of connecting the dots?

 

  1. Was your measurement of pi accurate?

 

  1. Based on the class data was the technique for determining pi precise?

 

  1. Based on the class data was the technique for determining pi accurate?

 

  1. How many significant digits are in the accepted value of Pi?