Instructions for Sample Lab

Experimental Investigation of C/D

Introduction: How is the circumference of a circle related to its diameter? In this lab, you design an experiment to test a hypothesis about the geometry of circles. This activity is an introduction to physics laboratory investigations. It is designed to give practice taking measurements, analyzing data, and drawing inferences without requiring any special knowledge about physics.

Equipment (per group):

• Metric ruler
• Vernier calipers
• at least 5 objects with diameters ~1 cm to ~10 cm: (penny, marble, "D" cell, PVC cylinders)

Procedure: Design an experimental procedure to test the following hypothesis:

Hypothesis: The circumference (C) of a circle is directly proportional to its diameter (D).

Make sure you record what you do as you do it, so that the procedure section of your report accurately and completely reflects what you did. Some helpful hints for taking and recording data are in the lab tips and in the grading rubric.

Analysis:

Note: As the semester progresses, you will be expected to take more and more responsibility for deciding how to analyze your data. Drawing valid inferences from data is a vital skill for engineers and scientists. The instructions for analyzing data for most labs will not be as detailed as the instructions below.

• Numerical Analysis: Calculate the ratio C/D for each object. Estimate the precision of each value of C/D.
• Graphical Analysis: Use Excel to construct a graph of C versus D. Use Excel to display the equation of the best fit line through your data. Use the LINEST function to estimate the uncertainty in the slope and intercept of the best fit line. Make sure you interpret the meaning of both the slope and intercept. A checklist for graphs is in the grading rubric.
• Questions to consider:
  • How do your calculations and graph support or refute the hypothesis?
  • Does your graphical analysis agree with your calculations?
  • Do your results for the C/D ratio agree with accepted theory?

Report: A sample lab report for this activity is provided as an example for you to follow when writing future lab reports.