Uncertainty Error Analysis and Graph Plotting

Uncertainty Error Analysis and Graph Plotting

Introduction

The purpose of this experiment is intended to demonstrate the effects of uncertainty and error on data and conclusions. Primarily, this experiment focused on collecting information with a tape measurement to show that there is uncertainty from both human involvement and a lack of precision from lab equipment.

Equipment

 ο‚· Tape measurement

  ο‚· 2 different sized disks

Procedure

 First, we measured the circumference of each disk four times with the tape measurement by wrapping it around each disk. This data was added to a table used and then we measured the radius of each disk once with the tape measurement and added this information to a chart comparing circumference with diameter. This information was plotted, and the slope of the line was recorded and compared to what the slope should have been. For part two of this lab, we simply created a graph for each data chart including a title, independent x-axis, dependent y-axis, calculated a scale for each axis, plotted the data points and drew a line of best fit. Finally, we calculated a slope for each line of best fit and reported the values.

Data

  • Measure the radius and circumference of the disks and quote the uncertainty for each measurement disk.
  • Calculate what the circumference should have been, if you used the formula C = 2πœ‹r (for the part of the lab pretend that the radius measurement was perfect – zero uncertainty). Find the error percentage in each measurement. This can be calculated quickly, and just tells you how off you were from the formula/theory (expected value). Take the absolute value, as negative error is meaningless:

πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ = 𝑇hπ‘’π‘œπ‘Ÿπ‘’π‘‘π‘–π‘π‘Žπ‘™ π‘π‘–π‘Ÿπ‘π‘’π‘šπ‘“π‘Ÿπ‘’π‘›π‘π‘’ βˆ’ π‘€π‘’π‘Žπ‘ π‘’π‘Ÿπ‘’π‘‘ π‘π‘–π‘Ÿπ‘π‘’π‘šπ‘“π‘Ÿπ‘’π‘›π‘π‘’) βˆ— 100% divided by 𝑇hπ‘’π‘œπ‘Ÿπ‘’π‘‘π‘–π‘π‘Žπ‘™ π‘π‘–π‘Ÿπ‘π‘’π‘šπ‘“π‘Ÿπ‘’π‘›π‘π‘’

ObjectsRadiusMeasured circUncertaintyTheorical circ
Small Disk4.4 cm27.646 cm0.48%0.133 cm
Large Disk2.6 cm16.336 cm0.77%0.124 cm
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