Lab 6 (3rd): Propagated Uncertainty

Title:
Propagated uncertainty in measurements

Purpose:
This lab explores the uncertainties in real-life measurements and calculations to provide a better understanding of the significance of knowing uncertainty in practical applications.

Theory:
Uncertainty in calculations is propagated through all calculations. This means that uncertainties from a number of different measurements will have a larger cumulative effect on the resulting calculation. The ultimate goal of calculating uncertainty is then to determine the tolerance range of measurements where a final product is produced within acceptable limits. Measurements more critical to the final product generally must have lower uncertainties.

Apparatus:

• Aluminum rod (1)
• Zinc rod (1)
• Digital scale (1)
• Vernier caliper (1)

Procedure:

Measure the diameter and length of both the aluminum and zinc rods. Note the uncertainty of the Vernier caliper when measuring. Weigh each rod. Using these values, calculate density of the rod.

Data and Graphs:

Analysis:

Calculations are shown on the paper. 

Conclusion:

This lab demonstrated the effects of uncertainty as more calculations are done. Relatively small uncertainties in measurements of length and mass produced larger percentage uncertainties in the final calculation. It was noted that uncertainty in length measurements contributed more to uncertainty in the final calculation compared to uncertainty in mass calculations. In addition to uncertainty of the measuring devices themselves, the zinc had various surface impurities which affected the measured diameter. This means that to produce more precise results, it was necessary to measure the diameter at a number of points to find an average value. This method can also be applied to other measurements where the same dimension is measured multiple times to help reduce the impact of random error.