Halliday Resnick Krane Example Problem: Uncertainty on Weighing Machine

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SUMMARY

The discussion centers on the concept of uncertainty in measurements using a digital weighing scale, specifically addressing the example of weighing a pet cat with a scale that displays whole numbers. Participants clarify that the scale reading of 119 lb indicates a range of possible weights between 118.5 lb and 119.5 lb, establishing an absolute uncertainty of ±0.5 lb. The conversation also contrasts digital and analog scales, emphasizing that analog scales involve different uncertainty calculations due to their continuous nature. The formula for absolute uncertainty is discussed, highlighting the importance of understanding measurement precision in both digital and analog contexts.

PREREQUISITES
  • Understanding of measurement uncertainty concepts
  • Familiarity with digital and analog weighing scales
  • Knowledge of statistical methods for combining uncertainties
  • Basic principles of significant figures in measurements
NEXT STEPS
  • Research "Measurement Uncertainty in Digital Instruments" for deeper insights
  • Learn about "Statistical Methods for Combining Uncertainties" in engineering
  • Explore "GUM: Guide to the Expression of Uncertainty in Measurement" for standards
  • Study "Precision and Accuracy in Measurement Techniques" to enhance understanding
USEFUL FOR

Students, engineers, and professionals involved in measurement science, particularly those working with weighing instruments and seeking to understand the implications of measurement uncertainty in their work.

  • #31
vcsharp2003 said:
So, which type of error is included when absolute uncertainty is specified for a measuring device?
Up until now, we have been focusing on a situation where the only source of error was our ability to read the result from the gauge. Alternately, we have been focusing on a situation where the granularity of the lines on the gauge is our only hint as to the accuracy of the device.

Now you ask about a situation where someone has told us the uncertainty of the device. That uncertainty could include error from various sources. Systematic error, random error, quantization error, whatever.

If all we are given is an uncertainty range (for instance a maximum error bar), we do not know what sort of errors to expect, what kind of error distribution to expect or how the errors might correlate between different measurements.
 

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