What Is the % Error in the Density of a Metal Bar?

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SUMMARY

The discussion focuses on calculating the percentage error in the density of a metal bar based on its dimensions and mass. The metal bar's length has a precision of ±1%, mass ±2%, and radius ±3%. The relevant equations for this calculation are volume (V = πr²h) and density (D = m/V). Participants seek guidance on applying error propagation techniques to derive the overall percentage error in density.

PREREQUISITES
  • Understanding of basic geometry, specifically volume calculations for cylinders.
  • Familiarity with the concept of density and its formula (D = m/V).
  • Knowledge of error propagation techniques in measurements.
  • Basic proficiency in calculus for handling derivatives in error calculations.
NEXT STEPS
  • Study error propagation methods in physics and engineering contexts.
  • Learn how to apply partial derivatives to calculate percentage errors.
  • Review resources on density calculations and their applications in material science.
  • Explore online platforms or textbooks that cover measurement uncertainties and their implications.
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Students in physics or engineering courses, educators teaching measurement techniques, and professionals involved in material testing and quality assurance.

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Homework Statement



A metal bar has a length measured to a precision of +-1%, a mass measured to +-2% and a radius masured to +-3%. What would be the % error in the value of the density of the metal in the bar calculated from these?

Homework Equations



V=(pi)r^2h
D=m/v

The Attempt at a Solution



I can calculate the actual density no problem.

However, i was away while we studies calculating with errors and am stuck.

If someone could help me with this problem or recommend a site/book i use to catch up, i'd really appreciate it :).
 
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