What is the density and uncertainty of a given object?

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SUMMARY

The discussion focuses on calculating the density and uncertainty of an object using the formula p = 6M/πD³, where mass (M) is 0.0163 kg with an uncertainty of 0.0001 kg, and diameter (D) is 0.015 m with an uncertainty of 0.001 m. The calculated density is 9223.9 kg/m³, and the uncertainty in density is determined to be 1901 kg/m³. The relative uncertainty of the density is approximately 0.2, which is significantly higher than the relative uncertainty of the diameter at 0.067, confirming that the density calculation is accurate despite the large uncertainty value.

PREREQUISITES
  • Understanding of basic physics concepts, particularly density and uncertainty.
  • Familiarity with the formula for density calculation: p = 6M/πD³.
  • Knowledge of how to propagate uncertainties in measurements.
  • Basic mathematical skills for performing calculations involving fractions and exponents.
NEXT STEPS
  • Study the principles of uncertainty propagation in physical measurements.
  • Learn about the significance of relative uncertainty in experimental physics.
  • Explore advanced density calculation methods for irregular objects.
  • Investigate the impact of measurement precision on scientific results.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in experimental science who needs to understand density calculations and uncertainty analysis.

gdogga
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Homework Statement


Calculate the density and its ucertainty...

Mass = 0.0163 kg
Uncertainty Mass = 0.0001 kg
Diameter = 0.015m
Uncertainty Diameter = 0.001m


Homework Equations


p=6M/piD^3
^p/p=^m/m + 3^D/D

The Attempt at a Solution


p= 6 x (0.0163)/ pi(0.015^3)
= 9223.9 kg/m^3

^p/9223.9= 0.0001/0.0163 + 0.003/0.015
^p= 1901 kg/m^3

The value for ^p just seems too large?
 
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Your result is correct. The relative uncertainty of the density is about 0.2, which is not too big compared to the 0.067 relative uncertainty of the diameter.

ehild
 

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