Formula to calculate the uncertainty in the density

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Homework Help Overview

The discussion revolves around calculating the uncertainty in the density of a sphere, given its radius and mass along with their respective uncertainties. The subject area includes concepts of density, measurement uncertainty, and error propagation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply a formula for uncertainty in density but expresses confusion about its application, particularly in relation to the results they are obtaining. Some participants clarify the definitions of the uncertainties and provide the measured values for radius and mass. Others suggest a method for calculating the uncertainty based on the provided formula.

Discussion Status

Participants are actively discussing the application of the uncertainty formula and have provided some guidance on how to approach the calculation. There is an acknowledgment of the original poster's confusion, and some clarification has been offered regarding the values involved in the calculation.

Contextual Notes

The original poster has converted measurements to meters and is working with the formula for uncertainty in density. There is an indication of uncertainty in the results they are obtaining, which has prompted further discussion.

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Homework Statement


A radius of a sphere is measured to be (6.45 ± 0.27) cm, and the mass is measured to be (1.78 ± 0.09) kg. Determine the density of the sphere in kilograms per cubic meter and the uncertainty in the density.


Homework Equations


Use the following formula to calculate the uncertainty in the density:
Δρ/ρ = Δm/m + 3Δr/r.)


The Attempt at a Solution


I already found the density: 1583.62 kg/m3
I just want to know how to get the uncertainty. I don't know how to use the formula given. i always get a really low number with it.
 
Last edited by a moderator:
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Welcome to PF!

The uncertainties are the ranges by which the measured quantities can vary, and these ranges are indicated using the symbol 'Delta.' Hence:

Δr = 0.27 cm

Δm = 0.09 kg

and of course, the measured values are:

r = 6.45 cm

m = 1.78 kg
 


This is what i did after converting to meters:
(0.09/1.78)+(3*.0027/.0645)
 
Last edited:


0.17614 = Δρ/ρ so you don't need to divide by anything.
To find the actual uncertainty in p you multiply 0.17614 by the density you have calculated.
.
 


ok, thank you.
 

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