How to calculate density from specific weight in imperial units

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SUMMARY

The discussion focuses on calculating the density of a clay unit using a specific weight of 120 lb/ft³ and a gravity constant of 32.17 ft/s². The formula used is density = specific weight / gravity, which leads to the calculation of density as 3.73 lb/ft²·s². However, participants point out that the units are incorrect, indicating a misunderstanding of unit cancellation in imperial measurements. The correct interpretation of units is crucial for accurate density calculation.

PREREQUISITES
  • Understanding of specific weight and density relationships
  • Familiarity with imperial units of measurement
  • Basic knowledge of unit conversion and dimensional analysis
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Review the concept of specific weight and its relation to density in imperial units
  • Learn about dimensional analysis to ensure unit consistency in calculations
  • Study examples of density calculations in imperial units
  • Explore the implications of using different unit systems in engineering problems
USEFUL FOR

Students in engineering or physics courses, educators teaching unit conversions, and professionals needing to apply density calculations in imperial units.

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Homework Statement


alright so i have to find the density of a clay unit. I am given a specific weight of the clay as 120 b/ft^3, the gravity constant as 32.17 ft/s^2. i need to find the density of the clay, i have no problem arranging the equation below to solve for density but I am not used to working in imperial units and I am not allowed to switch to metric. I've attempted it below and just wondering if i did it correctly


Homework Equations


specific weight= gravity x density


The Attempt at a Solution


density= specific weight/gravity
= 120 lb/ft^3/32.17 ft/s^2
= 3.73 lb/ ft^2 s^2

so are my units correct?
 
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No, your units aren't correct. Check your work.
 
ideasrule said:
No, your units aren't correct. Check your work.

could you give me a hint?
to me it seems correct, I am dividing lb/ft^3 by ft/s^2. so the only thing that would cancel is the ft in the numerator and denomanator.

i understand that in metric it kg/m^3, but I've never used imperial. would it be lb/ft^3? how would the units cancel out?
 

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