Deriving the gravitational constant factor for lbf

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SUMMARY

The discussion focuses on deriving the conversion factor for gravitational units in the English Engineering System, specifically how to convert between pound-force (lbf) and pound-mass (lbm) using the acceleration due to gravity. The key equations presented are 1 lbf = 1 lbm x 32 ft/sec² and 1 lbf = 1 slug x 1 ft/sec². Participants emphasize that the conversion factor of lbm-ft/lbf-sec² arises from the relationship between these units and the acceleration of gravity, which is crucial for understanding force calculations in this inconsistent system of units.

PREREQUISITES
  • Understanding of the English Engineering System
  • Familiarity with basic physics concepts, particularly force and mass
  • Knowledge of unit conversion principles
  • Basic grasp of acceleration due to gravity (32 ft/sec²)
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  • Research the derivation of unit conversion factors in physics
  • Study the relationship between mass, force, and acceleration in different unit systems
  • Learn about the implications of using inconsistent units in engineering
  • Explore the historical context of gravitational units and their applications
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Students and professionals in physics, engineering, and applied sciences who need to understand unit conversions in the English Engineering System, particularly those dealing with force calculations and gravitational factors.

ankh
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I have never had to use the English Engineering System so I am having a bit of a struggle here.

I understand the concept of an inconsistent system of units. I understand the following 2 statements:
1lbf = 1lbm x 32 ft/sec^2
1lbf = 1slug x 1 ft/sec^2

When given a problem that is asking for the force answer in lbf for an object that is being accelerated at something different than 32 ft/sec^2, i understand why i need to divide the answer by 32 to get the answer in lbf. However, i am stuck in trying to derive the units required for this conversion factor. I can follow why the conversion units are (lbm-ft/lbf-sec^2) once i cancel all the units, but I can not derive those units on my own for some reason. Can someone help out with the steps for figuring out the conversion units? How do you get to lbm-ft/lbf-sec^2 if it was my first time trying to discover a conversion factor?
 
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It is an inconsistent set of units. I don't think that you can derive the conversion factor from first principles.
 
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You could do it starting from SI units if you know each of those conversion factors.
 
ankh said:
Can someone help out with the steps for figuring out the conversion units? How do you get to lbm-ft/lbf-sec^2 if it was my first time trying to discover a conversion factor?
For historical reasons, the conversion factor is the acceleration of gravity. That is why it is considered a "gravitational" system of units.
 

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