Deriving the gravitational constant factor for lbf

[ankh]

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?

 

[Dale]

It is an inconsistent set of units. I don't think that you can derive the conversion factor from first principles.

 

[Dale]

You could do it starting from SI units if you know each of those conversion factors.

 

[jbriggs444]

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.