Quandaries & Queries - Math Central

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Quandaries & Queries

Question from Ray, a student:

Good Day! I was confused about lbm and lbf and slug. I knew that lbm is a unit
for mass and lbf is a unit for weight. my problem is some books follow this
relationship where lbf=(lbm times the gravitational pull) which is 32.2 ft/(s2)
while other books treat lbm=lbf. other books also treat lbm=(lbf times 32.2)...
which is correct?

Is 1kg=2.205 lbm or 1kg=2.205lbf?
Is 1BTU=778.16 lbf-ft or 1BTU=778.16 lbm-ft?

what is the relationship of slug on these two, lbm and lbf?

Hi Ray,

Conversion between units can be a little confusing, especially if you you do not understand what they represent. Slugs, kilograms and pound-mass (lbm) are all units of mass so you can convert from one to the other:

1 kg = 2.205 lbm	1 lbm = 0.454 kg	1 slug = 14.594 kg
1 kg = 0.0685 slugs	1 lbm = 0.031 slugs	1 slug = 32.174

Mass is the amount of matter of an object and is often confused with weight. Weight is the strength of the force of gravity on an object. From Newton's 2nd Law of Motion: Force = mass x acceleration. Since force and mass are measurements of different things, we cannot convert the units from one to the other. In the metric system, the unit of force is Newtons which can be defined as N=kg·m/s². Some other common units of force are pound-force (lbf) and lbm·ft/s². You can convert one to the other:

1 N = 0.224808943 lbf	1 lbf = 32.17405 lbm·ft/s²	1 lbm·ft/s² = 0.03108095 lbf
1 N = 7.233013851 lbm·ft/s²	1 lbf = 4.44822162 N	1 lbm·ft/s² = 0.138254954 N

Hope this helps.

Janice

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