This has always bugged me. In high school, whenever we measured something for chemistry, we’d use a triple-beam balance, IIRC. Although technically the scale was designed to measure weight, the weight was expressed in units of kg. But really, I’d learn they were pulling a fast one. For simplicity sake, it really was measuring kgm (kilogram mass). OK, but.
Now, in physics class, we’d often want weight, not mass. Still, we’re using the same scales. People will say that 1 kgm (kilogram mass) = 1 kgf (kilogram force). But, 1 kgf <> 1 Newton, correct? 1 kgf = 1 kgm = 1/9.8 N = 1 slug, correct? (What was the English equivalent to a slug? A dyne is cgs units, correct?)
It got worse when, in engineering classes they’d quickly throw in a correction factor called “gc” which allows us the benefit of workin with kgf, but really complicates your calculations until you get used to working with it!
A 1-kg object weighs 9.8 N on the surface of the Earth. Both of these are SI units. A slug, on the other hand, is a U.S. Customary System unit of mass that weighs 32.17 pounds (on the surface of the Earth).
Oh, and g[sub]c[/sub] is a bastardized correction factor used by U.S. engineers to make equations work with an inherently inconsistent set of units (such as lb[sub]f[/sub] and lb[sub]m[/sub]).
Slugs haven’t been used in ages. What is typically used is that lb[sub]m[/sub] or “pound-mass”. Here on Earth, the pound (or pound-force) is equivalent to the pound-mass.
The truth is that the pound-mass is a bastardized unit in and of itself used to try and simplify things for the layman, eps. Pound-mass should never have been intorduced! You have pounds to measure force, and you have slugs by which to measure mass. If the engineering powers that be would have stuck to this, we wouldn’t need that damn g[sub]c[/sub] term which threw a wrench into everything, IMHO. (Maybe the term “slug” turned everybody off?)
I am always in doubt whether or not I need that g[sub]c[/sub] term in my equations. I guess if the equation calls for “mass”, and I have pound-mass, it must be adjusted by the g[sub]c[/sub] term to be a true measure of mass, correct?
(i.e.: I am, in effect, changing to slugs, am I not?)
The only way I know for sure is when my units don’t cancel out nicely to what I was expecting them to be! - Jinx
Right–as mentioned in my second post. Unfortunately, when used with pound-force, it leads to an internally inconsistent set of units which requires the use of a correction factor (g[sub]c[/sub]). This makes things much more difficult than they need to be.
When I was an undergraduate engineering student, I remember slogging through fluid calculations with U.S. customary units, and experienced the same frustration that Jinx appears to be experiencing.
When I taught college-level physics some time later, I used SI units throughout. Those same types of calculations are a breeze with an internally consistent set of units, and you never have to figure out where g[sub]c[/sub] belongs!
I had to do a fluids problem recently, with all of the info given in U.S. customary units. I found it easier to simply convert all units to SI, work the problem, and convert my answer back to U.S. units!
If you used a balance, you were measuring mass. If you used a scale, you were measuring weight. To a good approximation, on the Earth’s surface it’s easy to figure out the one from the other.
Historically, the word “weigh” was to use a balance to determine mass (before spring scales were invented). The distinction between mass and weight is a modern (and very useful) one. I was under the impression that the slug was a relatively recent invention, since the pound was used to measure mass and force.
It’s pretty simple, really. Mass is mass. The kilogram is the SI unit for mass. Weight is not mass; weight is force. The SI unit for force is Newton, thus weight can have units of Newton. But any unit that represents force can be used for weight. For whatever reason, most people use “pound-force” for weight instead of Newton. (Not to be confused with “pound-mass,” which is rarely used.)
Because both “pound-force” and “Newton” are units for the same thing (force), there is a direct, absolute, unitless conversion between Newton and pound-force:
1 pound-force = 4.4482216 Newton
1 Newton = 0.2248089 pound-force
To convert between mass and weight, we use the all-too-familiar f = ma equation, where “f” is force (Newton), “m” is mass (kg), and “a” is acceleration (ms[sup]-2[/sup]).
The big question is this: What is the acceleration? It depends on four things:
Longitude
Latitude
Altitude
Time (this can usually be safely neglected)
To accurately convert between mass and weight, you need to know the precise acceleration due to gravity at the particular location. If you don’t know this value, you can assume it’s around 9.81 ms[sup]-2[/sup]. But keep in mind that this is only an estimate, and simply using “9.81 ms[sup]-2[/sup]” will introduce error into your calculation.
That’s the PIA about the English system. You have to be totally anal about your units. You just throw in the g/g[sub]c[/sub] or whatever if your units don’t cancel. I’m forever having to calculate back and forth between English and SI in my head.
I had to relearn all of that crap when I took the Mechanical PE a few years back. That’s the standard test in the US and they use pound-mass. The entire test was in English but they may have finally moved over by now.
Another problem is that different industries in the US use different sets of units. Some are entirely SI, some are entirely English but most are a mish mash. The disk drive industry, at least when I was in it, was a mess. For example, all of the dimensions of the read/write head are in SI but the mechanical spacing between the head and the platters are in English, kind of. We used this hybrid called the microinch.