Weight

Updated: 8/21/2003
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Yes, I am a bit of a crackpot on this topic, but the reason is as follows: There are many times in introductory courses like this one where we deliberately lie to you about something because it is easier to learn a topic if you are not confused by extremely subtle details that have almost no observable consequences on the scale of building a bridge that won't fall down. Where teachers get in trouble is when they see the lie so often that they forget it was ever a lie. That is the case with "weight", and is one reason I think you should know this subtle distinction. The other reason is that it is my opinion that many students are confused about the distinction between kg and N because they see kg used (correctly, I should add) as the equivalent of the pound to specify the weight of a product they buy in the store.

Some comments on WEIGHT:

In this class we will define the "weight" of an object to be the force due to gravity on that object, which is given by W = mg and is measured in newtons (N). It is important to realize that this force, W, varies from place to place because the acceleration of gravity, g, varies from place to place. (Assume g = 9.81 m/s2 unless told otherwise.) This convention was widely adopted around 1950 for use in physics textbooks, and reflects a colloquial use of "weight" that refers to the "heaviness" you feel when you try to lift an object in a gravitational field.

In the real world, however, contrary to statements in our textbook (and most other introductory physics textbooks) the legal (and oldest) meaning of "weight" is that of a mass measured on a balance by comparison to other masses, and mass is a quantity of matter that does not vary from place to place. This is the meaning of "weight" used when you go shopping and the one that the U.S. uses to define the pound as a mass. It reflects the "heaviness" you feel when you try to accelerate an object.

To summarize, in legal and commercial usage, the "net weight" listed on a can of corn is a mass and is the same everywhere in the United States. In contrast, the textbook definition of "weight" as the force W=mg means that the "weight" of a can of corn is different in different places in the United States.

Do not confuse these two meanings!

You find both meanings if you look in a dictionary.
[The links below open in a separate browser window.]

 
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Units:

One of the reasons these two meanings for weight are confused is the fact that our conventional "english" unit for weight is not what most people (including our textbook authors) think it is. The pound you use in everyday commercial transactions in the US is actually a unit of mass in the avoirdupois system (the pound is defined by reference to the kilogram). However, the pound is also used as a unit of force in some other systems of measurement that are in common use and the subtle differences (mass is the same everywhere but the force of gravity on that mass is not) make it a distinction without a difference in daily life.

(The one place you might get in trouble is if you use force units by mistake and get caught by the FDA or Florida Dept of Agriculture with a product that is "short weight". The force is about 0.1% less in Aspen, Colorado, than in Tallahassee, Florida, which would mean getting $1000 for $999 worth of material. This is why the spring scales in stores, which measure a force, are marked "not legal for commerce". The scale at checkout has been calibrated and certified to measure the mass of what you buy and, to be legal, its load cell must be recalibrated whenever it is moved.)

There are a variety of unit systems in practical use:

System Unit of Mass Unit of Force
SI
sometimes called MKS
(international standard)
kg   (kilogram) N   (newton)
US Engineering pound (lb) poundal
US Engineering pound-mass (lb) pound-force (lbf)
British Aeronautical
(textbook "US customary")
slug pound (lb)
cgs
(used by astronomers)
gram dyne

In the above table, the "pound" of mass referred to is in the Avoirdupois system. This non-trivial detail is what leads to the famous question:

       "Which is heavier, a pound of feathers or a pound of gold?".

 
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Need a conversion factor?

This table has everything you might need to know to convert grains per acre-foot to SI units.

 
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 ?? Contact me if you have any questions.