Re: What is a good artifact for a unit quantity of mass?

> The metric kilogram (k) in the archives at Sevres'
> France was built to
> physically represent a unit of mass for the metric
> system: Within the
> limits of manufacturing tolerences it serves this
> purpose.
>
> Throughout the history of science there have been
> many similar
> artifacts. It seems that some sort of such artifact
> has become
> indispensible, mostly for calibrating weight-scales
> to determine the
> heaviness of the many different quantities of matter
> that we handle and
> trade.
>
> AFAIK, there has never been a standard artifact for a
> pound; which has
> long been used as a quantity of matter. The reason of
> course, is that a
> pound varies depending on its location; so that it's
> always been a
> problem to define a standard pound. It's easier to
> define mass; as the
> quantity of matter in a particular body; so that the
> ratio of it's
> weight (w), divided by the acceleration (g) at which
> it will free fall
> is a constant; which is equal to the ratio of the net
> force (f),
> divided by the acceleration (a) that it causes.
>
> For starters; neglecting frictional force, a net
> force of one pound,
> will accelerate any body weighing one pound anywhere
> on Earth, at one
> foot per second^2.
>
> Don
>

Assuming gravity does not affect a body, if the body weighs one pound, then a force of one pound will accelerate the body at 32.2 ft/sec^2, the acceleration due to gravity at sea level. Think about it. Suppose a body is sitting on a table, and that it weighs one pound. Then the table excerts one pound force upward to counter the downward force due to gravity. The downward force due to gravity is f = mg, where m is the bodies mass and g is the acceleration due to gravity. The mass of the body is m = f/g. In the present case

m = (1 lb)/(32.2 ft/sec^2)

The problem comes when people misuse pounds, a measure of force, for a measure of mass. Then they try to write things like f = mg = (1 lb) x (32.2 ft/sec^2), which is not correct. The units on the right hand side do not give units of force when multiplied together.

In engineering on must be careful to specify what is meant by a pound. If one wants to use pounds as a measure of mass, then the unit is clearly labeled as a "pound mass" or lbm. Then you have f = mg = (1 lbm) x (32.2 ft/sec^2) = 1 lbf = 1 "pound force".

- MO
.

Relevant Pages

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