Newton's Gravitation Constant

[Ygmaince241]

You all know the equation. F=G x M x m div by d squared. I would like to know what Newton's gravitation constant represents. I would appreciate it if someone could tell me the procedure. By what measurments are the two masses weighed (kilograms, etc.)? Do you first multiply the two masses and then multiply the product by the "G"? Thanks.

 

[Gza]

G is just an experimentally derived constant. Yes, you just multiply the masses and G and then divide by the distance squared to obtain the force of gravity.

 

[chroot]

The constant is just a conversion factor between man-made units. With the proper selection of units, G becomes 1, and can be "ignored."

- Warren

 

[Rahmuss]

The units you use for the masses (M1 & M2) will be the units reflected in the force (F). So if you use lbs for the masses, then the force would also be in pounds. If you use kilos, then the force would also be in kilos. Of course, then the force could be written in terms of Newtons, which would be much more accurate and usable.

 

[chroot]

Rahmuss,

The pound (which assumed to be a short-hand of pound-force) is not a unit of mass, it's a unit of force. The pound-mass is a unit of mass.

The kilogram, however, is clearly a unit of mass, and cannot ever be used as a unit of force.

- Warren

 

[Rahmuss]

True Chroot. You really can't use lbs for just the masses. And as mentioned the force can be written with kilograms; but then as I stated it would be written in terms of Newtons. So my apologies. :)

 

[Metric1000]

Newton's Gravitational Constant--pounds

The pound (which assumed to be a short-hand of pound-force) is not a unit of mass, it's a unit of force. The pound-mass is a unit of mass.

The kilogram, however, is clearly a unit of mass, and cannot ever be used as a unit of force.

- Warren

You have that assumption backwards, according to the rules followed by the experts in the field. Go look at how the keepers of our standards do it, such as NIST, the U.S. national standards laboratory, or the NPL, the U.K. national standards laboratory. Here's American Society for Testing and Materials, Standard for Metric Practice, E 380-79, ASTM 1979.

3.4.1.4 The use of the same name for units of force and mass causes confusion. When the non-SI units are used, a distinction should be made between force and mass, for example, lbf to denote force in gravimetric engineering units and lb for mass.​

Pounds are and always have been units of mass. Pounds force are a recent alteration, a unit never well defined before the 20th century, and one which even today do not have an "official" definition.

Pounds are, since a 1959 international agreement, defined as 0.45359237 kg, exactly. Read about this agreement, and the prior U.S. definition as a slightly different exact fraction of a kilogram, in the current U.S. law:
http://www.ngs.noaa.gov/PUBS_LIB/FedRegister/FRdoc59-5442.pdf

Pounds are never called "pounds-mass" and never use "lbm" on all those zillions of items in the U.S. grocery stores and hardware stores, and our pantries and workshop shelves, even though they are every bit as much units of mass as the grams and kilograms which appear right alongside them. Clear evidence that you have your assumption wrong.

Some people define pounds force using the pound as defined above and 32.16 ft/s² for the standard acceleration of gravity. That is the value given in some textbooks, and in the still common formula in ballistics for the kinetic energy of a bullet using grains and pounds force, E=m·v²/450240, with that value in the denominator. But the value often used is the one which is official for defining kilograms force: 9.80665 m/s². Using that value, the number in the denominator in that ballistics formula is 450437 (sometimes 450436 with intermediate rounding involved).

So kilograms force were also once legitimate units, officially endorsed by the CGPM in 1901 by the adoption of that "standard acceleration of gravity." We still see far too many vestiges of their use (thrust of jet and rocket engines--they were the primary units used in the Soviet space program until about the time of the breakup of the Soviet Union, bicycle spoke tension, torque wrenches in "meter kilograms," pressure gauges in "kg/cm²"), though kilograms force are not a part of the modern metric system, the International System of Units (SI) introduced in 1960.

 

[cepheid]

Huh?

The imperial unit for mass is the "slug". If, as you've asserted, the pound had always been used as a unit for mass (which is false), then the slug would not exist. The pound is a measure of weight. Weight is a force.

I'm sure we can all agree on one thing though...the imperial system is convoluted and stupid.

Oh and by the way...

Pounds are never called "pounds-mass" and never use "lbm" on all those zillions of items in the U.S. grocery stores and hardware stores, and our pantries and workshop shelves, even though they are every bit as much units of mass as the grams and kilograms which appear right alongside them. Clear evidence that you have your assumption wrong.

NO! I'm afraid that in a sense it's everyone who's got it wrong (except the physics people). The juxtaposition of lbs and kg is an unfortunate phenomenon. The pound is a measure of weight. The kilogram is a measure of mass. From a practical standpoint, on Earth it doesn't really matter, because objects don't change their weight (unless they change in mass). So something with a mass of 1kg will always measure 2.2lbs (or whatever the hell the conversion is) on a grocery weigh scale. That means you can calibrate the weigh scale so that every 2.2lbs, you put down a tick on the other scale (the metric one) allowing the person weighing the object to see both the object's weight (in imperial units) and the corresponding mass (in SI units) that the object must have if it weighs that much on Earth. This system works, but does little to combat society's inablity to distinguish between weight and mass.

 

[Chronos]

Huh? I assume you had a point to make. Apparently I missed it.

 

[jamesrc]

The imperial unit for mass is the "slug". If, as you've asserted, the pound had always been used as a unit for mass (which is false), then the slug would not exist. The pound is a measure of weight. Weight is a force.

That's not the whole story. There are 3 systems of units being covered here: metric, British Gravitational (which uses slugs and is also known as American Standard), and English Engineering (which uses pound-mass as its unit of mass). Whereas the first 2 systems can be treated as either force-based or mass-based, the old English Engineering system is mixed (it has a mass base unit (lbf) and a force base unit (lbm)).

If you've never seen g_c before, this will probably make you taste vomit in your mouth or something, but keep in mind that I'm just relaying facts here. I have no interest in debating the merits or demerits of any of these systems. Anyhow, Newton's second law looks like this:

$$F = \frac m {g_c} a$$

so weight is:

$$W = \frac m {g_c} g$$

g_c is a constant of proportionality.

$${\rm metric: } g_c = 1.0 \frac{\rm kg\cdot m}{\rm N\cdot s^2}$$
$${\rm British Gravitational: } g_c = 1.0 \frac{\rm slug\cdot ft}{\rm lb\cdot s^2}$$
$${\rm English Engineering: } g_c = 32.174 \frac{\rm lbm\cdot ft}{\rm lb\cdot s^2}$$

If you think all of this g_c business is never used, all I can say is: you wish. All 3 systems of units were used in just about every core engineering course (I'm talking mechanics, fluids, thermo, etc.) I had as an undergrad (or at least covered in the first chapter; we were expected to be facile in all three). (BTW, I know there are other systems of units too, like cgs, but I was just mentioning the 3 that are near the root of this discussion.)