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| Physics Question - ma = mg |
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| RJSV:
I did some looking for 'g' subscripts ( although my Android smart phone makes subscripts difficult text to enter). Looking at some May 13 posts, there are subscripts; (moon), (sun), etc. usually by antiprotonboy and also Brumby, so that's helpful. Plus the process suggested kind of relating back to Earth, as a benchmark. |
| bostonman:
I agree with both these last two posts. I feel some contributors began reading halfway through and felt that they needed to explain the difference between 'g' and 'G'. To say 'g' is a constant or not I feel can be open for discussion, however, it is based on where you are on Earth, therefore I feel it's more of a calculation and not a constant. Pi, as an example, doesn't need to be calculated, in fact, it's a button on many calculators. Therefore, it's obviously a constant, but with some long term polishing. |
| TimFox:
Ignoring for a while the controversy about little-g being a legitimate constant, I have some observations about weight and mass, and an historical question at the end of this post. My first formal course in physics, at age 16, was the first time I became aware of the important difference between mass and weight. Prior to that, everything of interest to me was in terms of weight: my own weight, the net weight on a box of cereal, etc. In the US, this also introduced me to the problem of the word "pound", which in physics class was always a unit of force or weight, and the ugly word "slug" for the unit of mass in the same system, which never appeared outside of physics textbooks. Since the space race was underway, we were all interested in weightlessness, how much one would weigh on the Moon, and other topics in gravitation away from the Earth. Now to earlier history and laws: The United States Constitution, Article I, section 8 gives Congress the power to “fix the standard of weights and measurement", where the framers saw the need for uniform measurements across the several States of the Union. At about the same time, the founders of the Metric System had a similar need to unify French measurements across the new Republic. Their work lead to the "BIPM", which I believe translates to "International Bureau of Weights and Measures". Note that in both cases, the language (and further statutes in the US and elsewhere) refers to "weight", rather than "mass". As one should not go to a physicist for legal advice, one might not trust a lawyer for scientific clarity. In Principia, Newton defined mass as the product of volume and density. (Translated from the Latin: "The quantity of matter is the measure of the same, arising from its density and bulk conjointly".) The original definition of the gram was 1 cm3 of water (at the temperature of its maximum density), although that was later changed to the prototype kilogram. My question: historically, was this original definition of the gram considered "weight" or "mass"? Logically, it would be mass, since the corresponding unit of force was already the "dyne". |
| CatalinaWOW:
I can't over emphasize the need to know what problem you are working on. If you are designing a spring scale for the bath room, or calculating how high your model rocket will fly or most of the other problems you will encounter the variation of g over the Earth's surface doesn't matter. Other parts of the problem will have unknowns greater than the differences. You terminal velocity when you jump out of an airplane and how fast you reach it will be far more dependent on air density than on g for example. If you are doing something where the variatíon of g with location matters I hope that your general understanding of the problem is such that you aren't concerned with the existence of a standardized version of the answer. In much the same way several governing bodies define pi as a rational number (like 3.14 or 3.14159). This isn't an attack on mathematics, but a way to avoid legal arguments in trade and commerce how many decimal points to use when computing circumferences and areas |
| TimFox:
"Standardized version of the answer": Is there a legal definition of g? The classic textbook "Physics", D Halliday and R Resnick, John Wiley & Sons 1966 (one of a series of revisions of this calculus-based freshman physics textbook) in section 5-6 on systems of units (pp 90 ff), discusses the problem of mass, weight, force, and gravity. They state that "in the British engineering system....Legally, the pound is a unit of mass but in engineering practice the pound is treated as a unit of force or weight....The pound-force is the force that gives a standard pound an acceleration equal to the standard acceleration of gravity, 32.1740 ft/sec2." The book later notes that "the acceleration of gravity varies with distance from the center of the earth, and this 'standard acceleration' is, therefore, the value at a particular distance from the center of the earth. Any point at sea level and 45 deg N latitude is a good approximation". In this section, the term "g" is not explicitly mentioned. Moving forward to section 5-8 (pp 93 ff), discussing the vectors W and g, with the scalar mass m, we read "The quantitative relation between weight and mass is given by W = mg. Because g varies from point to point on the earth, W, the weight of a body of mass m, is different in different localities." In later examples, the authors are careful to state "at a point where g = 32.0 ft/sec2" or "in a locality where g = 9.80 m/sec2...in a locality where g = 9.78 m/sec2" for quantitative discussions of a particular weight and mass. This is the standard discussion from the point of view of physics. This may not matter to backyard rocketry, but is obviously important to interplanetary rocketry. The point of what many here think of as my nitpicking is that in the traditional British units, where objects are measured by weight and that is converted to mass (pound-force vs. pound-mass), a legal definition of the acceleration of gravity is required, but modern physicists do not call that "g", since the actual value of g varies from place to place. In metric countries that use SI units, this problem does not occur, since material is sold by mass (in kg), not weight (in N). Again, I emphasize that the importance of g is that its value applies to all objects in the region of interest, as opposed to older theories where a heavy object drops faster than a lighter object. |
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