11 thoughts on “A Weighty Matter”

  1. Is the problem the universe or rigidity of thought? Have we chosen constants that are not? Had we chosen a calculation for mass rather than a physical reference and mass didn’t therefore change would the thought that mass doesn’t change be affirmed? Scientists must be the most humble of us all.

    Is it contradictory to be both skeptical and humble? I think not, but I find most to disagree (if not in principle, in actuality.)

  2. “the joule is defined as work needed to move one kilogram distance x over time y”….

    Hmm, sounds like Daniel is less than comfortable with actual, you know, units, despite being “the kind of fella who finds this stuff interesting in its own right”. A joule is a Newton-meter (work equals force times distance). A mass times a distance divided by a time has the dimensions of momentum, not energy.


    1. In terms of SI base units, which is all I’m concerned with here, 1 joule = 1 Kg*m2/s2. In other words, “a mass times a distance divided by a time” as you put it. I wrote it in English because because people who don’t know how a joule is defined don’t know how a Newton-meter is defined, and because comprehending it in terms of distance and time is easier (which both have corresponding SI base units) is easier than comprehending it in terms of force and acceleration.

      No, I’m not a scientist. Hope I’m still allowed to find it interesting.

      1. Well, it’s a mass times a distance squared divided by a time squared. Or a mass times a distance times an acceleration. It’s OK to simplify, but not to the point at which it’s physically wrong.

        And yes, I’m glad you find this stuff interesting. Don’t want to discourage you from posting about it — just offering an opportunity to fix if you wish.

        1. My ordinary language explanation could have been clearer, but I think it’s pedantic to say it’s “physically wrong.” The only way it’s wrong is if “move” is not a plausible simplification of “accelerate.” Obviously you can “move” an object without accelerating it, but you can’t accelerate it without moving it. There’s no delta-v without v. Consider it from another angle. Yes, there is a conceptual difference between meters per second and meters per second squared. One corresponds to the concept of velocity and the other to the concept of acceleration. But acceleration doesn’t *stop* being a function of distance and time just because it’s been raised to a power. If I said “Einstein’s famous equation defines energy in terms of mass and the speed of light,” is that “physically wrong” as a simplification because I haven’t included the square?

          1. If I said “Einstein’s famous equation defines energy in terms of mass and the speed of light,” is that “physically wrong” as a simplification because I haven’t included the square?

            No, but you didn’t say “…in terms of.” You used mathematical language (e.g., “divided by”) in what sounded like a mathematical description of a word (“energy”). In that context it was misleading, and mistaken.

            I think we’ve probably beaten this into the ground by now, though.

          2. “Move” is not an accurate simplification of “accelerate”. I don’t know what you mean by a “plausible” simplification. If an object is already moving at a speed x/y, then it takes no work at all for it to move a distance x in a time y. A joule is specifically the amount of work it takes to accelerate a 1 kg mass at 1 m/s^2 over a distance of 1 meter. Under this uniform acceleration, if the object starts from zero velocity, it take sqrt(2)=1.414 seconds to traverse 1 meter, at which point it is traveling sqrt(2)=1.414 meters per second and has kinetic energy (1/2)Mv^2 = 1 kg m^2/s^2 = 1 J. There are lots of ways to accelerate the mass non-uniformly so that it moves 1 meter in 1.414 seconds, but darn few of them require work of exactly 1 joule. I’m surprised that someone who thinks these details are unimportant would be interested in the definition of the kilogram.

            Oh, and by the way, E=mc^2 is not a definition of energy. The equality is a result derived from independent definitions of energy and mass and the assumptions of special relativity. And if you were to say that Einstein’s equation defines energy as the product of mass and the speed of light, I would have two reasons to be pedantic.

          3. You absolutely can accelerate an object without moving it. Every object on the surface of the earth is accelerating toward the center of mass of the earth under the attraction of gravity. Objects that are not moving toward the center of the earth (i.e. are still) are being held fast by the opposing force of the ground. That’s the force we call “weight.”

            They definition in physics of “work” is: the energy expended by a force moving through a distance (more precisely, it’s the integral of the dot product of force and differential distance). In the case of the definition you cite, the unit of force called the “Newton” is that required to accelerate a kilogram at one meter/second^2. Applying that force through a distance of 1 meter requires one joule of energy, whence the 1 kg-m^2/sec^2.

  3. I thought that one gram was one cubic centimeter of pure liquid water at a specific temperature and pressure and a kilogram was one cubic decimeter of water. Did my teachers lie to me?

  4. No, your teachers didn’t lie, they just simplified. The original definitions of the second, meter, and kilogram weren’t accurate enough, so they were refined (and corrected). If you follow the link inside the linked article you’ll get a more detailed explanation.

Comments are closed.