CECIL: HEAD IN THE CLOUDS?
In your column on the weight of a cloud versus that of a 747 [March 13], you state: "Now of course, it's true that weight isn't the same as mass, and that a cloud put on a scale wouldn't weigh anything." Yuck! The weight of an object equals its mass times the acceleration due to gravity, 9.8 meters per second squared. Your cloud "weighs" a helluva lot!! The fact that you can't weigh something on a scale doesn't mean it has no weight. The reason that a cloud floats is that the water vapor is less dense than the surrounding air, so the surrounding air exerts an upward buoyant force (remember Archimedes?) equal to the weight of the cloud. --Dave Morgan, PhD
Nobody appreciates what I go through on this job. The biggest problem your average columnist deals with is having ticked off some politician. I have to fend off the freaking theoretical physicists. Dave and I had a lengthy exchange via E-mail, which I paraphrase below:
Cecil: What's the problem? I said weight wasn't the same as mass. It's not. I said a cloud put on a scale wouldn't weigh anything. It wouldn't. My point was, "weight" could be misinterpreted. Evidence: this guy misinterpreted it. Had "mass" been used instead, there wouldn't have been an argument.
Dave: Nonsense. Weight has a precise scientific meaning.
C: Technically, yes, but as a practical matter weight is dependent on local conditions. Buoyancy makes clouds apparently weightless. Astronauts experiencing high g forces on liftoff weigh more than their nominal weight. Bodies in free fall, such as astronauts in orbit, are weightless, even though they experience the pull of gravity.
D: Weightless, schmeightless. They still have weight.
C: Then their weight has been defined into existence. In reality orbiting astronauts weigh nothing. Why, the equivalence principle, a fundamental concept of physics, tells us that the condition of a body in free fall is indistinguishable from one unaffected by gravity. If that's the case, why am I, an astronaut in free fall, obliged to believe I have weight? I cannot determine this weight by measurement or experiment. I might as well be in deep space. Suppose that I had selective amnesia and forgot my earth weight and the planet I was orbiting. It would be impossible for me to determine the weight I supposedly had! You'd have to radio up and tell me! I'd have to accept it on faith! Doesn't that strike you as an essentially, you know, religious concept?
D & C (shouting as one): Wait a minute!
D: Orbital observations!
C: I was going to say that.
D: Too bad, I beat you to it. The speed and altitude of an orbiting body of known mass are a function of the mass of the body (planet) it's orbiting around. By making orbital observations you can determine the mass of the earth, and you can use that to calculate your weight. What's more, even if you never look out the window, you can prove you're in orbit rather than in deep space, and thus are not truly weightless. Get two wrenches and put them at opposites sides of the cabin of your spacecraft. Over time the wrench farther away from the earth, which is in a higher orbit and thus is traveling more slowly with respect to earth, will drift toward the back of the cabin. The nearer wrench, which is in a lower, faster orbit, will drift toward the front.
C: Shoot, you're right. Now that I think about it, even if I were falling straight toward the earth, I would be able to detect tidal variation due to the fact that the strength of gravity diminishes rapidly with distance. A wrench at the front of the spacecraft would drift forward, but one at the back would drift rearward. The equivalence principle obviously applies only to single points (center of mass). As a practical matter, in the real world of three-dimensional objects, free fall can always be distinguished from zero gravity. But Dave, this proves my point! Even in the lofty realm of theoretical physics, we're obliged to consider practical matters! And as a practical matter clouds and orbiting astronauts are considered to be "weightless" because they behave as such. True, the letter writer's coworker was clearly talking about clouds' weight in the strict sense. I was just giving the guy a chance to weasel out of an argument in which he was, technically, wrong. You may think this unworthy. But weaseling is obviously a highly useful skill.
Art accompanying story in printed newspaper (not available in this archive): illustration by Slug Signorino.