Michael C
Graduate Poster
Anyway, you have said quite adamantly that weight must always be measured with respect to some frame of reference. But even the site you've give to support that view allows that there are different ways you could derive the "g" when we calculate weight using W = mg. The first option he lists is based on Newton's universal law of gravitation. That formula doesn't depend on any frame of reference and it gives you a force. If you divide the force by the mass of the object in question we get one version of "g" (acceleration due to gravity). You might not like that approach but it certainly seems to at least one possible definition and a naive reading of wikipedia and many other pages on the net (and many textbooks also I would suggest) doesn't seem to disagree or even suggest anything further needs to be considered.
The first option for g on that page reads thus:
"I-gravity is denoted gI and can be calculated using Newton’s law of universal gravitation, as follows: It has magnitude
|gI| = GM/r2
and is directed toward the center of the planet."
The key phrase is "directed toward the center of the planet": as long as we remain Earth-centred, we choose Earth as "the planet". But which planet do we choose when we are away from Earth? In particular, can you answer my previous question: what is the "real", "true" or "actual" weight of the Earth?
In other words (and this is copied almost directly from another forum I was reading), your view is that weight should be defined as the net force required to make an object accelerate at a rate equal to the local free fall acceleration. Is this right?
By definition there is no net force required to make an object accelerate at the rate of free fall.
I would have said that was what wikipedia, etc., call "apparent weightWP".
I am not saying that "weight" and "apparent weight" are the same thing. We can always choose a frame where our defined weight is the same as our apparent weight, but we don't have to. If we take another frame, accelerated with respect to the first frame, our weight will be something else. That is the essential point. For instance, if we are on the surface of the Earth, we usually take the local frame defined by the surface we're standing on. That means that our apparent weight, as measured by a simple spring balance, is the same as the weight we define with respect to the frame of reference of the Earth's surface. We could stay standing on the Earth and define our weight by the local free fall frame (accelerating with respect to the frame of the surface of the earth), in which case our weight is zero. Of course, usually we don't, and the "standard" frame of reference is the surface of the Earth. This is just like measuring the speed of a car running on the surface of the Earth. If we say that a car is travelling at 100 km/h, usually we don't need to specify "with respect to the surface of the Earth": it's understood.
For the person in a space station in orbit around the earth, it's no different: we may either choose to measure their weight in the freely-falling reference frame, or in one at a fixed distance from the surface of the earth. In the first case we conclude that they are "weightless", in the second case we conclude that they have weight. Both answers are right, as long as the frame of reference is made clear. It's like measuring the velocity of that same space station: it won't be the same if we measure it from a frame of reference rotating at the same speed as the Earth and from a frame of reference not rotating at the same speed as the Earth.
To sum up, I'm not really particularly concerned one way or the other because as I said earlier, it seems to me that "weight" is often likely to cause confusion rather than clarity, and so it's probably easier to just avoid it altogether whenever possible and talk in terms of mass and force and so forth instead.
I think you're right.
ETA: What's your opinion of this blog post: http://blog.dotphys.net/2008/09/gravity-weightlessness-and-apparent-weight/ ?
It's OK, but he doesn't give a clear definition of weight. It would be better if he simply insisted on the fact that your mass remains constant in all these situations. In any case, since this is the same guy who confidently predicts that a DDWFTTW vehicle can't work, calling it "free energy" and "magic" (see here and here), I'm not inclined to spend too much time reading his articles.
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