> If so, you're right and my intuition and everything else is wrong.
The reason you think this way is because magnets fall off by the power of 5 (approximately, it's not a specific number, but depends on the geometry of the magnet), because of the two poles.
If on the other hand you played around with charged objects (which are monopoles like gravity) your intuition would work better for this. But unlike magnets highly charged objects are not commonly found around the house.
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Also the second one is debatable - the acceleration of one magnet to another is higher that the acceleration of an object falling on earth.
Even a lightly charged object can accelerate another object at greater than what the earth can manage.
The reason I use acceleration to measure gross force is because gravity (and charge) depend on the product of the two objects and distance - the only single number you can assign a single object is acceleration and even that depends on distance.
I still think I am not explaining myself clearly enough.
When I say gross force, I mean the sum total of all relevant force exerted by the object. So the gross gravitational force of the earth is strong enough to hold the moon in orbit, but clearly the magnet has no such ...strength.
Now obviously (I shouldn't use that word!) in the case of massive bodies like earths and moons, there's a more complex interaction going on than a one-sided force. But there's a total magnitude of force that just doesn't exist in the magnet.
A lit match burns paper more readily than the sun, but clearly the sun distributes a larger amount of gross energy over a wider area than does a match.
> Even a lightly charged object can accelerate another object at greater than what the earth can manage
Ack. Considering acceleration without mass is no way to properly reason about force! Surely I remember that much, at least.
Regardless, I will desist and defer. Though I do wish I felt that I now understood something more clearly than I did before. :(
> When I say gross force, I mean the sum total of all relevant force exerted by the object.
There is no such concept. Really. I promise you, there is no such concept! The amount of force it exerts simply depends on who is close to it, rather than any property of the Earth. Like, if the moon was not there would you say the total of all relevant force is lower? But nothing changed on the Earth. So this concept does not apply to the Earth, rather it applies to the specific situation.
I do get what you are trying to say, but it's just not correct. The force depends on the specific setup of where the bodies are, not an intrinsic property of Gravity, or the Earth.
> So the gross gravitational force of the earth is strong enough to hold the moon in orbit, but clearly the magnet has no such ...strength.
Only because it is small, it would not take much charge to hold the moon. I did the math for you - it would take about 3 tons worth of electrons to hold the moon. That's it - about 1 car worth. (If you could somehow keep all those electrons in one place, which you can't.) Walk outside and look at a car - if it was replaced with equivalent mass of electrons it would be enough to hold the moon (if the moon had some extra protons on it). I mean you can push a car, that's how little mass it is, yet it's enough to hold something as heavy as the moon.
Another way to look at it is if you took 1 electron away from every grain of sand sized piece of the earth - just one single electron, the resulting charge would be enough to hold the moon. (And give one extra electron to every grain of sand sized piece of the moon.) Charging a grain of sand with one extra electron is nothing, it's a minuscule amount, it's too low to even measure.
> Ack. Considering acceleration without mass is no way to properly reason about force!
The nice thing about gravity is that it's invariant to mass since the force goes up right along with the mass. If you scale the charge of the object together with the mass then the acceleration of a charged object will also be invariant to mass.
i.e. if you made the magnet bigger (heavier) it would also be more magnetic, so the acceleration would stay the same (more or less).
> Regardless, I will desist and defer.
It's OK, I don't mind the conversation.
> Though I do wish I felt that I now understood something more clearly than I did before. :(
Remember that we started with you saying gravity is diffuse and electromagnetism is concentrated. All I did is try to show you that that is not a good way to look at it.
Your efforts are appreciated, and I'm sure you're correct in all you say, but I can't escape the feeling that we're talking about different things.
I readily concede that "diffuse" has ambiguous meaning and therefore a poor choice, however.
Beyond that, I don't think what I'm saying is any more complicated or controversial than the example of the match and the sun.
My attempts to clarify have revealed further gaps in my precision of phrasing, but your explanations haven't identified any specific points of confusion for me. I'm sure that says more about my comprehension than about your explanations.
We're now in open battle with HN's anti-dialogue margin creep -- and we know who wins that battle, every time -- so I'll take my distant memories of undergrad mechanics and E&M, mark the page dirty, invalidate the cache, etc.
Thanks again for your efforts, they're not as wasted as they appear.
Yes, the third one is incorrect.
> If so, you're right and my intuition and everything else is wrong.
The reason you think this way is because magnets fall off by the power of 5 (approximately, it's not a specific number, but depends on the geometry of the magnet), because of the two poles.
If on the other hand you played around with charged objects (which are monopoles like gravity) your intuition would work better for this. But unlike magnets highly charged objects are not commonly found around the house.
----------
Also the second one is debatable - the acceleration of one magnet to another is higher that the acceleration of an object falling on earth.
Even a lightly charged object can accelerate another object at greater than what the earth can manage.
The reason I use acceleration to measure gross force is because gravity (and charge) depend on the product of the two objects and distance - the only single number you can assign a single object is acceleration and even that depends on distance.