Originally posted by @apathist
The bottom penny gets vertical because of magnetism. But it sticks to the table top because of gravity, or acceleration towards the ground. R should be W.
Same with the other pennies stacking up. Until suddenly magnetism wins and gravity becomes negligible.I don't know how to e-shrug.
"R should be W"
Actually, R will be less than W but greater than 0. or option c) 0 < R < W.
"R = W" is what will register on the scale in the absence of a magnetic field.
The next step is to jack the penny up ( decrease the distance between the magnet and the penny) until a critical point of unstable equilibrium is reached. What will the scale readout be at that point?
You should be arriving at the conclusion "R = 0".
At that point you can remove the scale/jack and the penny will appear to levitate. Note: This position is above the point where the penny is resting on the box, and above the point where it is resting (elevated) on his fingertip. It would most likely be extraordinarily difficult to find in practice. However, its no different in believing in going from 0 to 2 on a continuum 1 is passed.
So the reason a single penny is not "snatched up" is because it has not passed closer to the magnet beyond that point of equilibrium.
"Same with the other pennies stacking up. Until suddenly magnetism wins and gravity becomes negligible.I don't know how to e-shrug."
Its only "sudden" because the penny is an extended body ( it has size, volume, etc... ).
Its kind of like this: pretend I am the magnetic force and you are the pennies. I'm 50 ft above you trying to lift you with a rope. You are standing on a scale. I cant lift you, but I can appear to make you weigh less. A copy of you jumps on to of your shoulders. The copy grabs the rope and you grab his legs. How the magnetic force behaves is he is 5 ft closer and I can grab the rope with 2 of my copies. So there is me tugging on you and two of my copies tugging on your copy and you tugging on him. The process repeats, you get one more copy on the shoulders of your other copy, and I get lets say 4 more copies of me pulling on the rope. At some point, "I" ( and all my copies) will be able to hoist "you" ( and all your copies) with ease because my copies are increasing at a greater rate. All your copies have to do is be able to hold on to each other. It should also be said that your copies are gaining in strength as they climb ( due to increased magnetic interaction between you copies). That is the top copy is strong enough to lift the entire chain, the next is strong enough to lift the remaining, etc...you being the weakest ( you only have to withstand lifting your body weight and the inertial forces of acceleration.
If none of this is helping you get a better picture...let me know, Ill stop. If you have specific questions I'll try and elaborate. If you're satisfied with Deepthought's response, by all means be satisfied!