There are two magnets, M1 and M2. Let's say that there is an attractive force existing between M1 and M2. M1 is attached to a surface, while M2 is free to move. Now slow this motion down, and M1 is in the process of attaching to M2. There is a distance x between the magnets, and M1 is exerting a force on M2 which is causing M2 to travel in the direction of M1 with an acceleration. Now, suddenly M1 starts moving away from M2. However, it is moving with a velocity such that M2 is still attracted to M1, but the distance x does not change. As a result of this, M2 is traveling in the same direction as M1 but never completely touches M1.

Now, I have two questions:

1) In this situation, let's say a machine is pulling M1 away from M2. Is the machine doing work on just M1, or is the machine that is pulling M2 as well (thus doing more work)?

2) Is this velocity reachable/possible? My guess is that the force needs to equalled out to zero for both M1 attracting M2 and M1 moving at such velocity that keeps the distance x the same (thus canceling out net acceleration). But then with no acceleration M2 would not be attracted in the direction of M1 anymore. So, how do we reach a perfect velocity where M2 is still attracted to M1 but is never able to touch it?

By the way, this is a real physical situation that I can do using two bar magnets, but because my hands are not sensitive enough, I cannot know whether I am really just pulling one magnet or two magnets. Which is why the above question.

  • $\begingroup$ 1) Hint: What would it mean if the machine can pull M1 & M2 with the exact same energy input as if it were pulling M1 only? $\endgroup$ – PM 2Ring Apr 16 '19 at 8:19

The magnets exert a force on each other(Wikipedia) .So in order to reach the "just not touching" point, you have to accelerate the magnets.

To convince you about the force exerted by the machine, do this experiment. It's not wise to keep on accelerating for keeping the magnets in this position, so we use gravity to provide the necessary acceleration. Put the first magnet in your palm. Place the other magnet below the palm (with unlike pole on top) such that it just begons to fall. Release it to freefall, now you must be getting a upward jerk on you palm. You are the machine, accelerating the magnets against gravity.

enter image description here

Note that there's a magnet on my palm too, not seen in the picture.

If the force done by you was on the magnet on your palm alone, you wouldn't have recieved any jerks. If you are careful, you can levitate the magnet for a few milliseconds!

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