Would whether or not a magnet's moving effect the momentum of something that's attracted to it?

As I understand it; Newton’s second law states F = ma, so ignoring any other variables the acceleration of an object being pulled towards a magnet would be a = m/F, where F is the pull of the magnet. Fair enough.

What’s bothering me, is if the magnet is moving (e.g. the magnet was being pulled along on a piece of string and the object was trailing behind, or on the other side of a surface), would its own momentum have any effect on what it was pulling’s acceleration?

I don’t see how the magnet’s momentum, per se, would have any bearing on the acceleration of the object it was pulling due to magnetic force. Certainly any changes in velocity relative between the two would affect the object’s acceleration toward it though.

I think cmyk is right, though I don’t quite understand his second sentence.

If the force is constant (which it wouldn’t be), the acceleration would be constant. The force isn’t constant simply because (at least, as far as I know) there aren’t any fields where the force is equal, except when you follow a specific curve where the force is equal (which wouldn’t be a straight line or a free-fall path).

In either case, the magnetic force affects both bodies as you’d expect, but just as a force; the relative motion between them is irrelevant except as it defines the force between them.

Except for the electrons. That is, if you move a magnet past a coil, it creates a potential difference across the coil’s leads. Again, though, this isn’t due to the relative motion of the objects, but the relative motion of the test object and the field. The object doesn’t care whether the field is moving because the field is a moving magnet, or it’s moving because it’s an electrically generated field like in an AC motor.

I’m not an expert here, so if I goofed, please fight my ignorance!

The magnet’s moving will have no effect. In physics you can always choose the frame of reference you wish to use. Just choose to use a frame of reference in which the magnet is stationary. In that frame of reference the force on the object will depend only on the magnetic field strength and the distance between the magnet and the object.

disclaimer: I’m not a physicist or student of physics, so I’m probably wrong.

Magnetic field strength decreases with the square of distance which is why an object accelerates toward a magnet (as it gets closer, pull is stronger, acceleration increases). That same amount of acceleration will only slow or stop the distance from increasing if the magnet is already moving.

I could’ve phrased it better, but what I meant was the decay in the magnetic force would shift due to any arbitrary distance put between the magnet and the object as the magnet undergoes velocity changes (relative to the object in tow).

There is also the inertia the object will attain as it undergoes acceleration from the magnetic field.

Thanks for the replies, guys! I think I’ve got it now.

Actually the answer is that in general the electromagnetic field experienced by a test particle in its rest frame does depend on the velocity of the source.

And how would that make a difference in terms of, say, a 1kg magnet being used to pull around a 1kg chunk of iron?

At realistic laboratory speeds? Not much difference at all. You’d need high speeds for the effects to be large.

a = F/m, not m/F