Ironwing posted:
Force = mass x acceleration
Since nothing in the system is accelerating, acceleration is zero for both cases. Therefore, the force in each system is zero.
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This equation only applies when the object subject to the force is free to move. It may be easier to understand if you realize that the "Force" it uses is the NET force composed of ALL forces acting on the object. In the case of a magnet stuck onto a metal plate, there is one force (from the magnetic field interaction with the plate) that pulls the magnet against the plate. There is another (exactly equal) force of the plate pushing back against the magnet that prevents the magnet from simply plowing though the plate - the plate is strong enough to prevent this penetration. So the NET force between plate and magnet is zero, and no movement happens.
Now, it you come along and grab the magnet and pull, you are adding a new force to the system. If you pull hard enough (that is, increase the force away from the plate), your new force can exceed the attractive force of magnet to plate, and that DOES result in a NET force AWAY from the plate. It does accelerate away from the plate.
This is exactly the same as the effect of gravity that holds a book on a table. There is a force pushing down on the table because of the interaction of the mass of the book with the gravitational field, and the table in return exerts a matching upward force to prevent the book from falling though it. You can pick up the book by adding a new force upwards. Now, if the supporting surface were not a solid table, but merely a flimsy piece if tissue paper in a frame, that might not be strong enough to prevent the gravitational force on the book from exceedinging the strength of the paper, and the paper would fracture and allow the book to fall through.
