How to hover without an anchor below you.

It's true the net force would result in zero net acceleration, but the energy of those forces just don't vanish though.  The allomancer here is being simultaneously pushed/pulled in 2 opposite directions at 6 g-force each.  OUCH!

 

3 hours ago, Subvisual Haze said:

It's true the net force would result in zero net acceleration, but the energy of those forces just don't vanish though.

If the system is static, then no work is being done, and there's no actual energy transfer. Forces don't intrinsically have energy; they transfer energy when causing a displacement.

3 hours ago, Subvisual Haze said:

The allomancer here is being simultaneously pushed/pulled in 2 opposite directions at 6 g-force each.  OUCH!

Fortunately, the two forces applied to the allomancer both target the center of mass, so the net force on any particle of the allomancer is straight upwards, and they feel no torque. At least in theory. On the other hand, we know that allomancers can 'crush' themselves by flaring pushes in opposite directions simultaneously, so the forces aren't perfectly distributed throughout the body.

We don't know exactly how the forces are distributed, but given that the two force vectors here have only a small angle between them, I wouldn't expect it to cause severe problems. An experiment worth trying in-universe: Push and pull on the same object at the same time. Whether and where you feel bodily pressure would tell about how the forces are applied.

The building on the other hand does experience extreme torque, which is counteracted by the ground if the anchor points are stable enough.

 

Everything is energy transfer.  Even you just standing in place requires your body to withstand the internal stress of perfectly opposing gravitational and normal forces.  Your feet hurt, your joints get sore, your spine slowly compresses etc.

How do you think it would feel if gravity was suddenly 6 times its current strength?  That's roughly the situation occurring here.  No net work does not mean the forces disappear, just that they don't generate a change in kinetic energy/acceleration.   Instead they would exert a painful sustained stress on the allomancer's body in the horizontal plane, in this example one roughly 6 times the force you normally feel when gravity and normal force counter one another to keep you from falling through the Earth.

The question just becomes if the body in question is experiencing 6g tension or compression.

Edited April 17, 2019 by Subvisual Haze

Well, technically, there is still no energy transfer, but the forces don’t just disappear. The reason there is no energy transfer is that the force is not applied across a distance, therefore no work is being done. If there was an energy transfer when no work is being done, we could theoretically power everything with bricks sitting on a table.

however, yes, you are still correct, the forces Involved would be far to large for this to be practical.