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Hello team,
This is my problem, given an object that weighs a 1000 pounds and hovers in one spot on a nine inch cushion of air, how would you calculate the minimum force needed to move the object forward, backward, side to side and or in a circle? Given, that there will be an unknown variable force resistance of matter. Also, air force can only be used.
Just to move the 1000lb mass, in theory, you're looking at the starting or static frictional force, not the dynamic friction force - usually in fluid mechanics you would use the latter to work out the drag to be overcome at a certain fluid velocity. For a cushion of air, this wouldn't be realistic - the forces involved in keeping the thing hovering on the cushion of air would be significantly larger and would involve a fluid flow already - there would have been no 'starting friction' to overcome.
If you want a proper answer you'll have to look a lot further, as the frictional forces in a fluid cushion get complicated - and you'd be better off with an empirical measurement. If you're after an easy answer, throw in Newton's Second Law - F x dt = m x dv. So for any force applied for a given time, you'll get an acceleration - works in any direction too, even in a circle!