Blowing Mechanics!
A uniform rectangular plate is hanging vertically downward from a hinge that passes along its left edge. By blowing air at over the top of the plate only, it is possible to keep the plate in a horizontal position, as illustrated in part of the drawing.
To what value of speed (in m/s) should the air be blown so that the plate is kept at a angle with respect to the vertical, as in part of the drawing?
The answer is 8.485.
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1 solution
There are two torques in opposition to each other: Gravity and the lift pressure. The gravitational force is effectively applied at the center of the plate, and is always downward. The lift pressure force is effectively applied at the center of the plate, is normal to the surface, and is proportional to the square of the air speed. From the geometry, it is evident that the gravitational torque at (b) is half that at (a) (same force with half the moment arm). The lift pressure force has the same moment arm in both cases.
Therefore:
2 1 = v a 2 v b 2 ⟹ v b = 2 v a ≈ 8 . 4 8 5