A ladder of uniform mass and length (2L) is lying on the floor, horizontally. It has weight, which is being neutralised by the reaction force from the ground. But, there are two forces applying, upwards, at the edge of the ladder, both of magnitude 7N. Thus, their moments cancel, as both their moments are (7L), but in the opposite directions. But how the heck do the sum of forces here result in zero???????????

Uniform mass? So uniform weight. Say the ladder weighs w N/meter.

Without the two 7-N upward forces, the whole weight of the ladder is supported by the ground. The ground offers w N/meter too. Upwards. To neutralize the w N/m weright of the ladder. The ladder is in equilibrium.

Apply the two 7-N upward forces, one at each end of the L-meter long ladder. The ladder doesn't move.

----Maybe because the total weight of the ladder, wL newtons, is heavier than 14N. Why are the vertical forces equal then? It's because the ground now offers only (wL -14)/L newtons/meter upwards. Not (wL)/L newton/meter anymore.

----Or, the ladder weighs less than 14N but it is tied/anchored to the ground at the middle. So, technically, the ladder is off the ground but won't be lifted anyway because it is pulled back, downwards, by the anchor at its middle. The anchor offers 14N downward to neutralize the two 7N upward forces. [The total force on the anchor is not 14N downwards. It is (14 minus wL) newtons downwards.] So net, or the sum of vertical forces is zero. Then, as you said, the moments of the two upward forces cancel each other. So net moment at the anchor is zero. The net moment anywhere on the ladder is zero. The ladder won't move or tilt whichever way. The ladder is in equilbrium.

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In any of those cases you mentioned, the ball, etc, even if there millions of upward forces apllied on the object and the object still won't be lifted, then something is neutralizing all those millions of upward forces---rendering the object to be in equilibrium verticaly. The weight of the object is greater than all those million upward forces most probably, or the object is anchored vertically.

Apply that to horizontal forces.

To moments.

If the object does not move even after all those billions of random forces are applied on the object, then the object is in equilibrium. You have to investigate why the dang object won't move.