You can tell a lot about an object that's not moving,
and also a lot about the forces acting on it:
==> If the box is at rest on the table, then it is not accelerating.
==> Since it is not accelerating, I can say that the forces on it are balanced.
==> That means that the sum of all forces acting on the box is zero,
and the effect of all the forces acting on it is the same as if there were
no forces acting on it at all.
==> This in turn means that all of the horizontal forces are balanced,
AND all of the vertical forces are balanced.
Horizontal forces:
sliding friction, somebody pushing the box
All of the forces on this list must add up to zero. So ...
(sliding friction force) = (pushing force), in the opposite direction.
If nobody pushing the box, then sliding friction force = zero.
Vertical forces:
gravitational force (weight of the box, pulling it down)
normal force (table pushing the box up)
All of the forces on this list must add up to zero, so ...
(Gravitational force down) + (normal force up) = zero
(Gravitational force down) = -(normal force up) .
