Question

A box is resting on the floor. To move it, a (variable) force is applied as shown
in the diagram below.
why does the box stay at rest in the cases corresponding to fig a) and b)?​

Answer 1

Explanation:

Because the frictional force was acting on it in the opposite direction.

The magnitude of frictional force acting on its opposite was 2 f .Equal balanced forces acting from opposite directions on an object cancel out the effect of each other and does not change the state of rest or uniform motion of an object.

That's why when 3 f Force was applied

then an unbalanced force acted on the box which caused to move .