A vertical force$\overrightarrow{\mathbf{F}}$ is applied to a block of mass m that lies on a floor. What happens to the magnitude of the normal force${\overrightarrow{\mathbf{F}}}_{\mathbf{N}}$ on the block from the floor as magnitude$\overrightarrow{\mathbf{F}}$ is increased from zero if force is (a) downward and (b) upward?

The problem deals with Newton’s third law of motion which states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. If the box is at rest then it exerts the force on the floor, that is the weight of the box, and the floor exerts the normal force on the box. This is Newton’s third law, which says every action has an equal and opposite reaction. This normal force by the floor depends directly upon the force applied to the box.

For downward force, we can write,

${\mathrm{F}}_{\mathrm{N}}=\mathrm{Mg}+\mathrm{F}$

As F increases,${\mathrm{F}}_{\mathrm{N}}$i.e. normal force would also increase.

For upward force, we can write,

$$\begin{gathered} {\mathrm{F}}_{\mathrm{N}}+\mathrm{F}=\mathrm{Mg} \\ {\mathrm{F}}_{\mathrm{N}}=\mathrm{Mg}-F \end{gathered}$$

From this, we can conclude that the normal force would decrease as we increase the upward applied force.