5.2.4 Normal Force

If you sit on a bed, the springs in the mattress compress and, as a consequence of the compression, exert an upward force on you. Stiffer springs would show less compression but still exert an upward force. The compression of extremely stiff springs might be measurable only by sensitive instruments. Nonetheless, the springs would compress ever so slightly and exert an upward spring force on you.

FIGURE 5.6 shows an object resting on top of a sturdy table. The table may not visibly flex or sag, but—just as you do to the bed—the object compresses the spring-like molecular bonds in the table. The size of the compression is very small, but it is not zero. As a consequence, the compressed “molecular springs” push upward on the object. We say that “the table” exerts the upward force, but it is important to understand that the pushing is really done by molecular bonds.

FIGURE 5.6 The table exerts an upward force on the book.

The figure illustrates a book kept on a table and the magnified view of the surface of the table in contact with the book.
FIGURE 5.6 Full Alternative Text

We can extend this idea. Suppose you place your hand on a wall and lean against it. Does the wall exert a force on your hand? As you lean, you compress the molecular bonds in the wall and, as a consequence, they push outward against your hand. So the answer is yes, the wall does exert a force on you.

The force the table surface exerts is vertical; the force the wall exerts is horizontal. In all cases, the force exerted on an object that is pressing against a surface is in a direction perpendicular to the surface. Mathematicians refer to a line that is perpendicular to a surface as being normal to the surface. In keeping with this terminology, we define the normal force as the force exerted perpendicular to a surface (the agent) against an object that is pressing against the surface. The symbol for the normal force is n⃗.

We’re not using the word normal to imply that the force is an “ordinary” force or to distinguish it from an “abnormal force.” A surface exerts a force perpendicular (i.e., normal) to itself as the molecular springs press outward. FIGURE 5.7 shows an object on an inclined surface, a common situation.

FIGURE 5.7 The normal force.

The figure illustrates a frog on a slope inclined toward the upper right. A dot is placed in line with the slope. A force vector arrow labeled vector n points toward the upper left from the dot. The surface pushes outward against the bottom of the frog.

In essence, the normal force is just a spring force, but one exerted by a vast number of microscopic springs acting at once. The normal force is responsible for the “solidness” of solids. It is what prevents you from passing right through the chair you are sitting in and what causes the pain and the lump if you bang your head into a door.