# The Normal Force by David Halliday and Robert Resnick

If you stand on a mattress, Earth pulls you downward, but you remain stationary. The reason is that the mattress, because it deforms downward due to you, pushes up on you. Similarly, if you stand on a floor, it deforms (it is compressed, bent, or buckled ever so slightly) and pushes up on you. Even a seemingly rigid concrete floor does this (if it is not sitting directly on the ground, enough people on the floor could break it).

The push on you from the mattress or floor is a normal force . The name comes from the mathematical term normal, meaning perpendicular:The force on you from, say, the floor is perpendicular to the floor.

When a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force ${\stackrel{\to }{F}}_{\mathrm{Net}}$ that is perpendicular to the surface.

Figure 5-7 (a) A block resting on a table experiences a normal force ${\stackrel{\to }{F}}_{N}$ perpendicular to the tabletop. (b) The free-body diagram for the block.

Figure 5-7a shows an example. A block of mass m presses down on a table, deforming it somewhat because of the gravitational force ${\stackrel{\to }{F}}_{g}$ on the block. The table pushes up on the block with normal force ${\stackrel{\to }{F}}_{N}$. The free-body diagram for the block is given in Fig. 5-7b. Forces ${\stackrel{\to }{F}}_{g}$ and ${\stackrel{\to }{F}}_{N}$ are the only two forces on the block and they are both vertical. Thus, for the block we can write Newton's second law for a positive-upward y axis (Fnet,y = may) as

FN - Fg = may

From Eq. 5-8, we substitute mg for Fg, finding

FN - mg = may.

Then the magnitude of the normal force is

FN = mg + may = m(g + ay) (5-13)

for any vertical acceleration ay of the table and block (they might be in an accelerating elevator). (Caution: We have already included the sign for g but ay can be positive or negative here.) If the table and block are not accelerating relative to the ground, then ay = 0 and Eq. 5-13 yields

FN = mg. (5-14)

David Halliday was an American physicist known for his physics textbooks, Physics and Fundamentals of Physics, which he wrote with Robert Resnick. Both textbooks have been in continuous use since 1960 and are available in more than 47 languages.

Robert Resnick was a physics educator and author of physics textbooks. He was born in Baltimore, Maryland on January 11, 1923 and graduated from the Baltimore City College high school in 1939. He received his B.A. in 1943 and his Ph.D. in 1949, both in physics from Johns Hopkins University.

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