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
${\overrightarrow{F}}_{\mathrm{Net}}$
that is perpendicular to the surface.

**Figure 5-7** (a) A block resting on a table experiences a normal force
${\overrightarrow{F}}_{N}$
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
${\overrightarrow{F}}_{g}$
on the block. The table pushes up on the block with normal force
${\overrightarrow{F}}_{N}$.
The free-body diagram for the
block is given in Fig. 5-7b. Forces
${\overrightarrow{F}}_{g}$
and
${\overrightarrow{F}}_{N}$
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 (F_{net,y} = ma_{y}) as

F_{N} - F_{g} = ma_{y}

From Eq. 5-8, we substitute mg for F_{g}, finding

F_{N} - mg = ma_{y}.

Then the magnitude of the normal force is

F_{N} = mg + ma_{y} = m(g + a_{y}) (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 a_{y} can be positive or negative here.) If the table and block are
not accelerating relative to the ground, then a_{y} = 0 and Eq. 5-13 yields

F_{N} = m_{g}. (5-14)

**About the Authors**

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.

The 10th edition of Halliday's Fundamentals of Physics, Extended building upon previous issues by offering several new features and additions. The new edition offers most accurate, extensive and varied set of assessment questions of any course management program in addition to all questions including some form of question assistance including answer specific feedback to facilitate success. The text also offers multimedia presentations (videos and animations) of much of the material that provide an alternative pathway through the material for those who struggle with reading scientific exposition.

Furthermore, the book includes math review content in both a self-study module for more in-depth review and also in just-in-time math videos for a quick refresher on a specific topic. The Halliday content is widely accepted as clear, correct, and complete. The end-of-chapters problems are without peer. The new design, which was introduced in 9e continues with 10e, making this new edition of Halliday the most accessible and reader-friendly book on the market.

A Reader says,"As many reviewers have noted, this is a great physics book used widely in university technical programs as a first course in technical physics, with calculus. I find it is the one book I start with when trying to understand physical concepts at a useful but basic level. It has broad coverage and is well written . To go beyond this book requires specialized books on each topic of interest (electromagnetics, quantum mechanics, thermodynamics, etc.)."

Reader Frank says, "The treatment is sound, thorough, and clear. I've owned the early editions of Halliday and Resnick for years. I'm very happy that I updated my library with this 10th edition. The topics are covered in a very logical order. The study features and worked examples are outstanding. Don't hesitate to buy this book! Reading it is awesome on the Kindle app on the iPad."

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