For Scientists and
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`CORNINGEX!
`
`CORNING EXHIBIT 1024
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`

`
`Physics
`
`For Scientists and Engineers
`
`Paul A. Tipler
`
`Worth Publishers
`
`
`
`

`
`Physics for Scientists and Engineers, Third Edition, Volume 1
`
`Paul A. Tipler
`
`Copyright © 1991, 1982, 1976 by Worth Publishers, Inc.
`
`All rights reserved
`
`Printed in the United States of America
`
`Library of Congress Catalog Card Number: 89-52166
`
`Extended Version (Chapters 1—42) ISBN: 0—87901—432—6
`
`Standard Version (Chapters 1~35) ISBN: 0—87901-430—X
`
`Volume 1 (Chapters 1-17) ISBN: 0-87901-4334
`
`Volume 2 (Chapters 18-42) ISBN: 0—87901—434—2
`
`Printing:
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`5
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`4
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`3
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`2
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`1
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`Year:
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`95
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`94
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`93
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`Development Editors: Valerie Neal and Steven Tenney
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`Design: Malcolm Grear Designers
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`Art Director: George Touloumes
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`Production Editor: Elizabeth Mastalski
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`Production Supervisor: Sarah Segal
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`Layout: Patricia Lawson
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`Photographs: Steven Tenney, John Schultz of PAR/NYC, and
`Lana Berkovich
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`Line Art: York Graphic Services and Demetrios Zangos
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`Composition: York Graphic Services
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`Printing and binding: R. R. Donnelley and Sons
`
`Cover: Supersonic Candlelight. A stroboscopic color schlieren
`or shadow picture taken at one—third microsecond exposure
`shows a supersonic bullet passing through the hot air rising
`above a candle. Schlieren pictures make visible the regions
`of nonuniform density in air. Estate of Harold E. Edgerton/
`Courtesy of Palm Press.
`
`Illustration credits begin on p. IC-1 which constitute an
`extension of the copyright page.
`
`Worth Publishers
`
`33 Irving Place
`
`New York, NY 10003
`
`
`
`

`
`90
`
`Chapter 4 Newton's Laws I
`
`Contact forces exerted by one object on another
`produce deformations in the objects that are often not
`visible. Here, the forces exerted by the C-clamp on the
`plastic block produce stress patterns in the block that
`are made visible by polarized light.
`
`Contact Forces
`
`Most of the everyday forces we observe on macroscopic objects are contact
`forces exerted by springs, strings, and surfaces in direct contact with the
`object. The forces are the result of molecular forces exerted by the molecules
`of one object on those of another. These molecular forces are themselves
`complicated manifestations of the basic electromagnetic force.
`A spring made by winding a stiff wire into a helix is a familiar device.
`The force exerted by the spring when it is compressed or extended is the
`result of complicated intermolecular forces in the spring, but an empirical
`description of the macroscopic behavior of the spring is sufficient for most
`applications. If the spring is compressed or extended and released, it returns
`to its original, or natural, length, provided the displacement is not too great.
`There is a limit to such displacements beyond which the spring does not
`return to its original length but remains permanently deformed. If we allow
`only displacements below this limit, we can calibrate the extension or com(cid:173)
`pression Llx in terms of the force needed to produce the extension or com(cid:173)
`pression. It has been found experimentally that, for small Llx, the force ex(cid:173)
`erted by the spring is approximately proportional to Llx and in the opposite
`direction. This relationship, known as Hooke's law, can be written
`
`Fx = -k(x - xo) = -k Llx
`
`4-5
`
`where the constant k is called the force constant of the spring. The distance x
`is the coordinate of the free end of the spring or of any object attached to that
`end of the spring. The constant x0 is the value of this coordinate when the
`spring is unstretched from its equilibrium position. There is a negative sign
`in Equation 4-5 because, if the spring is stretched (Llx is positive), the force Fx
`is negative, whereas if the spring is compressed (Llx is negative), Fx is posi(cid:173)
`tive (Figure 4-6). Such a force is called a restoring force because it tends to
`restore the spring to its initial configuration.
`
`Figure 4-6 A horizontal spring attached to a block.
`(a) When the spring is unstretched, it exerts no force
`on the block. (b) When the spring is stretched such
`that .:lx is positive, it exerts a force on the block of
`magnitude k .:lx in the negative x direction. (c) When
`the spring is compressed such that .:lx is negative, the
`spring exerts a force on the block of magnitude k .:lx
`in the positive x direction.
`
`X
`
`x =x0
`
`(a)
`
`

`
`Section 4-5 Forces in Nature
`
`91
`
`(a)
`
`(b)
`
`(a) Model of a solid as
`Figure 4-7
`consisting of atoms connected to
`each other by springs. (b) The
`elasticity of nylon arises from the
`shape and cross linking of its
`fibers shown here under polarized
`light.
`
`The force exerted by a spring is similar to that exerted by one atom on
`another in a molecule or in a solid in the sense that, for small displacements
`from equilibrium, the restoring force is proportional to the displacement. It
`is often useful to visualize the atoms in a molecule or solid as being con(cid:173)
`nected by springs (Figure 4-7). For example, if we slightly increase the sepa(cid:173)
`ration of the atoms in a molecule and release them, we would expect the
`atoms to oscillate back and forth as if they were two masses connected by a
`spring.
`If we pull on a flexible string, the string stretches slightly and pulls back
`with an equal but opposite force (unless the string breaks). We can think of
`a string as a spring with such a large force constant that the extension of the
`string is negligible. Because the string is flexible, however, we cannot exert a
`force of compression on it. When we push on a string, it merely flexes or
`bends.
`When two bodies are in contact with each other, they exert forces on
`each other due to the interaction of the molecules of one object with those of
`the other. Consider a block resting on a horizontal table. The weight of the
`block pulls the block downward, pressing it against the table. Because the
`molecules in the table have a great resistance to compression, the table ex(cid:173)
`erts a force upward on the block perpendicular, or normal, to the surface.
`Such a force is called a normal force. (The word normal means perpendicu(cid:173)
`lar.) Careful measurement would show that a supporting surface always
`bends slightly in response to a load, but this compression is not noticeable to
`the naked eye. Since the table exerts an upward force on the block, the block
`must exert an equal force downward on the table. Note that the normal force
`exerted by one surface on another can vary over a wide range of values. For
`example, unless the block is so heavy that the table breaks, the table will
`exert an upward support force on the block exactly equal to the weight of the
`
`F X = - k Llx is negative
`because Ll x is positive.
`
`Fx =- k Llx is positive
`because Ll x is negative.
`
`X
`
`(b)
`
`X
`
`I
`I
`I
`I
`' - - Llx ------..1
`I
`I
`I
`I xo
`
`(c)