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Unformatted text preview: Chapter 6 Lecture Essential University Physics Richard Wolfson
2nd Edition Work, Energy, and Power Work: A Measure of Force Applied Over Distance  For an object moving in one dimension, the work Wdone on
the object by constant applied force I3 is W = ﬁrm: where F; is the component of the force in the direction of the
object’s motion and AX is the object’s displacement.  The SI unit for work is ioule (Ji: 1 J = 1 newtonmeter (Nmi Him: :IE'ILI. disl'nljutmul'l
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‘ .11 III. . I Work Can Be Positive or Negative  Work is positive if the force has a component in the same
direction as the motion.  Work is negative if the force has a component opposite the
direction of motion.  Work is zero if the force is perpendicular to the motion. “I. IIII'I'II :it‘iim' ':II III: ‘w.l'l'l.":1il'l‘l"[ :il': :IHIII'I 51‘ IIH'L'l‘i'i'HHEJ With~3'l""""“'31l“1l "Hm
whiprt? ]l.!li'."] L'UL‘H ['Uhjli'. .' IaIIIk. “Uni I~'i"'~‘~ﬁlili"i 3‘“ 551:: UT'IiL'I‘i.'*~ IiiLJl 'Jli 'JW“
I H" 5' '3 IHJIiilit'u work. Ur" 1'» II
— r _ _ _ _ r _' _ ' _
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in] IIII .‘I I'Irrt': IIL'Ei:I;.' III. I'igIII :IIIgIca II' '.iI._' IIII:IiIIII degh [H] ._II {llk 31'; I'i'II'L'L‘ il'.'_i.' i'I]II§I.:h'..' .EIL‘ lilLf'l'J'Ill it'll.” It: w n III*;,:':':I'rp 'II :'I'aI. Ur: H
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Itj id! The Scalar Product  Work is conveniently characterized using the scalar product,
a way of combining two vectors to produce a scalar that depends on the vectors’ magnitudes and the angle between
them.  The scalar product of two vectors 3 and 3 is defined as H? : ABcosd
where A and B are the magnitudes of the vectors and i9 is
the angle between them.  Work is the scalar product of force with displacement: Integration  The deﬁnite integral is the result of the limiting process in
which the area is divided into ever smaller regions.  Work as the integral of the force F over position X is written x:
W : j F(x) dx  Integration is the opposite of differentiation, so integrals of
simple functions are readin evaluated. For powers of X, the integral becomes I: n xn+1 I2 J(vizEH 342+]
I x dx : : —
I1 :1 +1 II H +1 n +1 Work Done in Stretching a Spring  A spring exerts a farce FEWinlg = —kx.  The agent stretching a spring exerts a terse F =+kx, and the
work the agent dees is =ihE—%k(0f=éhg I
U 2 W = E'me = Ems: 2 gal  In this case the work is the area under the triangular
feroe—versus—distance curve: i’nree inerenses with This~ 1x the. innit,"
when the HJ‘IE'Eﬂg
i2; ’r".1i}' stretehetl. .. m} the 'esnrit is 'L.
:j ]''.'IH t1: .'.{.t.li.t I. t‘u'
E ' .
3 Hit: urea ui iht'.
'_ tramWells. 15.114.
'n' 1. Distance... .1: Work Done Against Gravity  The werk done by an agent lifting an object of mass m
against gravity depends enly en the vertical distance h: W= mgh Sinee gram}: is vertiezilr will}; [lie _reeiii}mneiil
eiiiiir'ii‘itlies it} Ilie Wiii‘k. Thai eenirihuiien is I. The work is pOSitiVe the
ill" “a object Is raised and
negative if it’s lowered. H.131 _ _ _ _ _ _ _ . _ _ _ _ _ _ _ —_...1li....——1 A ll ml: _rem'n penenis
add up In the ltiilli
height ii. at: the LeLul
wnr'lx is well. The WorkEnergy Theorem  Applying Newton’s second law to the net work done on an
object results in the workenergy theorem: of a"
W t :JF tdx=Jmadx= m—vdx: m—ldr*:JmL*dv
“9 “e dr dr  Evaluating the last integral between initial and final velocities
v1 and V2 gives "2
_1 2_1 2
—§mv2 EH11? 1. 1'32 3
W : J mv dv : émv
net 1,1 1,1 l  So the quantity imvg changes only when network is done on an object, and the change in this quantity is equal to the net
work. Kinetic Energy and the WorkEnergy Theorem  Kinetic energy is a kind of energy associated with motion.  The kinetic energy K of an object of mass m moving at speed v is 1 K:—mﬁ
2  The workenergy theorem states that the change in an object's kinetic energy is equal to the network done on the
object: _l 2_l 2_
iﬂ\[('—2;r’.ra.r122 2mvl —W IIEI Power and Energy  Power is the rate at which work is done or at which energy is
used or produced. If work AW is done in time At, then the average power over this time is — AW
P : —_ (average power)
A:
 When the rate changes continuously, the instantaneous
power is Pzﬁmaﬂﬂ
Na” Ar dr  Power is measured in watts (W), with l W = l J/s.  Total work or energy follows from power by multiplying (for
constant power) or integrating (for varying power): W:Pm or W: IEPdt I1 ...
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This note was uploaded on 02/12/2012 for the course PHYSICS 104 taught by Professor Staff during the Fall '10 term at Rutgers.
 Fall '10
 Staff
 Physics

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