Chapter 6 Review

# Chapter 6 Review - Chapter 6 Lecture Essential University...

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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 newton-meter (N-mi Him: :IE'ILI. disl'nljutmul'l LII:[TE'I11E'ILLIiL'-.|§i|[. 5"-.~:'L'<.' slid Liiwpint't'riic'il no wnrk is rlnn: :In'. nol i11hu ~11'L1L:Liiru:1:nn: ” ‘ I nrt': and Lli.~|1|:lt':rnc:nl hi“ 11' '73- J”- ..i . . I ' # iLI'L‘ :I'I Lil: ~i|.ii._' Ltll'L:.'|.1||L .'_"-_I.' 1.: F :I I ", .I . I . . ~'.r . . fi- — :_. .1. _. ' 4 "I I '.:r-"""-=.. ' . f 'l 'l :I. :1. F i'. i 'I I ‘ .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‘ II-H'L'l‘i'i'HHEJ With~3'l"""-|"“'31l“1l "Hm whip-rt? ]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 IHJI-iilit'u work. Ur" 1'» II — r _ _ _ _ r _' _ ' _ f- I _ I I I I. ' I l I ---------.h -----ﬁ----'r _'|.I" J”. in] IIII .-‘I I'Ir-rt': IIL'Ei:I;.' III. I'igIII :IIIgIca II' '.iI._' IIII:IiIIII deg-h [H] -._II {ll-k 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|'a-I. Ur: H I ' r _ _ _ _| ' I 'II ' I I I ---------‘y ---------ib ﬁr. _"I.I" 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(viz-EH 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'. '_ tram-Wells. 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 _r-eeiii}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: _r-em'n penenis add up In the ltiilli height ii. at: the LeLul wnr'lx is well. The Work-Energy Theorem - Applying Newton’s second law to the net work done on an object results in the work-energy 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 Work-Energy 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 work-energy 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.

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Chapter 6 Review - Chapter 6 Lecture Essential University...

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