First Eam Cming Up! Sunda, 1 Octber 6:10 7:30 PM. Lcatins t be psted nline. Yes this is a Sunda! There will be 17 questins n eam. If u have a legitimate cnflict, u must ask Prf. Shapir b Oct. 8 fr permissin t take the make-up eam. Email him the reasn fr missing the eam, and ur schedule fr Oct. 15 18. Newtn s Laws f Mtin TOPICS FROM PREVIOUS LECTURE (mtin in -D) Cmpnents f Equatin f Mtin v = v 0 + a t v = v 0 + a t = 0 + v 0 t + ½ a t = 0 + v 0 t + ½ a t Prjectile Mtin Superpsitin f tw mtins: Cnstant v and free-fall v Then slve fr : = f() r trajectr: v v v h v h sin g Relative Velcit: (e.g.,carsnhighwa,airplaneinwind,batnriver, ) R v sin R g Fied Frame: A Mving Frame: B Mving Object: P v P/ A vp/ B vb/ A 1 The change in velcit fr the ball during the bunce is m/s 3 m/s a) 1 m/s dwnward b) m/s upward c) 1 m/s upward d) 5 m/s dwnward e) Nne f the abve Befre After Between pint A and B, the directin f the average acceleratin fr this mtrcclist is a) b) c) d) e)
NEWTON S LAWS OF MOTION S Far: DESCRIPTION f mtin in terms f psitin vectr, velcit, acceleratin.(kinematics) NOW: What is the CAUSE f mtin?(dynamics) Laws f Mtin frmulated b Newtn ver 300 ears ag Frces and interactins Cmmneperience: Frceisa push ra pull pull push Frceisavectr Different tpes f frces: CntactFrce (kicksccerball,pushbk,twcar, ) Lng range frces, act thrugh empt space (electric frce, magnetic frce, gravitatinal frce, ) v v v h R UnitffrceinSIunits: Newtn[N] a =0 ; a = -g We will fcus n cntact frces and gravit. Superpsitin f frces Frcesarevectrs addtgiveresultant. F R 1 R NET FORCE: F R EQUILIBRIUM: Net frce = 0 F F F F R 1 3 R F F F F... R F F F F... F 3 1 3 F 3 R F 3 R R R F 1... F 0; F 0; F 0 R 1 3 F 0? F! Newtn s first law AncientIdea: Thenaturalstatefanbjectisatrest. Ifanbjectmves,it sbecauseafrceactsnit. NEWTON: Thenaturefabdistresistchangeinmtin. Newtn s First Law Whennnetfrceactsnanbject,itsacceleratiniser If F 0 then a 0 Anislatedbjectwithnnetfrceactingnitiseitherat rest, r is mving with a cnstant velcit. INERTIA: Thetendencfabdtresistchangein v. INERTIAL FRAMES OF REFERENCE AninertialframefreferenceisneinwhichNewtn s1 st Law is valid(the frame is nt accelerating!!) A A Inertial frame A B B v B / A An elevatr mving at cnstant velcit is an inertial frame. An accelerating elevatr is NOT an inertial frame. B Als inertial frame if v B/ A cnstant.
Newtn s Secnd Law Frce and acceleratin If the net frce n an bject is nt er, it causes the bject t accelerate. The acceleratin f an bject is directl prprtinal t the net frce (sum f all the frces) n the bject. Cnversel, the net frce is prprtinal t the acceleratin. The prprtinalit cnstant is called the mass f the bject. Cpright 01 Pearsn Educatin Inc. Cpright 01 Pearsn Educatin Inc. F Newtn s Secnd Law When 0 the net frce causes the bject t accelerate inthesamedirectinasthenetfrce. The net frce F is directl prprtinal t. The prprtinalit cnstant is the mass f the bject. F ma Mass and Frce: Frcechangesmtinfanbject Mass(inertia) resists change in mtin Mass weight a Statement Of Newtn s Secnd Law The acceleratin f an bject is prprtinal t the net frce acting n that bject and inversel prprtinal t its mass. F a r F ma m F ma F ma ; F ma ; F ma Unit f frce: Newtn[N] 1N=(1kg)X(1m/s )=1kgm/s EXAMPLE: Ablck (m=5.0kg)isatrestatt=0. Then,a cnstantfrce F actsnit. Att=3.0s,theblckhasmved.3m. Find F. m F F ma scalar vectr Have: m,need a. But,alshave tand( - ) a Weightisthefrcenabdduetgravit. Weight is prprtinal t mass. Themassfabdisthesameeverwhereinthewrld. Theweightfabddependsnwhereuare(earth? mn?) ( ) v t a t 1 ( ) (.3 m) a t (3.0 s) F 0.51m/s (5.0 kg)(0.51m/s ).6 kg m/s.6 N
Mass And Weight Weight is the attractive frce, F g, eerted b the earth s gravit n an bject. F g = weightfbject = w Because F ma and a g then in free fall(i.e., n frce ther than gravit acting n bject) we have w mg S we can cmpare masses b measuring weight at earth s surface. Nte: Weightisafrcethatactsnabdatalltimes g varieswithlcatin,wewilluse g=9.8m/s. Avid incrrect usage(i.e. an bject s weight is kg) English unit fr weight: 1 Pund = 4.448 Newtns Englishunitfrmass:1Pund=0.45359kg Measuring frces: Cnvenient t use elngatin f a spring. (Elngatin f a spring is prprtinal t the frce eerted n it.) Si identical curling stnes are pushed hrintall alng the ice. Fr each stne, the instantaneus velcit and acceleratin are given. Assume the ice is frictinless. Rank the stnes based n the magnitude f the frce eerted n them. a) C = F > A = D > B = E b) B = D = F > A = C = E c) F > C > D > A > B > E d) The magnitude f the frce is equal and nn er fr all. e) The magnitude f the frce is er fr all. T Anbjectmvesalnga straight path frm its starting pinttasecndpint,and then returns t its starting pint.thegraphfthespeed fthebjectasafunctinf timeisshwnttheright. mg Elevatrmves,butatcnstantvelcita = 0 F = ma,therefre F 0 inparticular F 0 Therefre, T mg = 0 ; T = mg. What wuld a plt f the frce versus time graph lk like? a) It will be cnstant, because the slpe f the velcit never changes. b) It will be kick in the psitive directin at t= and be er everwhere else. c) It will be a kick in the negative directin at t= and be er everwhere else. d) It will be psitive frm t=0 t t= and negative frm t= t t=4. e) It will be negative frm t=0 t t= and psitive frm t= t t=4.
Newtn s Third Law Whenever tw bjects interact, the frces that the bjects eertneachtherarealwasequalinmagnitudeand ppsite in directin. Restated: IfbjectAeertsafrcenB( actin )thenb eerts an equal and ppsite frce n A ( reactin ). These tw frces: Have the same magnitude Are ppsite in directin Act n different bdies!!!!! A Suppse tw balls cllide actin reactin pair n A Frces eist in pairs, acting n different bjects (e.g.,bathitsball;hammerhitsnail; ftkicksbutt ) B F B F A n B F A n B Cnsiderabnatablentheearth w F g F g n (nrmalfrce: frce f table n b) Simpler t understand if cnsider frces n b alne: n Bisatrest,s: n and w are F 0 NOT actin/reactin pair. F 0 0 w F The act n same bject. n and n ' : n frces ARE actin/reactin pair : n mg = 0 n = mg Free Bd Diagrams: an aid t slving prblems F ma appliedtnebjectwithmass m (ragrupmvingasne). Use nl frces applied t this bd Draw diagram fr each bd separatel n ' Reactin t n (frce f b n table) Reactintweightfb Appling Newtn s Third Law Newtn s apple rests n a table. Identif the frces that act n it and the actinreactin pairs. A baseball is thrwn frm right field t hme plate (HP), traveling frm right t left in the diagram. If we ignre air frictin, which is the crrect free-bd diagram fr the baseball at pint T? Cpright 01 Pearsn Educatin Inc. 0
EXAMPLE: Apparent cntradictin a hrse pulling a cart. Ifthefrcefhrsencartequalsthefrcefcartnhrse hw des the cart mve???? F C n H F H n C EXAMPLE:Askierfmass65.0kgispulledbatwrpeup asnw cveredskislpeatacnstantspeed. Therpe andtheslpeareinclinedb6. Drawafreebd diagram and calculate the tensin in the tw rpe. T n T Islate cart and draw free bd diagram At the instant the cart mves, it accelerates: 1 st law: F 0 s v isnotcnstant(acceleratin) nd law: n w F ma F F ma F n w 0 n w F H n C FHC a m 3 rd law: Ntethat, arenotreactinpair!!! HC n w F H n C 6 w 6 wsin(6 ) mving,butnacceleratin F 0 cnsider cmpnents in tilted crdinate sstem: F F 0 n wcs(6 ) 0 T wsin(6 ) T wsin(6 ) mgsin(6 ) T = (65.0 kg)*(9.80 m/s )*sin(6 ) T = 79 N First Eam Cming Up! Sunda, 1 Octber 6:10 7:30 PM. Lcatins t be psted nline. Yes this is a Sunda! There will be 17 questins n eam. If u have a legitimate cnflict, u must ask Prf. Shapir b Oct. 8 fr permissin t take the make-up eam. Email him the reasn fr missing the eam, and ur schedule fr Oct. 15 18. actin/reactin pair F T n C MILK F C n T F H n T n C m C g F T F n C C n T n T m T g 4