Help students learn physics by doing physics

Transcription

1 Help sdens learn physics by doing physics Dear Colleage, Welcome o he second ediion of or exbook College Physics: Explore and Apply and is spporing maerials (Masering TM Physics, he Acie Learning Gide (ALG), and or Insrcor s Gide) a coheren learning sysem ha helps sdens learn physics by doing physics! Experimens, experimens Insead of being presened physics as a saic se of esablished conceps and mahemaical relaions, sdens deelop heir own ideas js as physiciss do: hey explore and analyze obseraional experimens, idenify paerns in he daa, and propose explanaions for he paerns. They hen design esing experimens whose ocomes eiher confirm or conradic heir explanaions. Once esed, sdens apply explanaions and relaions for pracical prposes and o problem soling. A physics ool ki To bild problem-soling skills and confidence, sdens maser proen isal ools (represenaions sch as moion diagrams and energy bar chars) ha sere as bridges beween words and absrac mahemaics and ha form he basis of or oerarching problem-soling sraegy. Or niqe and aried problems and aciiies promoe 21s-cenry compeences sch as ealaion and commnicaion and reinforce or pracical approach wih phoo, ideo, and daa analysis and real-life siaions. A flexible learning sysem dens can work collaboraiely on ALG aciiies in class (lecres, labs, and problem-soling sessions) and hen read he exbook a home and sole end-of-chaper problems, or hey can read he ex and do he aciiies sing Masering Physics a home, hen come o class and discss heir ideas. Howeer hey sdy, sdens will see physics as a liing hing, a process in which hey can paricipae as eqal parners. Why a new ediion? Wih a wealh of feedback from sers of he firs ediion, or own ongoing experience and ha of a gifed new co-ahor, and changes in he world in general and in edcaion in pariclar, we embarked on his second ediion in order o refine and srenghen or experienial learning sysem. Experimens are more focsed and effecie, or mliple-represenaion approach is expanded, opics hae been added or moed o proide more flexibiliy, he wriing, layo, and design are sreamlined, and all he sppor maerials are more ighly correlaed o or approach and opics. Working on his new ediion has been hard work, b has enriched or lies as we e explored new ideas and applicaions. We hope ha sing or exbook will enrich he lies of yor sdens! This book made me hink deeper and ndersand beer. Egenia Ekina Gorazd Planinsic Alan Van Heelen sden a Horry Georgeown Technical College

2 3 Newonian Mechanics ea bels and air bags sae abo 250,000 lies worldwide eery year becase hey significanly redce he risk of injry (bels alone by abo 40% and bels wih air bags by abo 54%). How do sea bels and air bags proide his proecion? How do sea bels and air bags sae lies? If yo sand on a bahroom scale in a moing eleaor, does is reading change? Can a parachis srie a fall if he parache does no open? IN THE LAT CHAPTER, we learned o describe moion for example, o deermine a car s acceleraion when i sops abrply dring a collision. Howeer, we did no discss he cases of he acceleraion. In his chaper, we will learn why an objec has a pariclar acceleraion. This knowledge will help s explain he moion of many objecs: cars, car passengers, eleaors, skydiers, and een rockes. BE URE YOU KNOW HOW TO: Draw a moion diagram for a moing objec (ecion 2.2). Deermine he direcion of acceleraion sing a moion diagram (ecion 2.7). Add ecors graphically and deermine heir componens (ecions 2.3, 2.4, and 2.6). 51

3 52 CHAPTER 3 Newonian Mechanics 3.1 Describing and represening ineracions Wha cases objecs o accelerae or mainain a consan elociy? Consider a simple experimen sanding on Rollerblades on a horizonal floor. No maer how hard yo swing yor arms or legs yo canno sar moing by yorself; yo need o eiher psh off he floor or hae someone psh or pll yo. Physiciss say ha he floor or he oher person ineracs wih yo, hs changing yor moion. Objecs can inerac direcly, when hey och each oher, or a a disance, as when a magne aracs or repels anoher magne wiho oching i. FIGURE 3.1 A skech of a car skidding o aoid a collision wih a an. Choosing a sysem in a skech of a process We learned (in Chaper 2) ha he firs sep in analyzing any process is skeching i. Figre 3.1 shows a skech of a car skidding o aoid a collision wih a an. In his and laer chapers we choose one pariclar objec for deailed analysis. We call his objec he sysem. All oher objecs ha are no par of he sysem can inerac wih i (och i, pll i, or psh i) and are in he sysem s enironmen. Ineracions beween he sysem and objecs in he enironmen are called exernal ineracions. The car is he sysem. FIGURE 3.2 Represening exernal ineracions (forces exered on a sysem). (a) A bowling ball (ysem 1) A olleyball (ysem 2) ysem A sysem is he objec or grop of objecs ha we choose o analyze. Eeryhing oside ha sysem is called is enironmen and consiss of objecs ha migh inerac wih he sysem (och, psh, or pll i) and affec is moion hrogh exernal ineracions. On he skech, we draw a bondary arond he sysem o emphasize he sysem choice (shown by he red dashed line arond he skidding car in Figre 3.1). omeimes, a single sysem objec has pars like he wheels on he car and is axles. The pars inerac wih each oher. ince boh pars are in he sysem, hese are called inernal ineracions. In his chaper we will model an objec like a car as a poin-like objec and ignore sch inernal ineracions. (b) (c) Hand pshes p on bowling ball. F H on B F H on B F E on B Earh plls down on bowling ball. Hand pshes p on olleyball. F H on V F H on V F E on V Earh plls down on olleyball. Represening ineracions Exernal ineracions affec he moion or lack of moion of a sysem. Consider holding a bowling ball in one hand and a olleyball in he oher. Each ball is considered as a sysem (Figre 3.2a). Wha objecs inerac wih each ball? Yor hand pshes p hard o keep he bowling ball seady and mch less hard o keep he olleyball seady (Figre 3.2b). We se an arrow o represen he pward psh exered by each hand on one of he balls. Noice ha he arrow for he ineracion of he hand wih he bowling ball is longer han ha for he hand wih he olleyball. The arrow represens a force ha is exered by he hand on he ball. A force is a physical qaniy ha characerizes how hard and in wha direcion an exernal objec pshes or plls on he sysem. The symbol for force is F wih a sbscrip ha idenifies boh he exernal objec ha exers he force and he sysem on which he force is exered. For example, he hand pshing on he bowling ball is represened as F H on B. The force ha he hand exers on he olleyball is F H on V. The arrow aboe he symbol indicaes ha force is a ecor qaniy wih a magnide and direcion. The I ni of a force is he newon (N). When yo hold a 100-g ball, yo exer an pward force ha is a lile less han 1.0 N. Do any oher objecs exer forces on he balls? Iniiely, we know ha somehing ms be plling down o balance he pward force yor hands exer on he balls. The concep of graiy represens he ineracion of plane Earh wih he ball. Earh plls

4 3.1 Describing and represening ineracions 53 downward on an objec oward Earh s cener. Becase of his ineracion we need o inclde a second arrow represening he force ha Earh exers on he ball F E on B (see Figre 3.2c). Iniiely, we know ha he wo arrows for each ball shold be of he same lengh, since he balls are no moing. Do oher objecs besides he hands and Earh inerac wih he balls? Air srronds eeryhing close o Earh. Does i psh down or p on he balls? Le s hypohesize ha air pshes down. If so, hen or hands hae o psh p harder on he balls o balance he combined effec of he downward psh of he air and he downward pll of Earh. Le s es he hypohesis ha air pshes down on he balls. Tesing a hypohesis To es a hypohesis in science means o firs accep i as a re saemen (een if we disagree wih i); hen design an experimen whose ocome we can predic sing his hypohesis (a esing experimen); hen compare he ocome of he experimen and he predicion; and, finally, make a preliminary jdgmen abo he hypohesis. If he ocome maches he predicion, we can say ha he hypohesis has no been disproed by he experimen. When his happens, or confidence in he hypohesis increases. If he ocome and predicion are inconsisen, we need o reconsider he hypohesis and possibly rejec i. To es he hypohesis ha air exers a downward force on objecs, we aach an empy closed waer bole o a spring and le i hang; he spring sreches (Figre 3.3a). Nex we place he bole and spring inside a large jar ha is conneced o a acm pmp and pmp he air o of he inside of he jar. We predic ha if he air inside he jar pshes down on he bole (he hypohesis), hen when we pmp he air o of he jar, i shold be easier o sppor he bole he spring shold srech less (he predicion ha follows from he hypohesis). When we do he experimen, he ocome does no mach he predicion he spring acally sreches slighly more when he air is pmped o of he jar (Figre 3.3b). Eidenly he air does no psh down on he bole; insead, i helps sppor he bole by exering an pward force on i. This ocome is srprising. If yo sdy flids, yo will learn he mechanism by which air pshes p on objecs. FIGURE 3.3 A esing experimen o deermine he effec of air on he bole. (a) 0 We aach a bole o a spring. The spring sreches. Reflec Le s reflec on wha we hae done here. We formlaed an iniial hypohesis air pshes down on objecs. Then we designed an experimen whose ocome we cold predic sing he hypohesis he bole on a spring in a acm jar. We sed he hypohesis o make a predicion of he ocome of he esing experimen he spring shold srech less in a acm. We hen performed he experimen and fond ha somehing compleely differen happened. We reised or hypohesis air pshes p slighly on objecs. Noe ha air s pward psh on he bole is ery small. Therefore, in many siaions, and in all siaions in his chaper, he effecs of air can be ignored. (b) 0 When he air is remoed, he spring sreches farher. The air ms hae been exering a small pward force on he bole. Drawing force diagrams A force diagram (someimes called a free-body diagram) represens he forces ha objecs in a sysem s enironmen exer on i (see Figre 3.2c). We represen he sysem by a do o show ha we model i as a poin-like objec. Arrows represen he forces. Unlike a moion diagram, a force diagram does no show s how a process changes wih ime; i shows s only he forces a a single insan. For processes in which no moion occrs, his makes no difference. B when moion does occr, we need o know if he force diagram is changing as he sysem moes. Consider a rock dropped from aboe and sinking ino sand, making a small craer. We consrc a force diagram for he insan shorly afer he rock oches he sand b before i compleely sops moing. Vacm pmp

5 54 CHAPTER 3 Newonian Mechanics PHYIC TOOL BOX 3.1 Consrcing a force diagram 1. kech he siaion (a rock sinking ino sand). 2. Circle he sysem (he rock). 3. Idenify exernal ineracions: The sand pshes p on he rock. Earh plls down on he rock. 4. Place a do a he side of he skech, represening he sysem. F on R F E on R 5. Draw force arrows o represen he exernal ineracions. 6. Label he forces wih a sbscrip wih wo elemens. Remember ha on he force diagram, TIP yo only draw forces exered on he sysem. Do no draw forces ha he sysem exers on oher objecs! For example, he rock exers a force on he sand, b we do no inclde his force in he force diagram since he sand is no par of he sysem. Noice ha he pward-poining arrow represening he force exered by he sand on he rock is longer han he downward-poining arrow represening he force exered by Earh on he rock. The difference in lenghs reflecs he difference in he magnides of he forces. CONCEPTUAL EXERCIE 3.1 Force diagram for a book Book A sis on a able wih book B on op of i. Consrc a force diagram for book A. kech and ranslae We skech he siaion below. We choose book A as he sysem. Noice ha he dashed line arond book A passes beween he able and book A, and beween book B and book A. I s imporan o be precise in he way yo draw his line so ha he separaion beween he sysem and he enironmen is clear. In his example, Earh, he able, and book B are exernal enironmenal objecs ha exer forces on book A. force F B on A. In addiion, Earh exers a downward force on book A F E on A. Iniiely, we feel ha hese forces shold somehow cancel each oher. The diagram shows his by careflly represening he lengh of he forces. Noe ha if yo add he wo downward forces, heir combined lengh is he same as he pward force. Below we show how o find a reslan force ecor when seeral forces are exered on an objec. Book B, able, and Earh are in he enironmen. implify and diagram Draw a force diagram for book A, which is represened by a do. Two objecs in he enironmen och book A. The able pshes p on he boom srface of he book, exering a force F T on A, and book B pshes down on he op srface of book A, exering Try i yorself Consrc a force diagram for book A afer anoher book C is placed on op of book B. Answer The same hree objecs inerac wih book A. Earh exers he same downward force on book A ( F E on A). C does no direcly och A and exers no force on A. Howeer, C does psh down on B, so B exers a greaer force on A ( F B on A). Becase he downward force of B on A is greaer, he able exers a greaer pward force on book A ( F T on A). Conac and nonconac forces Yo can see in he aboe Concepal Exercise ha some of he forces exered on book A are exered by he objecs direcly oching he book he able and book B. B Earh does no need o och he book o exer a force on i. The force ha Earh as a whole

6 3.2 Adding and measring forces 55 plane exers on eery objec is an example of a graiaional force. Forces ha reqire he ineracing objecs o be oching are called conac forces, while forces ha do no reqire oching are called nonconac forces. The force a rope plling on a crae exers (someimes called a ension force) is anoher example of a conac force; he force of a magne on anoher magne (a magneic force) is anoher example of a nonconac force. When we wrie Earh wih a capial E TIP and no he before i, i means ha we are alking abo he whole plane, no he srface. REVIEW QUETION 3.1 How do we deermine how many forces o draw on a force diagram? 3.2 Adding and measring forces Usally, more han one enironmenal objec exers a force on a sysem. How can we add hem o find he oal force? In his chaper we will resric or aenion o forces ha are exered and poin along one axis. Consider he process of lifing a sicase. Adding force ecors graphically Yo lif a sicase sraigh p (Figre 3.4a). Earh plls down on he sicase, exering a force of magnide F E on = 100 N, and yo exer an pward force of magnide F Y on = 150 N (Figre 3.4b). Wha are he magnide and direcion of he oal force exered on he sicase? The ne effec of he wo forces exered along a erical axis is he same as a 50-N force poined sraigh p. Why? Remember ha force is a ecor. (We discssed he rles for ecor addiion in Chaper 2.) To add wo ecors o find F = F E on + F Y on, we place hem head o ail (see Figre 3.4c) and draw he ecor ha goes from he ail of he firs ecor o he head of he second ecor. This new ecor is he sm ecor, or he reslan ecor. In he case of forces i is called he ne force. To simplify operaions wih ecors, we will se componens in or calclaions. In his chaper we will only analyze siaions when all forces are exered along one axis (x or y) or when forces along one direcion add o zero and all he remaining forces are along he oher (perpendiclar) direcion. To find he componen of a force along a pariclar direcion, we firs need o idenify he posiie direcion, hen compare he direcion of he force wih he idenified posiie direcion. Forces ha poin in he posiie direcion of an axis hae componens eqal o heir magnides; forces ha poin in he negaie direcion hae componens eqal o heir magnides wih a negaie sign (see ecions 2.4 and 2.6 o reiew componens of a ecor). In or example of lifing a sicase, he y-axis poins p. The y-componen of he force ha yo exer on he sicase is posiie and eqal o F Y on y = 150 N, and he y-componen of he force ha Earh exers on he sicase is F E on y = -100 N. The sm of he y-componens is F y = 150 N = 50 N. This is he y-componen of he sm of he forces if he y-axis poins p. If he posiie direcion is down, he sm of he forces has a y-componen F y = -50 N. If seeral exernal objecs in he enironmen exer forces on he sysem, we sill se ecor addiion o find he sm of he forces exered on he sysem: F on = F 1 on + F 2 on + g + F n on (3.1) Measring force magnides The simples deice o measre forces is a spring scale (Figre 3.5a, on he nex page); we will demonsrae his wih a simple experimen. Imagine ha a ligh plasic bag hangs from a ligh spring. The spring is no sreched. We hen place one golf ball ino he bag and obsere ha he spring sreches o a new lengh. We add a second ball and FIGURE 3.4 The sm of he forces (he ne force) exered on he sicase. (a) (b) F Y on F E on y Draw a force diagram for he sysem showing he exernal forces exered on he sysem. kech he siaion and choose a sysem. (c) 150 N 100 N Place he arrows head o ail. The sm of he forces goes from he ail of he firs arrow o he head of he las arrow. The sm of he force ecors is no TIP a new force being exered. Raher, i is he combined effec of all he forces being exered on he sysem. Becase of his, he reslan ecor shold neer be inclded in he force diagram for ha sysem. y F (50 N p)

7 56 CHAPTER 3 Newonian Mechanics FIGURE 3.5 Using a spring scale o measre forces. (a) (b) (c) 0 y 0 balls 0 1 y F on 1B F E on 1B y F on 2B F E on 2B y F on 3B F E on 3B 53F E on 1B obsere ha he spring sreches wice as far. We add a hird ball and obsere ha he spring sreches hree imes as far. Figre 3.5b shows he for siaions; for each one, noice he change in he lengh of he spring. Yo can see ha he spring sreches he same amon for each ball, and ha i sreches hree imes more for hree balls han for one ball. Nex, we choose he bag wih he golf balls as he sysem and analyze he forces exered in each case. We assme ha Earh exers he same force on each ball F E on 1B ha is independen of he presence of oher balls. Ths, he oal force exered by Earh on he hree-ball sysem is hree imes greaer han he force exered on he oneball sysem. Figre 3.5c shows force diagrams for each case. Becase he bag does no fall, he spring in each case ms exer a force on he sysem F on #B ha is eqal in magnide and opposie in direcion o he force ha Earh exers on he sysem F E on #B so ha he sm of he forces exered on he sysem wih a nmber (#) of golf balls is zero. This experimen proides s wih one mehod o measre an nknown force ha an objec exers on a sysem. We calibrae a spring in erms of some sandard force, sch as Earh s pll on one or more golf balls. Then if some nknown force is exered on a sysem, we can se he spring o exer a balancing force on ha sysem. The nknown force is eqal in magnide and opposie in direcion o he force exered by he spring. In his case, we wold be measring force in nis eqal o Earh s pll on a golf ball. We cold se any spring o balance a known sandard force (1 N, or approximaely he force ha Earh exers on a 100-g objec) and hen calibrae his spring in newons by placing marks a eqal disances as yo pll on is end wih increasing force. We hs bild a spring scale he simples insrmen o measre forces. In physics, force is a physical qaniy ha characerizes he direcion and TIP magnide of an ineracion beween wo objecs. For a force o exis, here ms be wo objecs ha inerac, js as a hg reqires he ineracion of wo people. Force does no reside in an objec. Howeer, he idea ha force resides in an objec remains ery srong; people say, The rck s force cased a lo of damage o he elephone pole. We will be carefl in his book o always idenify he wo ineracing objecs when speaking abo any force. Remember, if yo are considering a force ha is exered on a moing objec b canno find anoher objec ha ineracs wih i, hen yo are hinking of somehing else, no force. REVIEW QUETION 3.2 A book bag hanging from a spring scale is parially sppored by a plaform scale. The plaform scale reads abo 36 N and he spring scale reads abo 28 N. Draw a skech of he siaion, consrc a force diagram, and se hem o find he magnide of he force ha Earh exers on he bag. 3.3 Concepal relaionship beween force and moion When we drew a force diagram for a ball held by a person, we iniiely drew he forces exered on he ball as being eqal in magnide. Wha if he person caches a ball falling from aboe? Wold she sill need o exer a force on he ball ha has a magnide eqal o ha Earh exers on he ball? In oher words, is here a relaionship beween he forces ha are exered on an objec and he way he objec moes? Obseraional Experimen Table 3.1 helps s find o wheher here is a paern beween he moion diagram and he force diagram for a moing objec.

8 3.3 Concepal relaionship beween force and moion 57 OBERVATIONAL EXPERIMENT TABLE 3.1 How are moion and forces relaed? VIDEO OET 3.1 Analysis Obseraional experimen Moion diagram Force diagrams for firs and hird posiions Experimen 1. A bowling ball B rolls on a ery hard, smooh srface wiho slowing down. B D 5 0 F on B F E on B F on B F E on B Experimen 2. A rler R lighly pshes he rolling bowling ball opposie he ball s direcion of moion. The ball conines o moe in he same direcion, b slows down. R D F R on B F on B F E on B FR on B F on B F E on B Experimen 3. A rler R lighly pshes he rolling bowling ball in he direcion of is moion. The ball speeds p. D F on B F on B FR F on B FR on B E on B F E on B Paern In all he experimens, he erical forces add o zero and cancel each oher. We consider only forces exered on he ball in he horizonal direcion. In he firs experimen, he sm of he forces exered on he ball is zero; he ball s elociy remains consan. In he second and hird experimens, when he rler pshes he ball, he elociy change arrow (D arrow) poins in he same direcion as he sm of he forces. mmary: The D arrow in all experimens is in he same direcion as he sm of he forces. Noice ha here is no paern relaing he direcion of he elociy o he direcion of he sm of he forces. In Experimen 2, he elociy and he sm of he forces are in opposie direcions, b in Experimen 3, hey are in he same direcion. In each of he experimens in Table 3.1, he D arrow for a sysem and he sm of he forces F ha exernal objecs exer on he sysem are in he same direcion. In addiion, we ofen obsere ha he arrow for a sysem (he direcion he objec is moing) is in he same direcion as he sm of he forces exered on i. For example, a grocery car moes in he direcion he shopper pshes i and a soccer ball moes in he direcion he player kicks i. We shold es boh ideas. Tesing possible relaionships beween force and moion We hae wo possible ideas ha relae moion and force: 1. An objec s elociy always poins in he direcion of he sm of he forces F ha oher objecs exer on i. 2. An objec s elociy change D always poins in he direcion of he sm of he forces F ha oher objecs exer on i.

9 58 CHAPTER 3 Newonian Mechanics To es hese wo relaionships, we se each o predic he ocome of he experimens in Tesing Experimen Table 3.2. Then we perform he experimens and compare he ocomes wih he predicions. From his comparison, we deermine wheher we can rejec one or boh of he relaionships. TETING EXPERIMENT TABLE 3.2 Tesing elociy and he sm of he forces F Tesing experimen Predicion Ocome Experimen 1. Tanya, wearing a blinking LED on her bel, coass o he righ on Rollerblades. Her friend plls her back lighly on a rope. If yo ook a long-exposre phoo of Tanya moing, predic wha he LED races will look like afer her friend sars plling he rope. Predicion based on idea 1: The sm of he forces exered on Tanya poins o he lef. Ths Tanya s elociy shold immediaely change from righ o lef. The LED races shold reerse direcion he momen her friend sars plling back. F R on T F on T Tanya slows down and eenally sops. The races are shown below. R T Predicion based on idea 2: Becase he F E on T sm of he forces poins oward he lef, he D arrow shold poin lef. Tanya shold conine moing o he righ, slowing down nil she sops. The races shold conine in he same direcion as before, only hey shold ge shorer and shorer. Experimen 2. Yo hrow a ball (wih an aached LED) pward. If yo ook a long-exposre phoo of he moing ball, predic wha he LED races will look like. B Predicion based on idea 1: The only force exered on he ball in fligh poins down. Ths he ball shold immediaely begin moing downward afer yo release i. The LED races shold no appear aboe he heigh a which he ball was released. F E on B Predicion based on idea 2: Becase he only force exered on he ball in fligh poins down, he D arrow shold poin down, oo. The ball shold slow down nil i sops, and hen i will sar speeding p moing down. The races conine pward b will become shorer nil he ball sops. Then hey increase in lengh in he opposie direcion. Conclsion The ball moes p a decreasing speed and hen reerses direcion and sars moing downward. The LED races are shown a righ. All ocomes conradic he predicions based on idea 1 we can rejec i. All ocomes are consisen wih he predicions based on idea 2. This does no necessarily mean i is re, b i does mean or confidence in he idea increases. Recall ha he D arrow in a moion diagram is in he same direcion as he objec s acceleraion a. Ths, based on his idea and hese esing experimens, we can now accep idea 2 wih greaer confidence.

10 3.3 Concepal relaionship beween force and moion 59 Relaing forces and moion The elociy change (D ) arrow in an objec s moion diagram (and is acceleraion a) poin in he same direcion as he sm of he forces ha oher objecs exer on i. If he sm of he forces poins in he same direcion as he objec s elociy, he objec speeds p; if he sm poins in he opposie direcion, i slows down. If he sm of he forces is zero, he objec conines wih no change in elociy. FIGURE 3.6 Force diagram for a ball being cagh. Reflec How did we deise a relaionship ha allows s o explain why objecs slow down, speed p, or conine a consan elociy? We firs obsered simple experimens and analyzed hem wih moion diagrams and force diagrams. We hen esed wo possible relaionships beween he objecs moion and he sm of all forces ha oher objecs exered on i. The aboe relaionship emerged from his analysis and esing. The relaionship beween forces and change in moion also applies o he siaion of caching a dropped ball. Figre 3.6 shows a ball wih an aached blinking LED being dropped and cagh and he corresponding force diagram for one insan dring he cach. F H on B F E on B CONCEPTUAL EXERCIE 3.2 Diagram Jeopardy The force diagram shown here describes he forces ha exernal objecs (he srface and Earh) exer on a woman (in his scenario, he force diagram does no change wih ime). Describe hree differen ypes of moion of he woman ha are consisen wih he force diagram. F on W F E on W kech and ranslae Two eqal-magnide, opposiely direced forces are being exered on he woman 1 F = 02. Ths, a moion diagram for he woman ms hae a zero elociy change 1D = 02. implify and diagram Three possible moions consisen wih his idea are shown below. 1. he sands a res on a horizonal srface. 2. he glides a consan elociy on Rollerblades on a smooh horizonal srface. 3. he sands on he floor of an eleaor ha moes p or down a consan elociy. Noe ha in all hree of he aboe, he elociy change arrow is zero. This is consisen wih he sm of he forces being zero. Try i yorself ppose ha he eleaor described aboe was moing p a decreasing speed insead of a consan speed. How hen wold he force diagram be differen? Answer A elociy change (D) arrow for he woman s moion wold now poin down, opposie he direcion of her elociy. Ths, he sm of he forces F ha oher objecs exer on her ms also poin down. This means ha he magnide of he pward force F on W ha he eleaor floor (srface) exers on her ms now be less han he magnide of he downward force FE on W ha Earh exers on her 1F on W 6 FE on W2. REVIEW QUETION 3.3 An eleaor in a all office bilding moes downward a consan speed. How does he magnide of he pward force exered by he cable on he eleaor F C on El compare o he magnide of he downward force exered by Earh on he eleaor F E on El? Explain yor reasoning.

11 60 CHAPTER 3 Newonian Mechanics 3.4 Inerial reference frames and Newon s firs law Or descripion of he moion of an objec depends on he obserer s reference frame. Howeer, in his chaper we hae acily assmed ha all obserers were sanding on Earh s srface. Are here any obserers who will see a chosen objec moing wih changing elociy een hogh he sm of he forces exered on he objec appears o be zero? Inerial reference frames In Table 3.3, we consider wo differen obserers analyzing he same siaion. OBERVATIONAL EXPERIMENT TABLE 3.3 Two obserers wach he same coffee mg VIDEO OET 3.3 Obseraional experimen Analysis done by each obserer Experimen 1. Obserer 1 is sloched down in he passenger sea of a car and canno see oside he car. ddenly, he obseres a coffee mg (M) sliding oward him from he dashboard (D). Obserer 1 creaes a moion diagram and a force diagram for he mg as he obseres i. On he moion diagram, increasingly longer arrows indicae ha he mg s speed changes from zero o nonzero as seen by obserer 1 een hogh no exernal objec is exering a force on i in ha direcion. D F D on M F E on M Experimen 2. Obserer 2 sands on he grond beside he car. he obseres ha he car sars moing forward a increasing speed and ha he mg remains saionary wih respec o her. Obserer 2 creaes a moion diagram and force diagram for he mg as she obseres i. There are no or D arrows on he diagram, and he mg is a res relaie o her. D F D on M F E on M Paern Obserer 1: The forces exered on he mg by Earh and by he dashboard srface add o zero. B he elociy of he mg increases as i slides off he dashboard. This is inconsisen wih he rle relaing he sm of he forces and he change in elociy. Obserer 2: The forces exered on he mg by Earh and by he dashboard srface add o zero. Ths he elociy of he mg shold no change, and i does no. This is consisen wih he rle relaing he sm of he forces and he change in elociy. VIDEO 3.1 Obserer 2 in Table 3.3 can accon for wha is happening sing he rle relaing he sm of he forces and changing elociy, b obserer 1 canno. For obserer 1, he mg s elociy changes for no apparen reason. imilarly, in he ideo in he margin, yo see he balls fly inside he box for no reason. For he obserer inside he box, Newon s laws canno explain heir behaior. Can yo hink of some oher obserers who wold be able o explain he balls moion? I appears ha he applicabiliy of he relaionship beween he force and moion diagram depends on he reference frame of he obserer. Obserers who can explain he behaior of he mg (obserer 2) and he balls by sing he relaionship beween he sm of he forces and changing elociy are said o be obserers in inerial reference frames. Those who canno explain he behaior of he mg (obserer 1) and he balls sing his relaionship are said o be obserers in noninerial reference frames. Any obserer who acceleraes wih respec o Earh is a noninerial reference frame obserer. Obserers in inerial reference frames can explain he changes in elociy of objecs by considering he forces exered on hem by oher objecs. Obserers in noninerial reference frames canno. From now on, we will always analyze phenomena from he poin of iew of obserers in inerial reference frames. This idea is smmarized by Isaac Newon s firs law.

12 3.5 Newon s second law 61 Newon s firs law of moion For an obserer in an inerial reference frame, when no oher objecs exer forces on a sysem or when he forces exered on he sysem add o zero, he sysem conines moing a consan elociy (inclding remaining a res). Isaac Newon. Isaac Newon ( ) inened differenial and inegral calcls, formlaed he law of niersal graiaion, deeloped a new heory of ligh, and p ogeher he ideas for his hree laws of moion. I is imporan o noe ha in physics some mahemaical erms and symbols TIP hae seeral differen meanings. Zero cold mean a balance or an absence. For example, when we say ha wo forces add o zero, we mean ha hey balance he effecs of each oher; when we say an objec moes wih zero acceleraion, we mean ha he acceleraion is absen. A negaie sign in fron of a qaniy cold mean direcion or sbracion. Eery ime yo mee a zero or a negaie sign, sop and deermine how i is being sed in ha eqaion. Physiciss hae analyzed he moion of hosands of objecs from he poin of iew of obserers in inerial reference frames and fond no conradicions o he rle. Newon s firs law of moion limis he reference frames wih respec o which he oher laws ha yo will learn in his chaper are alid hese oher laws work only for he obserers in inerial reference frames. In his and following chapers we will assme ha obserers of eens are no acceleraing. REVIEW QUETION 3.4 Wha is he main difference beween inerial and noninerial reference frames? Gie an example. 3.5 Newon s second law Or concepal analyses in ecion 3.3 allowed s o dedce a qaliaie relaionship beween forces and changes in an objec s moion. In his secion we will learn how o predic he magnide of an objec s acceleraion if we know he forces exered on i. The experimens in Obseraional Experimen Table 3.4 will help s consrc his qaniaie relaionship. OBERVATIONAL EXPERIMENT TABLE 3.4 Forces and resling acceleraion Obseraional experimen Analysis VIDEO OET 3.4 Experimen 1. A car sars a res on a smooh horizonal rack. A spring scale coninosly exers one ni of force in he posiie direcion. The experimen is repeaed for more imes. Each ime, he force probe exers one addiional ni of force on he car (p o hree nis). We record he ale of he force, and se a moion deecor on he rack o record he car s speed and acceleraion. Using his informaion, we creae elociy-erss-ime and acceleraion-erss-ime graphs for wo of he fie differen magnides of force. Noe ha he greaer he force, he greaer he acceleraion. x F 5 1 ni a x D 1 0 D x x F 5 3 nis a x 3 (conined)

13 62 CHAPTER 3 Newonian Mechanics Obseraional experimen Experimen 2. We repea he same fie experimens, only his ime he car is moing in he posiie direcion, and he probe plls back on he car in he negaie direcion so ha he car slows down. Analysis We creae elociy-erss-ime and acceleraion-erss-ime graphs for he car when forces of wo differen magnides oppose he car s moion. D x F 5 1 ni a x 1 0 D x x F 5 3 nis a x 3 Paern When he sm of he forces exered on he car is consan, is acceleraion is consan he car s speed increases a a consan rae. When we plo acceleraion erss force sing he fie posiie and fie negaie ales of he force, we obain he graph a he righ. The eleenh poin is (0,0), which we know from preios experimens. The acceleraion is direcly proporional o he force exered by he spring scale (in his case, i is he sm of all forces) and poins in he direcion of he force. a x F x The ocome of hese experimens expressed mahemaically is as follows: a ~ F (3.2) where F is he sm of all he forces ha oher objecs exer on he sysem (no an addiional force), and a is he sysem s acceleraion. The symbol ~ means is proporional o. In oher words, if he sm of he forces dobles, hen he acceleraion dobles. When he sm of he forces is zero, he acceleraion is zero. When he sm of he forces exered on an objec is consan, he objec s resling acceleraion (no elociy) is consan. Mass, anoher physical qaniy Do oher physical qaniies affec acceleraion? Yo know from experience ha i is easy o pll an empy cardboard box across he floor, b i is mch harder when i is fll of books. The amon of maer being plled ms affec he acceleraion. Le s perform anoher experimen o find he qaniaie effec of he amon of maer being plled. We se a spring scale o pll one car, hen wo cars sacked on op of each oher, and hen hree and for cars on op of each oher. In each case, he spring scale exers he same force on he cars, regardless of how many cars are being plled. The experimen is smmarized in Obseraional Experimen Table 3.5.

14 3.5 Newon s second law 63 OBERVATIONAL EXPERIMENT TABLE 3.5 Amon of maer and acceleraion Obseraional experimen Analysis We pll he indicaed nmber of sacked cars sing an idenical plling force and measre he acceleraion wih a moion deecor. Nmber n of cars Acceleraion 1m,s Moion deecor Cars pring scale Paern We graph he acceleraion erss nmber of cars for consan plling force. From he graph, we see ha increasing he nmber of cars decreases he acceleraion. To check wheher his relaionship is inersely proporional, we plo a erss 1 n. a (m/s 2 ) Nmber n of cars a (m/s 2 ) /nmber n of cars n 1 n ince he graph a erss 1 n is a sraigh line, we conclde ha a is inersely proporional o n, which we wrie as a ~ 1 n. From he paern obsered in Table 3.5, we conclde ha he greaer he amon of maer being plled, he smaller he objec s acceleraion when he same force is exered on i. This propery of an objec, which affecs is acceleraion, is called mass. To measre he mass of an objec qaniaiely, we firs define a sandard ni of mass. The choice for he ni of mass is arbirary, b afer he ni has been chosen, he masses of all oher objecs can be deermined from his ni. The I sandard of mass is he kilogram (kg). A qar of milk has a mass of abo 1 kg. ppose, for example, ha yo exer a consan plling force on a 1.0-kg objec (and ha all oher forces exered on his objec add o zero), and yo measre is acceleraion. Yo hen exer he same plling force on anoher objec of nknown mass. Yor measremen indicaes ha i has half he acceleraion of he sandard 1.0-kg objec. Ths, is mass is wice he sandard mass (2.0 kg). This mehod is no pracical for eeryday se. Laer we will learn anoher mehod of measring he mass of an objec, a mehod ha is simple enogh o se in eeryday life. Or experimens indicae ha when he same force is exered on wo objecs, he one wih he greaer mass will hae a smaller acceleraion. Mahemaically: a ~ 1 m (3.3) Mass Mass m characerizes he amon of maer in an objec. When he same nbalanced force is exered on wo objecs, he objec wih greaer mass has a smaller acceleraion. The I ni of mass is he kilogram (kg). Mass is a scalar qaniy, and masses add as scalars. m of he forces, mass and acceleraion We hae fond ha he acceleraion a of a sysem is proporional o he ecor sm of he forces F exered on i by oher objecs [Eq. (3.2)] and inersely proporional o he mass m of he sysem [Eq. (3.3)]. We can combine hese wo proporionaliies ino a single eqaion on he nex page.

15 64 CHAPTER 3 Newonian Mechanics a ~ F on (3.4) m Rearrange he aboe o ge m a ~ F on. We can rn his ino an eqaion if we choose he ni of force o be kg # m>s 2. Becase force is sch a biqios qaniy, physiciss hae gien he force ni a special name called a newon (N). A force of 1 newon (1 N) cases an objec wih a mass of 1 kg o accelerae a 1 m>s 2. 1 N = 1 kg # m>s 2 (3.5) A force of one pond can also be defined (1 lb eqals 4.45 N). When he TIP sm of he forces exered on an objec of a ni of mass (called a slg in he Imperial sysem of nis) is eqal o 1 lb, he acceleraion of he objec is 1 foo >s 2. A slg is a relaiely massie ni: 1 slg = kg. Eqaion (3.4), rewrien wih an eqaliy sign insead of a proporional sign, is called Newon s second law. Noice ha he ecor sm of TIP he forces menioned in he definiion a righ does no mean he sm of heir magnides. Vecors are no added as nmbers; heir direcions affec he magnide of he ecor sm. Newon s second law The acceleraion a of a sysem is proporional o he ecor sm of all forces being exered on he sysem and inersely proporional o he mass m of he sysem: a = F on = m F 1 on + F 2 on + g m (3.6) Here he sbscrips 1 and 2 sand for he objecs exering forces on he sysem. The acceleraion of he sysem poins in he same direcion as he ecor sm of he forces. Does his new eqaion make sense? For example, does i work in exreme cases? Firs, imagine an objec wih an infiniely large mass. According o he law, i will hae zero acceleraion for any process in which he sm of he forces exered on i is finie: a = F on ` This seems reasonable, as an infiniely massie objec wold no change moion de o finie forces exered on i. On he oher hand, an objec wih a zero mass will hae an infiniely large acceleraion when a finie magnide force is exered on i: = 0 In he case-effec relaionship, he TIP qaniies on he righ side of he eqaion can be aried independenly. In or case, hese are he sm of he forces and he mass. Each can be changed independenly of he oher o affec acceleraion. In he operaional definiion, he qaniies on he righ side of he eqaion canno be aried independenly. The elociy change depends on he ime ineral dring which i occrs. a = F on 0 = ` Boh exreme cases make sense. Newon s second law is a so-called case-effec relaionship. The righ side of he eqaion (he sm of he forces being exered diided by he mass of he sysem) is he case of he effec (he acceleraion) on he lef side. Effec a = F on m Case On he oher hand, a = D > D is called an operaional definiion of acceleraion. I ells s how o deermine he qaniy acceleraion b does no ell s why i has a pariclar ale. For example, sppose ha an eleaor s speed changes from 2 m>s o 5 m>s in 3 s as i moes erically along a sraigh line in he posiie y-direcion. The eleaor s acceleraion (sing he definiion of acceleraion) is 5 m>s - 2 m>s a y = = +1 m>s 2 3 s This operaional definiion does no ell yo he reason for he acceleraion. If yo know ha he mass of he eleaor is 500 kg and ha Earh exers a 5000-N downward

16 3.5 Newon s second law 65 force on he acceleraing eleaor and he cable exers a 5500-N pward force on i, hen sing he case-effec relaionship of Newon s second law: 5500 N N2 = +1 m>s kg Ths, yo obain he same nmber sing wo differen mehods one from kinemaics (he par of physics ha describes moion) and he oher from dynamics (he par of physics ha explains moion). Force componens sed for forces along one axis Yo can se he componen form of Newon s second law for he x- and y-direcions insead of he ecor eqaion [Eq. (3.6)]: and a x = F on x m (3.7x) a y = F on y (3.7y) m The nex example shows yo how o apply Newon s second law in componen form o sole problems. EXAMPLE 3.3 Lifing a sicase Earh exers an approximaely 100-N force on a 10-kg sicase. ppose yo exer an pward 120-N force on he sicase. If he sicase sars a res, how fas is i raeling afer lifing for 0.50 s? kech and ranslae Firs, we skech he iniial and final saes of he process, choosing he sicase as he sysem. The skech helps s isalize he process and also brings ogeher all he known informaion, leing or brains focs on oher aspecs of soling he problem. One common aspec of problems like his is he se of a wo-sep sraegy. Here, we se Newon s second law o deermine he acceleraion of he sicase and hen se kinemaics o deermine he sicase s speed afer lifing for 0.50 s. he sicase s acceleraion (noice how he sbscrips in he eqaion below change from sep o sep): a y = F on y m = F Y on y + F E on y m = 1+F Y on F E on 2 = F Y on - F E on m m Afer sing Newon s second law o deermine he acceleraion of he sicase, we hen se kinemaics o deermine he sicase s speed afer raeling pward for 0.50 s: y = 0y + a y The iniial elociy is 0y = 0. ole and ealae Now sbsie he known informaion in he Newon s second law y-componen eqaion aboe o find he acceleraion of he sicase: implify and diagram Nex, we consrc a force diagram for he sicase while being lifed. The y-componens of he forces exered on he sicase are yor pward pll on he sicase F Y on y = +F Y on = +120 N and Earh s downward pll on he sicase F E on y = -F E on = -100 N. Becase he pward force is larger, he sicase will hae an pward acceleraion a. Represen mahemaically ince all he forces are along he y-axis, we apply he y-componen form of Newon s second law o deermine a y = F Y on - F E on m = 120 N N 10 kg = +2.0 m>s 2 Inser his and oher known informaion ino he kinemaics eqaion o find he erical elociy of he sicase afer lifing for 0.50 s: y = 0y + a y = m>s s2 = +1.0 m>s The ni for ime is correc and he magnide is reasonable. Try i yorself How far p did yo pll he sicase dring his 0.50 s? Answer The aerage speed while lifing i was m>s2>2 = 0.50 m>s. Ths yo lifed he sicase y - y0 = m>s s2 = 0.25 m.

17 66 CHAPTER 3 Newonian Mechanics REVIEW QUETION 3.5 Yor friend says ha m a is a force exered on an objec and i shold be represened on he force diagram. Do yo agree or disagree wih him? Explain yor answer. 3.6 Graiaional force law In he las example, we were gien he mass of a sicase (10 kg) and he approximae magnide of he graiaional force ha Earh exers on i (100 N). Is i possible o deermine he magnide of his force by js knowing he mass of he sicase? Imagine ha we eacae all he air from a 3.0-m-long Plexiglas be, place a moion sensor a he op, and drop objecs of arios sizes, shapes, and composiions hrogh he be (as was done wih a feaher and an apple in Figre 2.26). The measremens aken by he moion sensor reeal ha all objecs fall sraigh down wih he same acceleraion, approximaely 9.8 m>s 2. Earh is he only objec ha exers he force on he falling objec F E on O dring he enire fligh. If we choose he posiie y-axis poining down and apply he y-componen form of Newon s second law, we ge a Oy = 1 F E on O y = 1 1+F E on m O m O2 = + F E on O O m O Eery objec dropped in or experimen had he same free-fall acceleraion, g = 9.8 m>s 2, een hose wih ery differen masses (sch as a ping-pong ball and a lead ball). Ths, he graiaional force ha Earh exers on each objec ms be proporional o is mass so ha he mass cancels when we calclae he acceleraion. Earh ms exer a force on a 10-kg objec ha is 10 imes greaer han ha on a 1-kg objec: a Oy = F E on O = g m O This reasoning leaes js one possibiliy for he magnide of he force ha Earh exers on an objec: F E on O = m Og = m O19.8 m>s 2 2 The raio of he force and he mass is a consan for all objecs he so-called graiaional coefficien g, already familiar o s as free-fall acceleraion. Graiaional force The magnide of he graiaional force ha Earh exers on any objec F E on O when on or near is srface eqals he prodc of he objec s mass m and he coefficien g: TIP Eqaion (3.8) is a case-effec relaion becase m O and g can be aried independenly. F E on O = m Og (3.8) where g = 9.8 m>s 2 = 9.8 N>kg on or near Earh s srface. This force poins oward he cener of Earh. The ale of he free-fall acceleraion g in he aboe graiaional force relaion [Eq. (3.8)] does no mean ha he objec is acally falling. The g is js sed o deermine he magnide of he graiaional force exered on he objec by Earh wheher he objec is falling, siing a res on a able, or moing down a waerslide. To aoid confsion, we will se g = 9.8 N>kg raher han 9.8 m>s 2 when calclaing he graiaional force. omeimes, when we do no need high precision in he calclaion, we will een se 10 N>kg. We will learn in he chaper on circlar moion (Chaper 5) ha he graiaional coefficien g a a pariclar poin depends on he mass of Earh and on how far his

18 3.7 kills for applying Newon s second law for one-dimensional processes 67 poin is from he cener of Earh. On Mars or he Moon, he graiaional coefficien depends on he mass of Mars or he Moon, respeciely. The graiaional coefficien is 1.6 N>kg on he Moon and 3.7 N>kg on Mars. Yo cold hrow a ball pward higher on he Moon since g is smaller here, resling in a smaller force exered downward on he ball. The weigh of an objec on a plane TIP is he force ha he plane exers on he objec. We will no se he erm weigh of an objec becase i implies ha weigh is a propery of he objec raher han an ineracion beween wo objecs. REVIEW QUETION 3.6 Newon s second law says ha he acceleraion of an objec is inersely proporional o is mass. Howeer, he acceleraion wih which all objecs fall in he absence of air is he same. How can his be? 3.7 kills for applying Newon s second law for one-dimensional processes In his secion we will deelop a sraegy ha can be sed wheneer a process inoles force and moion. We will inrodce he sraegy by applying i o he 2006 skydie of diing champion Michael Holmes. Afer more han 7000 sccessfl jmps, Holmes jmped from an airplane 3700 m aboe Lake Tapo in New Zealand. His main parache failed o open, and his backp che became angled in is cords. The parially opened backp parache slowed his descen o abo 36 m>s 180 mi>h2 as he reached a 2-m-high hicke of wild shrbbery. Holmes sried. In all problems, nless specifically TIP noed, we will assme ha he obserer is on he grond and is no acceleraing. PROBLEM-OLVING TRATEGY 3.1 Applying Newon s laws for one-dimensional processes EXAMPLE 3.4 Holmes s skydie Michael Holmes (70 kg) was moing downward a 36 m>s 180 mi>h2 and was sopped by 2.0-m-high shrbbery and he grond. Esimae he aerage force exered by he shrbbery and grond on his body while sopping his fall. kech and ranslae kech he process. Choose he sysem. Choose a coordinae sysem. Label he skech wih eeryhing yo know abo he siaion. Idenify he nknown ha yo need o find. Label i wih a qesion mark on he skech. We skech he process, choosing Holmes as he sysem (H). We wan o know he aerage force ha he shrbbery and grond (-G) exer on him from when he firs oches he shrbbery o he insan when he sops. We choose he y-axis poining p and he origin a he grond where Holmes comes o res. We se kinemaics o find his acceleraion while sopping and Newon s second law o find he aerage force ha he shrbbery and grond exered on him while sopping him. (conined)

19 68 CHAPTER 3 Newonian Mechanics implify and diagram Make appropriae simplifying assmpions abo he process. For example, can yo neglec he size of he sysem? Can yo assme ha forces or acceleraion is consan? Then represen he process wih a moion diagram and/or force diagram(s). Make sre he diagrams are consisen wih each oher. We model Holmes as a poin-like objec and assme ha he forces being exered on him are consan so ha hey lead o a consan acceleraion. A moion diagram for his moion while sopping is shown along wih he corresponding force diagram. To draw he force diagram we firs idenify he objecs ineracing wih Holmes as he slows down: he shrbbery and grond (combined as one ineracion) and Earh. The shrbbery and grond exer an pward force on H on Holmes. Earh exers a downward graiaional force F E on H. The force diagram is he same for all poins of he moion diagram becase he acceleraion is consan. On he force diagram he arrow for on H ms be longer o mach he moion diagram, which shows he elociy change arrow poining p. Represen mahemaically Coner hese qaliaie represenaions ino qaniaie mahemaical descripions of he siaion sing kinemaics eqaions and Newon s second law for moion along he axis. Deermine he signs for he force componens in he eqaions. Add he force componens (wih eiher posiie or negaie signs) o find he sm of he forces. The y-componen of Holmes s aerage acceleraion is a y = y 2 2-0y 21y - y 0 2 The y-componen of Newon s second law wih he posiie y-direcion p is a y = F on H y m H The y-componen of he force exered by he shrbbery-grond on Holmes is on H y = on H, and he y-componen of he force exered by Earh is F E on H y = -F E on H = -m Hg. Therefore, a y = on H y + F E on H y m H = on H2 + 1-F E on H2 m H = on H - m Hg m H 1 on H = m H a y + m H g ole and ealae bsie he known ales ino he mahemaical expressions and sole for he nknowns. Finally, ealae yor work o see if i is reasonable (check nis, limiing cases, and wheher he answer has a reasonable magnide). Check wheher all represenaions mahemaical, picorial, and graphical are consisen wih each oher. Holmes s aerage acceleraion was a y = m>s m2 = +324 m>s 2 Holmes s iniial elociy is negaie, since he is moing in he negaie direcion. His iniial posiion is +2.0 m a he op of he shrbbery, and his final posiion is zero a he grond. His elociy in he negaie direcion is decreasing, which means he elociy change and he acceleraion boh poin in he opposie direcion (posiie). The aerage magnide of he force exered by he shrbbery and grond on Holmes is on H = m H a y + m H g = 170 kg21324 m>s kg219.8 N>kg2 = 22,680 kg # m>s N = 23,366 N = 23,000 N The force has a magnide greaer han he force exered by Earh hs he resls are consisen wih he force diagram and moion diagram. The magnide is hge and he nis are correc. A limiing case for zero acceleraion gies s a correc predicion he force exered on Holmes by he shrbbery and grond eqals he force exered by Earh. Try i yorself Wha process inoling forces can be described by he eqaion 50 kg * 2 m>s 2 = 50 kg * 9.8 N>kg N2? Answer A 50-kg person is landing on a hick cshion ha exers a 390-N pward force on her b canno slow her down. he conines o accelerae down, b her acceleraion is less han g (only 2 m>s 2 ). The erical axis poins down.

20 An eleaor ride sanding on a bahroom scale In Example 3.5, we consider a mch less dangeros process, one yo cold ry he nex ime yo ride an eleaor. When yo sand on a bahroom scale, he scale reading indicaes how hard yo are pshing on he scale. The force ha i exers on yo balances he downward force ha Earh exers on yo, resling in yor zero acceleraion. Wha will he scale read if yo sand on i in a moing eleaor? 3.7 kills for applying Newon s second law for one-dimensional processes 69 EXAMPLE 3.5 Eleaor ride Yo sand on a bahroom scale in an eleaor as i makes a rip from he firs floor o he enh floor of a hoel. Yor mass is 50 kg. When yo sand on he scale in he saionary eleaor, i reads 490 N (110 lb). Wha will he scale read (a) early in he rip while he eleaor s pward acceleraion is 1.0 m>s 2, (b) while he eleaor moes p a a consan speed of 4.0 m>s, and (c) when he eleaor slows o a sop wih a downward acceleraion of 1.0 m>s 2 magnide? kech and ranslae We skech he siaion as shown a righ, choosing yo as he sysem. The coordinae axis poins pward wih is origin a he firs floor of he eleaor shaf. Yor mass is m Y = 50 kg, he magnide of he force ha Earh exers on yo is F E on Y = m Y g = 490 N, and yor acceleraion is (a) a y = +1.0 m>s 2 (he pward elociy is increasing); (b) a y = 0 ( is a consan 4.0 m>s pward); and (c) a y = -1.0 m>s 2 (he pward elociy is decreasing, so he acceleraion poins in he opposie, negaie direcion). (a) (b) (c) D and ne force poin p. The pward elociy is increasing. D and ne force are zero. The elociy is consan. D and ne force poin down. The pward elociy is decreasing. implify and diagram We model yo as a poin-like objec and represen yo as a do in boh he moion and force diagrams, shown for each par of he rip in Figres a, b, and c. On he diagrams, E represens Earh, Y is yo, and is he scale. The magnide of he downward force ha Earh exers does no change (i eqals m Y g, and neiher m Y nor g changes). Noice ha he force diagrams and moion diagrams are consisen wih each oher for each par of he rip. The lengh of he arrows represening he force ha he scale exers on yo changes from one case o he nex so ha he sm of he forces poins in he same direcion as yor elociy change arrow. Represen mahemaically The moion and he forces are enirely along he erical y-axis. Ths, we se he erical y-componen form of Newon s second law [Eq. (3.7y)] o analyze he process. There are wo forces exered on yo (he sysem) so here will be wo erical y-componen forces on he righ side of he eqaion: he y-componen of he force ha Earh exers on yo, F E on Y y = -m Yg, and he y-componen of he force ha he scale exers on yo, F on Y y = +F on Y: a Yy = F y m Y = F E on Y y + F on Y y m Y = -m Yg + F on Y m Y Mliplying boh sides by m Y, we ge a Yym Y = -m Yg + F on Y. We can now moe -m Yg o he lef side: m Ya Yy + m Yg = F on Y, or F on Y = m Ya Yy + m Yg = m Ya Yy N Remember ha m Yg = 490 N is he magnide of he force ha Earh exers on yo. The expression for F on Y gies he magnide of he force ha he scale exers on yo. ole and ealae We can now se he las eqaion o predic he scale reading for he hree pars of he rip. (a) Early in he rip, he eleaor is speeding p, and is acceleraion is a Yy = +1.0 m>s 2. Dring ha ime ineral, he force exered by he scale on yo shold be F on Y = m Y a Yy N = 150 kg m>s N = 540 N (b) In he middle of he rip, when he eleaor moes a consan elociy, yor acceleraion is zero and he scale shold read F on Y = m Y a Yy N = 150 kg210 m>s N = 490 N (conined)

21 70 CHAPTER 3 Newonian Mechanics (c) When he eleaor is slowing down near he end of he rip, is acceleraion poins downward and is a y = -1.0 m>s 2. Then he force exered by he scale on yo shold be F on Y = m Y a Yy N = 150 kg m>s N = 440 N When he eleaor is a res or moing a consan speed, he scale reading eqals he magnide of he force ha Earh exers on yo. When he eleaor acceleraes pward, he scale reads more. When i acceleraes downward, een if yo are moing pward, he scale reads less. Wha is also imporan is ha he moion and force diagrams in Figres a, b, and c are consisen wih each oher and he force diagrams are consisen wih he prediced scale readings an imporan consisency check of he moion diagrams, force diagrams, and mah. Try i yorself Yo are sanding on he scale in he eleaor. The scale firs reads 490 N, hen 440 N, hen 490 N again, and finally 540 N. Wha cold possibly be happening o he eleaor? Answer The eleaor is a res, hen moes down wih downward acceleraion of 1 m>s 2, hen moes a consan elociy, and finally sars o slow down wih acceleraion of 1 m>s 2 poining pward. I migh no seem ery imporan o know wha a scale reads in an eleaor as i moes, b if we consider he cable spporing he eleaor, he ale of sch calclaions becomes apparen. We dedce ha he force ha he cable exers on he eleaor when he eleaor is acceleraing pward is greaer han ha when he eleaor is a res or moing wih consan elociy. This means ha he cable ms be srong enogh o wihsand a magnide of force of a leas mg + ma, where m is he mass of he eleaor and is maximm load, and a is he magnide of he eleaor s maximm erical acceleraion. REVIEW QUETION 3.7 Three friends arge abo he ype of informaion a bahroom scale repors: Egenia says ha i reads he force ha Earh exers on a person, Alan says ha i reads he sm of he forces exered on he person by Earh and he scale, and Mike says ha he scale reads he force ha he person exers on he scale. Who do yo hink is correc? Why? 3.8 Forces come in pairs: Newon s hird law o far, we hae analyzed a sysem s acceleraion de o he forces exered on i by exernal objecs. Wha effec does he sysem hae on hese exernal objecs? To help answer his qesion, we obsere he ineracion of wo objecs and analyze wha happens o each of hem. ppose, while wearing Rollerblades, yo psh abrply on a wheeled car ha is loaded wih a heay box. If yo and he car are on a hard smooh floor, he car sars o moe (i acceleraes), and yo also sar o moe and accelerae in he opposie direcion. Eidenly, yo exered a force on he car and he car exered a force on yo. ince he acceleraions were in opposie direcions, he forces ms poin in opposie direcions. Le s consider more qaniaiely he effec of sch a mal ineracion beween wo objecs. Consider he experimens in Obseraional Experimen Table 3.6. Two dynamics cars roll freely on a smooh rack before colliding. We mon force probes on each car in order o measre he forces ha each car exers on he oher while colliding. A moion sensor on each end of he rack records he iniial elociy of each car before he collision.

22 3.8 Forces come in pairs: Newon s hird law 71 OBERVATIONAL EXPERIMENT TABLE 3.6 Forces ha wo dynamics cars exer on each oher Obseraional experimen Analysis VIDEO OET 3.6 Experimen 1. Two cars of differen masses moe oward each oher on a leel rack. A moion deecor indicaes heir speed before he collision, and force probes record he forces exered by each car on he oher. Before he collision: m 1 = 1.0 kg, 1x = +2 m>s m 2 = 0.5 kg, 2x = -2 m>s 1 2 Becase boh cars changed elociies de o he collision, hey ms hae exered forces on each oher. The comper recordings from he force probes show ha he forces ha he cars exer on each oher ary wih ime and a each ime hae he same magnide and poin in opposie direcions. Car 1 exers a force on car 2 oward he righ, and car 2 exers a force on car 1 oward he lef. F Righ F 1 on 2 x 1 2 Force probes ame magnides for any clock reading Lef F 2 on 1 x Experimen 2. Car masses and elociies before collision: m 1 = 1.0 kg, 1x = 0 m>s 1a res2 m 2 = 0.5 kg, 2x = -1 m>s Alhogh he forces ha he cars exer on each oher are smaller han in he firs experimen, he magnides of he forces a each ime are sill he same. F Righ Lef F 1 on 2 x F 2 on 1 x ame magnides for any clock reading Experimen 3. Car masses and elociies before collision: The same analysis applies. 1 m 1 = 1.0 kg, 1x = +2 m>s m 2 = 0.5 kg, 2x = -1 m>s 2 F Righ F 1 on 2 x ame magnides for any clock reading 1 2 Lef F 2 on 1 x Paern In each experimen, independen of he masses and elociies of he cars before he collisions, a eery insan dring he collision he force ha car 1 exered on car 2 F 1 on 2 had he same magnide as b poined in he opposie direcion from he force ha car 2 exered on car 1 F 2 on 1. The car collisions in Table 3.6 indicae ha he force ha one car exers on anoher is eqal in magnide and opposie in direcion o he force ha he second car exers on he firs. F 1 on 2 = -F 2 on 1 Will he paern ha we fond allow s o correcly predic he resls of a new experimen?

23 72 CHAPTER 3 Newonian Mechanics TETING EXPERIMENT TABLE 3.7 Tesing he relaionship beween he forces ha ineracing objecs exer on each oher Tesing experimen Predicion Ocome Two people are holding spring scales ha are hooked ogeher. The scales remain horizonal dring he experimen. Person 1 plls her scale so ha scale 1 reads 10 N, while person 2 js holds scale 2. Predic he reading of scale 2. cale 1 cale 2 Person 1 Person N F 1 on N N F 2 on 1 5? Predic he reading of scale 1 when person 2 plls scale 2 exering an arbirary force. 0 Conclsion If he paern relaing he wo forces ha ineracing objecs exer on each oher (hey hae he same magnides and opposie direcions) is correc, and scale 1 plls on scale 2 exering a force of 10 N, hen scale 2 shold pll on scale 1 in he opposie direcion exering a force of 10 N. Boh scales will hae he same reading. The same is re for he readings of he scales when scale 2 plls on scale 1. The experimens show ha no maer who plls on a scale, he scales hae he same reading. The ocome sppors he paern in he forces ha wo objecs exer on each oher dring he ineracion. These forces are of he same magnide and opposie in direcion. VIDEO TET 3.7 To be coninced of he alidiy of his conclsion, we need many more esing experimens. o far, physiciss hae fond no experimens inoling he dynamics of eeryday processes in which ineracing objecs exer forces on each oher ha are no of eqal magnide and opposiely direced. This relaionship beween he forces is called Newon s hird law. Newon s hird law When wo objecs inerac, objec 1 exers a force on objec 2. Objec 2 in rn exers an eqal-magnide, opposiely direced force on objec 1: F 1 on 2 = -F 2 on 1 (3.9) Noe ha hese forces are exered on differen objecs and canno be added o find he sm of he forces exered on one objec. Remember ha he forces in TIP Newon s hird law are exered on wo differen objecs. This means ha he wo forces will neer show p on he same force diagram, and hey shold no be added ogeher o find he sm of he forces. Yo hae o choose he sysem and consider only he forces exered on i! I seems coneriniie ha wo ineracing objecs always exer forces of he same magnide on each oher. Imagine a game of ping-pong. A paddle his he ball and he ball flies rapidly oward he oher side of he able. Howeer, he paddle moes forward wih lile change in moion. How is i possible ha he ligh ball exered a force on he paddle of he same magnide as he force he paddle exered on he ball? To resole his apparen conradicion, hink abo he masses of he ineracing objecs and heir corresponding acceleraions. If he forces are he same, he objec wih larger mass has a smaller magnide acceleraion han he objec wih smaller mass: a paddle = F ball on paddle m paddle and a ball = F paddle on ball m ball Becase he mass of he ball is so small, he same force leads o a large change in elociy. The paddle s mass, on he oher hand, is mch larger. Ths, he same magnide force leads o an almos zero elociy change. We obsere he elociy change and incorrecly associae ha alone wih he force exered on he objec.

24 3.8 Forces come in pairs: Newon s hird law 73 CONCEPTUAL EXERCIE 3.6 A book on a able A book sis on a ableop. Idenify he forces exered on he book by oher objecs. Then, for each of hese forces, idenify he force ha he book exers on anoher objec. Explain why he book is no acceleraing. Forces on book kech and ranslae Draw a skech of he siaion and choose he book as he sysem. Forces he book exers on oher objecs implify and diagram Assme ha he ableop is perfecly horizonal and model he book as a poin-like objec. A force diagram for he book is shown a righ. Earh exers a downward graiaional force on he book F E on B, and he able exers an pward force on he book F T on B. Newon s second law explains why he book is no acceleraing: he forces exered on i by oher objecs are balanced and add o zero. The sbscrips on each force idenify he wo objecs inoled in he ineracion. The Newon s hird law pair force will hae is sbscrips reersed. For example, Earh exers a downward graiaional force on he book 1 F E on B2. According o Newon s hird law, he book ms exer an eqal-magnide pward graiaional force on Earh 1 F B on E = - F E on B2, as shown a righ. The able exers an pward conac force on he book 1 F T on B2, so he book ms exer an eqal-magnide downward conac force on he able 1 F B on T = - F T on B2. Try i yorself A horse plls on a sled ha is sck in snow and no moing. Yor friend Chris says his happens becase he horse exers on he sled he same magnide force ha he sled exers on he horse. ince he sm of he forces is zero, here is no acceleraion. Wha is wrong wih Chris s reasoning? Answer Chris added he forces exered on wo differen objecs and did no consider all forces exered on he sled. If yo choose he sled as he sysem, hen he horse plls forward on he sled, and he snow exers a backward, resisie force. If hese wo horizonal forces happen o be of he same magnide, hey add o zero, and he sled does no accelerae horizonally. If, on he oher hand, we choose he horse as he sysem, he grond exers a forward force on he horse s hooes (since he horse is exering a force backward on he grond), and he sled plls back on he horse. If hose forces hae he same magnide, he ne horizonal force is again zero, and he horse does no accelerae. EXAMPLE 3.7 Hairdryer on a scale Hairdryers conain a small propeller ha pshes air away from he dryer hrogh a nozzle. Yo place a hairdryer on a scale wih he nozzle poining p, and i reads 0.99 lb. When yo rn he hairdryer on, so ha he hairdryer is pshing he air pward, he reading of he scale increases o 1.09 lb. Explain he change in he reading qaliaiely and qaniaiely. kech and ranslae We skech he process (a) before he hairdryer is rned on and (b) afer i is rned on. The sysem is he hairdryer (wih he propeller). We poin he posiie y-axis down. We know ha he force ha he scale exers on he hairdryer when i is off is F on HDoff = 0.99 lb = 4.40 N. When he hairdryer is on, he force he scale exers on i is F on HDon = 1.09 lb = 4.85 N. We need o qaliaiely explain he increase of he reading and hen explain he qaniaie increase of 0.45 N. (a) (b) (conined)

25 74 CHAPTER 3 Newonian Mechanics implify and diagram Afer he hairdryer is rned on, he scale moes downward a lile, b ery qickly he siaion sabilizes. Ths we will assme ha he rned-on hairdryer is no moing wih respec o he scale; he scale is saionary afer i reaches he reading of 4.85 N. Therefore, he acceleraion of he sysem is zero. There are wo objecs ha inerac wih he dryer: Earh and he scale. We draw a force diagram for he sysem (a) when he hairdryer is off and (b) when i is on. The force ha Earh exers on he dryer is he same in boh experimens. If diagram (a) is correc, his means ha diagram (b) needs an addiional downward force of 0.45 N o explain he increase in he reading. Wha objec is exering his force? Remember ha when he dryer is on, he propeller inside is roaing. I pshes he air p, exering a force F HDon on A ; herefore, according o Newon s hird law, he air shold psh he propeller and conseqenly he whole hairdryer down. Accordingly, we add anoher force o he diagram in (b), F A on HDon, so ha he sm of he forces is sill zero. We can now deermine he magnide of his force sing he reading of he scale. Represen mahemaically Using he force diagram in (b) we can wrie a y = F y m HD = F E on HDon y + F on HDon y + F A on HDon y m HD = F E on HDon + 1-F on HDon 2 + F A on HDon m HD = 0 1 F A on HDon = F on HDon + 1-F E on HDon 2 ole and ealae Using he las eqaion from he preios sep, we find he force ha he air exers on he hairdryer: F A on HDon = F on HDon + 1-F E on HDon 2 = 4.85 N N = 0.45 N The resl makes sense. The magnide is smaller han he force Earh exers on he hairdryer b no insignifican. ch an increase in spporing force can explain an obseraion yo may hae made while waering plans wih a hose. If he flow of waer is srong, yo can feel he expelled waer pshing back on he hose. The same principle explains he behaior of a roaing sprinkler. (a) (b) Try i yorself An 80-kg baskeball player pshes off a gym floor exering a force ha is 4 imes greaer han he force Earh exers on him and ha he psh lass 0.10 s (nrealisically shor). Esimae how fas he is moing when he leaes he floor? Answer Abo 3 m>s. He wold moe faser if he ook longer o psh off while exering he same force. EXAMPLE 3.8 Learning o linearize daa Alex is inesigaing he moion of a baery-powered fan aached o a low-fricion car (a fan car) ha is moing on a horizonal rack. As he fan blades roae, hey exer a force on he air, and he air exers an eqal and opposie force on he blades, making he car moe (an analogy for he fan car is a hairdryer on wheels). Using a moion deecor, Alex finds ha he car moes wih consan acceleraion. He also measres how he acceleraion of he car a x depends on he mass of he objecs ha he adds o he car (m added ). His measremens are shown in he able below. m added (kg) a x (m,s 2 ) (a) Draw a force diagram for he car and se i o explain why he car moes a consan acceleraion for fixed added mass. (b) Two physical qaniies ha are no lised in he able affec he moion of he car. Deermine hese wo qaniies sing he daa aboe. (Hin: Rearrange he mahemaical expression for he acceleraion of he car o obain linear dependence on added mass and hen plo he graph sing he daa in he able.) kech and ranslae The car is moing o he lef on a horizonal srface. The acceleraion of he car is also o he lef de o he fan pshing air o he righ (he fan works in a similar way o he hairdryer ha we inesigaed in he preios example). We know he masses of he addiional objecs on he car and he respecie acceleraions. We also know ha he acceleraion of any sysem is affeced by he sm of he forces exered on i and he sysem s mass. Becase he mass of he car (ogeher wih he fan) conribes o he sysem s mass, we hypohesize ha he qaniies ha we need o deermine are he sm of he forces and he mass of he car. implify and diagram We assme ha he fan car can be modeled as a poin-like objec and ha he rack is smooh, so we do no need o worry abo fricion. The only objecs ineracing wih he car (C) are Earh (E), he rack (T), and he air (A). The moion diagram and he force diagram for he car are shown in he figres below and a righ. From he force diagram, we see ha he forces exered on he car by Earh and he rack add o zero, and he only force ha is casing he acceleraion of he car o he lef is he force exered by he air.

26 3.9 ea bels and air bags 75 Represen mahemaically We wrie Newon s second law in componen form along he axis of moion: F A on C a x = m added + m C ince m added is changed in each experimen (i s an independen ariable), i is sefl o rearrange he eqaion so ha i is a linear fncion wih linear dependence on m added : and o plo 1>a x agains m added (see graph a righ). The fncion for 1>a x is a linear fncion of he form mx + b; hs m = 1>F A on C is he slope of he graph and he inercep is b = m C >F A on C. (Do no confse m for he slope wih he symbol m for mass.) 1 = m added + m C = m added + a x F A on C F A on C m C F A on C ole and ealae The inercep of he graph wih he erical axis is 1 diided by he acceleraion he car wold hae had if he added mass was zero. Ths m C >F A on C = 3.35 kg>n. We can find he slope of he graph as Dy diided by D x. For example, when Dy = and D x = 0.4-0, his raio is 2.65>0.4 = The slope of he graph is hs 1 = Dy F A on C Dx = N Therefore, F A on C = 0.15 N and m C = 0.51 kg. Try i yorself How wold he graph change (consider inercep and slope) if yo placed a second fan on he same car and repea he experimen? Answer The slope of he graph is inersely proporional o he force exered by he air on he car; herefore he slope will be c in half. The inercep is inersely proporional o he force ha he air exers on he car and direcly proporional o he mass of he car and fans, herefore here is no enogh daa o deermine i. B if we assme ha he mass of he fan is mch smaller han he mass of he car, hen he inercep will be beween he original one and half of is ale. REVIEW QUETION 3.8 Is he following senence re? When yo hold a heay objec in yor hands, yo exer he same magnide force on he objec as he objec exers on yo b in he opposie direcion, and becase hese forces add o zero, he objec says a res. 3.9 ea bels and air bags A he beginning of he chaper we posed a qesion abo air bags. How do hey sae lies? We now hae all he physics needed o inesigae his qesion. Consider Figre 3.7. An air bag is like a balloon ha is packed in a small box in he seering wheel or he passenger side dashboard. Air bags are designed o deploy when a car has a negaie acceleraion of magnide 10g m>s 2 2 = 98 m>s 2 < 100 m>s 2 4 or more. When a car has sch a rapid decrease in speed, he bag inflaes wih nirogen gas in abo 0.04 s and forms a cshion for he occpan s ches and head. The bag has wo imporan effecs: 1. I spreads he force ha sops he person oer a larger area of he body. 2. I increases he sopping disance, and conseqenly he sopping ime ineral, hs redcing he aerage force sopping he occpan. Why is spreading he sopping force oer a larger area of he body an adanage? If a person ses only a sea bel, his head is no beled o he sea and ends o conine moing forward dring a collision, een hogh his ches and wais are resrained. To sop he head wiho an air bag, he neck ms exer considerable force on he head. This can case a dangeros sreching of he spinal cord and mscles of he neck, a phenomenon known as whiplash. The air bag exers a more niform force across he pper body and head and helps all pars o sop ogeher. FIGURE 3.7 An air bag sops a crash es dmmy dring a collision.

27 76 CHAPTER 3 Newonian Mechanics How does he air bag increase he sopping disance? ppose a es car is raeling a a consan speed of 13.4 m>s (30 mi>h2 nil i collides head-on wih a concree wall. The fron of he car crmples abo 0.65 m. A crash es dmmy is rigidly aached o he car s sea and is frher proeced by he rapidly inflaing air bag. The dmmy also raels abo 0.65 m before coming o res. Wiho an air bag or a sea bel, he dmmy wold conine o moe forward a he iniial elociy of he car. I wold hen crash ino he seering wheel or windshield of he sopped car and sop in a disance mch less han 0.65 m like flying ino a rigid wall. The smaller he sopping disance, he greaer he acceleraion, and herefore he greaer he force ha is exered on he dmmy. Le s esimae he aerage force exered by he air bag on he body dring a collision. EXAMPLE 3.9 Force exered by air bag on drier dring collision A 60-kg crash es dmmy moing a 13.4 m>s 130 mi>h2 sops dring a collision in a disance of 0.65 m. Esimae he magnide of he aerage force ha he air bag and sea bel exer on he dmmy. kech and ranslae We skech and label he siaion as shown below, choosing he crash es dmmy as he sysem. The posiie x-direcion is in he direcion of moion, and he origin is a he posiion of he dmmy a he sar of he collision. Once we hae he dmmy s acceleraion, we apply he x-componen form of Newon s second law o find he force exered by he air bag and sea bels on he dmmy: a x = F A on D x m D = -F A on D m D 1 F A on D = -m D a x = - F A on D m D ole and ealae We know ha 0x = m>s and x = 0 (he dmmy has sopped). The iniial posiion of he dmmy is x 0 = 0 and he final posiion is x = 0.65 m. The acceleraion of he dmmy while in conac wih he air bag and sea bel is a x = m>s m - 0 m2 = -138 m>s2 Ths, he magnide of he aerage force exered by he air bag and sea bel on he dmmy is implify and diagram We model he dmmy D as a poin-like objec and assme ha he primary force exered on he dmmy while sopping is de o he air bag and sea bel s F A on D, shown in he force diagram. We can ignore he downward graiaional force ha Earh exers on he dmmy F E on D and he pward force ha he car sea exers on he dmmy F on D since hey add o zero and do no conribe o he acceleraion. Represen mahemaically To deermine he dmmy s acceleraion, we se kinemaics: F A on D = -160 kg m>s 2 2 = 8300 N This force N11 lb>4.45 N2 = 1900 lb4 is almos 1 on. Is his esimae reasonable? The magnide is large, b experimens wih crash es dmmies in he real world are consisen wih a force his large in magnide, a ery sriable collision. Try i yorself Find he acceleraion of he dmmy and he magnide of he aerage force needed o sop he dmmy if i is no beled, has no air bag, and sops in 0.1 m when hiing a hard srface. a x = 2 x - 2 0x 21x - x 0 2 Answer -900 m>s 2 and 54,000 N. REVIEW QUETION 3.9 Explain how an air bag and sea bel redce he force exered on he drier of a car dring a collision.

28 mmary 77 mmary A sysem is circled in a skech of a process. Oher objecs ha inerac wih he sysem are called he enironmen. (ecions 3.1 and 3.5) Cable ysem: eleaor Earh Enironmen: cable and Earh The force ha one objec exers on anoher characerizes an ineracion beween he wo objecs (a pll or a psh). The ni of force is he newon (N); 1 N = 11 kg211 m>s 2 2. (ecions 3.1 and 3.5) A force diagram represens he forces ha exernal objecs exer on he sysem. The arrows in he diagram poin in he direcions of he forces, and heir lenghs indicae he relaie magnides of he forces. (ecions 3.1 and 3.2) Cable y F C on E1 F E on E1 F E on O Ineracing objecs A force is denoed by he symbol F wih wo sbscrips indicaing he objec ha is exering he force and he sysem objec. Earh Newon s firs law of moion If no oher objecs exer forces on a sysem or if he forces exered on he sysem add o zero, hen he sysem conines moing a consan elociy (as seen by obserers in inerial reference frames). (ecion 3.4) Newon s second law The acceleraion a of a sysem is proporional o he sm of he forces ha oher objecs exer on he sysem and inersely proporional o is mass m. (ecion 3.5) m D y F C on E1 a = F on m = F 1 on + F 2 on + g m Eq. (3.6) F E on E1 Newon s hird law Two objecs exer eqal-magnide and opposie direcion forces of he same ype on each oher. (ecion 3.8) F F1 on 2 = -F 2 on 1 Eq. (3.9) C on E1 F E1 on C The graiaional force F E on O ha Earh exers on an objec of mass m when on or near Earh s srface depends on he graiaional coefficien g of Earh. If on or near anoher plane or he Moon, he graiaional coefficien near hose objecs is differen. (ecion 3.6) Magnide F E on O = m O g Eq. (3.8) where g = 9.8 m>s 2 = 9.8 N>kg when he objec is on or near Earh s srface.

29 78 CHAPTER 3 Newonian Mechanics Qesions Mliple Choice Qesions 1. An pward-moing eleaor slows o a sop as i approaches he op floor. Which answer below bes describes he relaie magnides of he pward force ha he cable exers on he eleaor F C on El and he downward graiaional force ha Earh exers on he eleaor F E on El? (a) F C on El 7 F E on El (b) F C on El = F E on El (c) F C on El 6 F E on El (d) No enogh informaion is gien o answer he qesion. 2. Yo apply he brakes of yor car abrply and yor book sars sliding off he fron sea. Three obserers explain his differenly. Obserer A says ha he book conined moing and he car acceleraed from nderneah i. Obserer B says ha he car pshed forward on he book. Obserer C says ha she ms be in a noninerial reference frame becase he book sared moing wiho any exra objecs ineracing wih i. Which of he obserers is correc? (a) A (b) B (c) C (d) A and C (e) All of he obserers 3. Which of he saemens below explains why a child lrches forward in a sroller when yo abrply sop he sroller? (a) The child does no lrch forward b insead conines her moion. (b) Yor pll on he sroller cases he child o moe in he opposie direcion. (c) Newon s hird law 4. Which obserers can explain he phenomenon of whiplash, which occrs when a car sops abrply, sing Newon s laws? (a) The drier of he car (b) A passenger in he car (c) An obserer on he sidewalk beside he car and road 5. Which ecor qaniies describing a moing objec are always in he same direcion? (a) Velociy and acceleraion (b) Velociy and he sm of he forces (c) Acceleraion and he sm of he forces (d) Acceleraion and force (e) Boh b and c are correc. 6. Yo hae probably obsered ha magnes FIGURE Q3.6 arac objecs made of cerain meals, sch as seel. Yo ie a seel paperclip o a ableop wih sring and bring a srong magne aboe i so ha he paperclip is posiioned as shown in Figre Q3.6. Which answer correcly compares he magnide of he force exered by he magne on he paperclip o he magnide of he force exered Magne by he paperclip on he magne? (a) F magne on clip 7 F clip on magne (b) F magne on clip 6 F clip on magne (c) F magne on clip = F clip on magne 7. Which of he following elociy-erss-ime graphs represen he moion of he objec for which F y 7 0? Choose all answers ha are correc. FIGURE Q3.7 (a) y (b) y (c) y (d) y 8. A book sis on a ableop. Wha force is he Newon s hird law pair o he force ha Earh exers on he book? Choose he correc answer wih he bes explanaion. (a) The force ha he able exers on he book becase i is eqal and opposie in direcion o he force ha Earh exers on he book (b) The force ha he able exers on he book becase he able and he book are oching each oher (c) The force ha he able exers on he book becase i describes he same ineracion (d) The force ha he book exers on Earh becase i describes he same ineracion (e) The force ha he book exers on Earh becase i is eqal and opposie in direcion o he force ha Earh exers on he book 9. A spaceship moes in oer space. Wha happens o is moion if here are no exernal forces exered on i? If here is a consan force exered on i in he direcion of is moion? If somehing exers a force opposie is moion? (a) I keeps moing; i speeds p wih consan acceleraion; i slows down wih consan acceleraion. (b) I slows down; i moes wih consan elociy; i slows down. (c) I slows down; i moes wih consan elociy; i sops insanly. 10. A 0.10@kg apple falls on Earh, whose mass is abo 6 * kg. Which is re of he graiaional force ha Earh exers on he apple? (a) I is bigger han he force ha he apple exers on Earh by almos 25 orders of magnide. (b) I is he same magnide. (c) We do no know he magnide of he force he apple exers on Earh. 11. A man sands on a scale and holds a heay objec in his hands. Wha happens o he scale reading if he man qickly lifs he objec pward and hen sops lifing i? (a) The reading increases, rerns briefly o he reading when sanding saionary, hen decreases. (b) The reading decreases, rerns briefly o he reading when sanding saionary, hen increases. (c) Nohing, since he mass of he person wih he objec remains he same. Ths he reading does no change. 12. Yo sand on a bahroom scale in a moing eleaor. Wha happens o he scale reading if he cable holding he eleaor sddenly breaks? (a) The reading will increase. (b) The reading will no change. (c) The reading will decrease a lile. (d) The reading will drop o 0 insanly. 13. A person pshes a 10@kg crae, exering a 200@N force on i, b he crae s acceleraion is only 5 m>s 2. Explain. (a) The crae pshes back on he person, hs he oal force is redced. (b) There are oher forces exered on he crae so ha he oal force is redced. (c) No enogh informaion is gien o answer he qesion. 14. Two small balls of he same maerial, one of mass m and he oher of mass 2m, are dropped simlaneosly from he Leaning Tower of Pisa. On which ball does Earh exer a bigger force? (a) On he 2m ball (b) On he m ball (c) Earh exers he same force on boh balls becase hey fall wih he same acceleraion. 15. A box fll of lead and a box of he same size fll of feahers are floaing inside a spaceship ha has lef he solar sysem. Choose eqipmen ha yo can se o compare heir masses. (a) A balance scale (b) A digial scale (c) A wach wih a second hand and a meer sick

30 Qesions Figre Q3.16 shows an nlabeled force diagram for a moing objec ha is missing one force. The lengh of he sides of he sqare grid corresponds o a force magnide of 1 N. Which addiional force has o be exered on he objec so ha he objec (I) moes a a consan speed, (II) acceleraes downward, (III) acceleraes pward, and (IV) moes down? For each case, choose all answers from (a) o (f) ha are correc. (a) (b) (c) (d) (e) (f) F 5 0 FIGURE Q3.16 No enogh informaion 17. A person jmps from a wall and lands siff-legged. Which saemen bes explains why he person is less likely o be injred when landing on sof sand han on concree? (a) The concree can exer a greaer force han he sand. (b) The person sinks ino he sand, increasing he sopping disance. (c) The pward acceleraion of he person in he sand is less han on concree, hs he force ha he sand exers on he person is less. (d) b and c (e) a, b, and c 18. A 3000-kg spaceship is moing away from a space saion a a consan speed of 3 m>s. The asrona in he spaceship decides o rern o he space saion by swiching on engines ha expel fel so ha he sm of he forces exered on he spaceship by he expelled fel poins oward he space saion. Wha is he magnide of he minimm force needed o bring he spaceship back o he space saion? (a) 9000 N (b) 1000 N (c) Any force larger han zero (d) The spaceship will keep moing away from he space saion no maer how large he force. (e) No enogh informaion is gien o answer he qesion. 20. Explain he prpose of crmple zones, ha is, he fron of a car ha collapses dring a collision. 21. Explain why when landing on a firm srface afer a fall yo shold no land wih siff legs. 22. A small car bmps ino a large rck. Compare he forces ha he rck exers on he car and he car exers on he rck if before he collision (a) he rck was saionary and he car was moing; (b) he car and he rck were moing in opposie direcions; (c) he car and he rck were moing in he same direcion. 23. Yo are plling a sled. Compare he forces ha yo exer on he sled and he sled exers on yo if yo (a) moe a consan elociy; (b) speed p; (c) slow down. 24. Yo sand on a bahroom scale in a moing eleaor. The eleaor is moing p a increasing speed. The acceleraion is consan. Draw hree consecie force diagrams for yo. 25. Yo are holding a 100-g apple. (a) Wha is he force ha yo exer on he apple? (b) Wha is he force ha he apple exers on yo? ppor yor answer wih a moion diagram and a force diagram. 26. Yo hrow a 100-g apple pward. (a) While he apple is sill in yor hand (we ll call his period he hrow ), is he force ha yo exer on he apple more han, less han, or he same as he force ha yo exer on he apple when yo are holding i a res? (b) ppor yor answer wih a moion diagram for he hrow and a force diagram for one insan dring he hrow. (c) Is he force ha he apple exers on yo a his insan more han, less han, or he same as he force ha yo exer on he apple when yo are holding i a res? Explain yor answer. 27. Afer haing been hrown pward, a 100-g apple falls back ino yor hand and yo cach i. (a) While yo are caching i, is he force ha yo exer on he apple more han, less han, or he same as he force ha yo exer on he apple when yo are holding i a res? (b) ppor yor answer wih a moion diagram and a force diagram for one insan of he cach. (c) Is he force ha he apple exers on yo a his insan more han, less han, or he same as he force ha yo exer on he apple when yo are holding i a res? Explain yor answer. Concepal Qesions 19. Figre Q3.19 is a elociy-erss-ime graph for he erical moion of an objec. Choose he correc combinaion (a, b, or c) of an acceleraionerss-ime graph and a force-erss-ime graph for he objec. FIGURE Q3.19 x x x (a) a x (b) a x (c) a x F x F x F x

31 80 CHAPTER 3 Newonian Mechanics Problems Below, indicaes a problem wih a biological or medical focs. Problems labeled ask yo o esimae he answer o a qaniaie problem raher han derie a specific answer. Aserisks indicae he leel of difficly of he problem. Problems wih no * are considered o be he leas difficl. A single * marks moderaely difficl problems. Two ** indicae more difficl problems. 3.1 and 3.2 Describing and represening ineracions and Adding and measring forces 1. * In Figre P3.1 yo see nlabeled force FIGURE P3.1 diagrams for balls in differen siaions. Mach he diagrams wih he following descripions. (1) A ball is moing pward afer i leaes yor hand. (2) Yo hold a ball in yor hand. (3) A ball is falling down. (4) Yo are hrowing a ball (sill in yor hand) sraigh p. (5) Yo are lifing a ball a a consan pace. Explain yor choices. Label he forces on he diagrams. (a) (b) (c) (d) 2. Draw a force diagram (a) for a bag hanging a res from a spring; (b) for he same bag siing on a able; and (c) for he same bag ha yo sar o lif so i moes p faser and faser. 3. For each of he following siaions, draw he forces exered on he moing objec and idenify he oher objec casing each force. (a) Yo pll a wagon along a leel floor sing a rope oriened horizonally. (b) A bs moing on a horizonal road slows down in order o sop. (c) Yo lif yor oernigh bag ino he oerhead comparmen on an airplane. 4. Yo hang a book bag on a spring scale and place he bag on a plaform scale so ha he plaform scale reads 25.7 N and he spring scale reads 17.6 N. (a) Draw a force diagram for he book bag o represen he siaion. (b) Wha is he magnide of he force ha Earh exers on he bag? 3.3 Concepal relaionship beween force and moion 5. A block of dry ice slides a consan elociy along a smooh, horizonal srface. (a) Consrc a moion diagram. (b) Draw posiion- and elociyerss-ime graphs. (c) Consrc a force diagram for he block for hree insans represened by dos on he moion diagram. Are he diagrams consisen wih each oher? 6. * Yo hrow a ball pward. (a) Draw a moion diagram and wo force diagrams for he ball on is way p and anoher moion diagram and wo force diagrams for he ball on is way down. (b) Represen he moion of he ball wih a posiion-erss-ime graph and elociy-erss-ime graph. 7. A sring plls horizonally on a car so ha i moes a increasing speed along a smooh horizonal srface. When he car is moing medim-fas, he plling is sopped abrply. (a) Describe in words wha happens o he car s moion when he plling sops. (b) Illsrae yor descripion wih moion diagrams, force diagrams, and posiion-erss-ime and elociyerss-ime graphs. Indicae on he graphs when he plling sopped. Wha assmpions did yo make? 8. * oling he preios problem, yor friend says ha afer he sring sops plling, he car sars slowing down. (a) Explain why yor friend wold hink his way. (b) Do yo agree wih him? Explain yor opinion. (c) Explain how yo can design an experimen o es his idea. 9. * A sring plls horizonally on a car so ha i moes a increasing speed along a smooh horizonal srface. When he car is moing medim-fas, he magnide of he plling force is redced o half is former magnide. (a) Describe wha happens o he car s moion afer he redcion in he sring plling. (b) Illsrae yor descripion wih moion diagrams, force diagrams, and posiion-erss-ime and elociy-erss-ime graphs. 10. A block of dry ice slides a a consan elociy on a smooh horizonal srface. A second block of dry ice slides wice as fas on he same srface (a a higher consan elociy). Compare he reslan forces exered on each block. Explain yor reasoning. 11. Three moion diagrams for a moing eleaor are shown in Figre P3.11. Consrc wo force diagrams (for wo consecie momens) for he eleaor for each moion diagram. Be sre ha he lenghs of he force arrows are he appropriae relaie lenghs and ha here is consisency beween he force diagrams and he moion diagrams. Wha assmpions did yo make? FIGURE P3.11 (a) (b) (c) D D D D 5 0 D * A sden holds a hin alminm pie pan horizonally 2 m aboe he grond and releases i. Using a moion deecor, she obains he graph shown in Figre P3.12. Based on her measremens, (a) draw force diagrams for he pie pan a imes 0.05 s, 0.3 s, and 0.7 s, and (b) esimae he disance ha he pan raels once i reaches consan speed. FIGURE P3.12 y (m/s) (s) 13. * Figres P3.11a, b, and c show hree moion diagrams for an eleaor moing downward. (a) For each diagram, say eeryhing yo can abo he eleaor s moion. (b) Draw a force diagram for each moion diagram. (c) Cold yo draw a differen moion diagram for each force diagram? Explain how ha is possible. 3.4 Inerial reference frames and Newon s firs law 14. * A rain raeling from New York o Philadelphia is passing a saion. A ball is siing on he floor of he rain no moing wih respec o he rain. (a) Draw a force diagram and a moion diagram for he ball as seen by he obserers on he rain and on he plaform. (b) The ball now sars acceleraing forward relaie o he floor. Draw force and moion diagrams for he ball as seen by he obserers on he rain and on he plaform. Which of he obserers can se Newon s firs law o explain he ball s acceleraion? Explain. 15. * Explain he phenomenon of whiplash from wo poins of iew: ha of an obserer on he grond and an obserer in he car. 3.5 Newon s second law 16. * An asrona exers a 100@N force pshing a beam ino place on he Inernaional pace aion. The beam acceleraes a 0.10 m>s 2. Deermine he mass of he beam. Wha is he percen ncerainy in yor answer? D D D

32 Problems For people paricipae in a rope compeiion. Two of hem pll he rope righ, exering forces of magnide 330 N and 380 N. The oher wo pll lef, exering forces of magnide 300 N and 400 N. Wha is he sm of he forces exered on he rope? 18. * ho p hrow Dring a pracice sho p hrow, he 7.0@kg sho lef world champion C. J. Hner s hand a speed 13 m>s. While making he hrow, his hand pshed he sho a disance of 1.7 m. Describe all he physical qaniies yo can deermine sing his informaion. Describe he assmpions yo need o make o deermine hem. 19. * Yo know he sm of he forces F exered on an objec of mass m dring D seconds. The objec is a res a he beginning of he ime ineral. Lis hree physical qaniies ha yo can deermine abo ha objec s moion sing his informaion. Then explain how yo will deermine hem. 20. * Yo record he displacemen of an objec as a consan force is exered on i. (a) If he ime ineral dring which he force is exered dobles, how does he objec s displacemen change? Indicae all he assmpions ha yo made. (b) Explain how yor answer changes if one of he assmpions is no alid. 21. * Eqaion Jeopardy 1 Inen a problem for which he following eqaion can be a solion: 140 kg2a x = 200 N - 40 N 3.6 and 3.7 Graiaional force law and kills for applying Newon s second law for one-dimensional processes 22. * Eqaion Jeopardy 2 Describe in words a problem for which he following eqaion is a solion and draw a force diagram ha is consisen wih he eqaion (specify he direcion of he axis): 3.0 m>s 2 * 3.0 kg = N - F R on O 23. Eqaion Jeopardy 3 Describe in words a problem for which he following eqaion is a solion and draw a force diagram ha is consisen wih he eqaion (specify he direcion of he axis): 0.8 m>s m>s 1.6 s = F x 50 kg 24. * Eqaion Jeopardy 4 Describe in words a problem for which he following eqaion is a solion and draw a force diagram ha is consisen wih he eqaion (specify he direcion of he axis): 2.0 m>s 2 = 196 N - F P on O 20 kg 25. * pider-man pider-man holds he boom of an eleaor wih one hand. Wih his oher hand, he holds a spider cord aached o a 50@kg box of explosies a he boom of he cord. Deermine he force ha he cord exers on he box if (a) he eleaor is a res; (b) he eleaor acceleraes p a 2.0 m>s 2 ; (c) he pward-moing eleaor s speed decreases a a rae of 2.0 m>s 2 ; and (d) he eleaor falls freely. 26. ** Ma is wearing Rollerblades. Beh pshes him along a hallway wih a large spring, keeping he spring compressed and conseqenly he force ha he spring exers on Ma consan a all imes. They condc seeral experimens in which Ma sars from res and raels 12.0 m while carrying objecs of differen mass in his backpack, recording he ime ineral for each rip. Their daa are shown in he able a righ. Added mass (kg) Time ineral (s) (a) Draw a force diagram for Ma and se i o explain why he is moing wih a consan acceleraion. (b) Two physical qaniies ha are no lised in he able also affec Ma s moion. Deermine hese wo qaniies sing he daa aboe. (Hin: This problem reqires linearizaion. ee Example 3.8 for help.) 27. * nwoman The downward acceleraion of a 60-kg snwoman near he end of a fall from a ery high bilding is 7.0 m>s 2. Wha resisie force does he air exer on her body a ha poin? 28. Esimae he aerage force ha a baseball picher s hand exers on a 0.145@kg baseball as he hrows a 40 m/s 190 mi>h2 pich. Indicae all of he assmpions yo made. 29. * per Horne je akeoff A 2.1 * 10 F-18 FIGURE P3.29 per Horne je airplane (see Figre P3.29) goes from zero o 265 km>h in 90 m dring akeoff from he fligh deck of he U Nimiz aircraf carrier. Wha physical qaniies can yo deermine sing his informaion? Make a lis and deermine he ales of hree of hem. 30. Lnar Lander The Lnar Lander of mass 2.0 * 10 4 kg made he las 150 m of is rip o he Moon s srface in 120 s, descending a approximaely consan speed. The Handbook of Lnar Pilos indicaes ha he graiaional consan on he Moon is N>kg. Using hese qaniies, wha can yo learn abo he Lnar Lander s moion? 31. Aisha hrows a 0.3-kg ball pward. Frances, sanding on a balcony aboe Aisha, caches he ball by exering a 1-N downward force on he ball. (a) Draw a moion diagram and a force diagram for he ball dring he ime ineral when Frances is caching i. (b) Deermine he acceleraion of he ball. 32. * dens Lcia, Isabel, and Asin are inesigaing how snow sops a dropped 500-g lemon jice bole. In pariclar, hey are ineresed in how he force exered by he snow depends on he age of he snow. They ake high-speed ideos of he bole while i sinks ino he snow, aking heir firs se of measremens 4 days afer fresh snowfall and he second se of measremens 2 days laer. Afer analyzing he ideos frame by frame (see phoo), hey plo a graph ha shows how he elociy of he bole from he momen he bole oches he snow changes for boh ypes of snow (Figre P3.32). FIGURE P3.32 y (m/s) day snow 4-day snow (s) They each explain heir resls as follows: Lcia: The 6-day snow exers a larger force on he bole becase i sops he bole in a shorer ime. Isabel: The ime aken o sop he bole does no say mch abo he force. The 6-day snow exers a larger force on he bole becase he slope of is y 12 graph is seeper. Asin: We canno compare he forces exered by he snow becase he iniial elociies are differen. We need o repea he experimens and make sre we always drop he bole from he same heigh. Explain how each sden reached her/his conclsion and decide who (if anyone) is correc. Indicae any assmpions ha yo hae made.

33 82 CHAPTER 3 Newonian Mechanics 33. * Asrona Karen Nyberg, a 60@kg asrona, sis on a bahroom scale in a rocke ha is aking off erically wih an acceleraion of 3g. Wha does he scale read? 34. * A 0.10@kg apple falls off a ree branch ha is 2.0 m aboe he grass. The apple sinks m ino he grass while sopping. Deermine he force ha he grass exers on he apple while sopping i. Indicae any assmpions yo made. 35. ** An 80@kg fireman slides 5.0 m down a fire pole. He holds he pole, which exers a 500@N seady resisie force on he fireman. A he boom he slows o a sop in 0.40 m by bending his knees. Wha can yo deermine sing his informaion? Deermine i. 3.8 Forces come in pairs: Newon s hird law 36. * Earh exers a 1.0@N graiaional force on an apple as i falls oward he grond. (a) Wha force does he apple exer on Earh? (b) Compare he acceleraions of he apple and Earh de o hese forces. The mass of he apple is abo 100 g and he mass of Earh is abo 6 * kg. 37. * Yo psh a bowling ball down he lane oward he pins. Draw force diagrams for he ball (a) js before yo le i go; (b) when he ball is rolling (for wo clock readings); (c) as he ball is hiing a bowling pin. (d) For each force exered on he ball in pars (a) (c), draw he Newon s hird law force beside he force diagram, and indicae he objec on which hese hird law forces are exered. 38. * (a) A 50@kg skaer iniially a res hrows a 4@kg medicine ball horizonally. Describe wha happens o he skaer and o he ball. (b) Esimae he acceleraion of he ball dring he hrow and of he skaer sing a reasonable ale for he force ha a skaer can exer on he medicine ball. (c) The skaer moing o he righ caches he ball moing o he lef. Afer he cach, boh objecs moe o he righ. Draw force diagrams for he skaer and for he ball while he ball is being cagh. 39. ** Baskeball player LeBron James can jmp erically oer 0.9 m. Esimae he force ha he exers on he srface of he baskeball cor as he jmps. (a) Compare his force wih he force ha he srface exers on James. Describe all assmpions sed in yor esimae and sae how each assmpion affecs he resl. (b) Repea he problem looking a he ime ineral when he is landing back on he floor. 40. * The coish Tg of War Associaion coness inole eigh-person eams plling on a rope in opposie direcions. Esimae he magnide of he force ha he rope exers on each eam. Indicae any assmpions yo made and inclde a force diagram for a shor secion of he rope. 41. Consider he experimen described in Qesion 3.6 (Figre Q3.6). (a) Draw force diagrams for he magne and for he paperclip. (b) Which of he forces ha yo hae drawn are pairs according o Newon s hird law? Assme all objecs are a res. (c) If he mass of he magne is kg and he force exered by he hand on he magne is 3.18 N, wha is he magnide of he force exered by he paperclip on he magne? (d) Can yo deermine he mass of he paperclip based on hese daa? Explain. 42. * A friend drops a kg baskeball from 2 m aboe yo. (a) Esimae he smalles force ha he baskeball exers on yor hands while yo are caching i. (b) How does i compare o he force ha yo hae o exer on he ball o cach i? Use force diagrams o sppor yor answer. 3.9 ea bels and air bags 43. Car safey The Naional Transporaion afey Board indicaes ha a person in a car crash has a reasonable chance of srial if his or her acceleraion is less han 300 m>s 2. (a) Wha magnide force wold case his acceleraion in sch a collision? (b) Wha sopping disance is needed if he iniial speed before he collision is 20 m>s (72 km>h, or 45 mi>h)? (c) Indicae any assmpions yo made. 44. * A 70@kg person in a moing car sops dring a car collision in a disance of 0.60 m. The sopping force ha he air bag exers on he person is 8000 N. Name a leas hree physical qaniies describing he person s moion ha yo can deermine sing his informaion, and hen deermine hem. General Problems 45. * Lef enricle pmping The lower lef chamber of he hear (he lef enricle) pmps blood ino he aora. According o biophysical sdies, a lef enriclar conracion lass abo 0.20 s and pmps 88 g of blood. This blood sars a res and afer 0.20 s is moing hrogh he aora a abo 2 m>s. (a) Esimae he force exered on he blood by he lef enricle. (b) Wha is he percen ncerainy in yor answer? (c) Wha assmpions did yo make? Did he assmpions increase or decrease he calclaed ale of he force compared o he acal ale? 46. ** Acorn his deck Yo are siing on a deck of yor hose srronded by oak rees. Yo hear he sond of an acorn hiing he deck. Yo wonder if an acorn will do mch damage if insead of he deck i his yor head. Make appropriae esimaions and assmpions and proide a reasonable answer. 47. ** Olympic die Dring a pracice die, Olympic dier F Mingxia reached a maximm heigh of 5.0 m aboe he waer. he came o res 0.40 s afer hiing he waer. Esimae he aerage force ha he waer exered on her while sopping her. 48. * Komila knows ha an egg breaks if i falls ono a concree floor from a heigh of 0.4 m. he finds, howeer, ha an egg does no break when i falls from he same heigh ono a floor ha is coered wih a 2.0-cm-hick carpe. Try o explain he ocome of her experimens. Draw a force diagram for he egg js before i sops. Based on yor explanaion, predic wha he hickness of he carpe shold be for an egg o srie a drop from a heigh of 1.0 m. Indicae any assmpions yo hae made. 49. ** Yo are doing sqas on a bahroom scale. Yo decide o psh off he scale and jmp p. Esimae he reading as yo psh off and as yo land. Indicae any assmpions yo made. 50. ** Esimae he horizonal speed of he rnner shown in Figre P3.50 a he insan she leaes conac wih he saring blocks. Indicae any assmpions yo made. FIGURE P ** Esimae he maximm acceleraion of Earh if all people go ogeher and jmped p simlaneosly. 52. ** Esimae how mch Earh wold moe dring he jmp described in Problem 51. Reading Passage Problems Col. John app crash ess From 1946 hrogh 1958, Col. John app headed he U.. Air Force Aero Medical Laboraory s sdies of he hman body s abiliy o olerae high acceleraions dring plane crashes. Conenional wisdom a he ime indicaed ha a plane s negaie acceleraion shold no exceed 180 m>s 2 (18 imes graiaional acceleraion, or 18g). app and his colleages bil a 700@kg Gee Whiz rocke sled, rack, and sopping pisons o measre hman olerance o high acceleraion. aring in Jne 1949, app and oher lie sbjecs rode he sled. In one of app s rides, he sled sared a res and 360 m laer was raeling a speed 67 m>s when is braking sysem was applied, sopping he sled in 6.0 m. He had demonsraed ha 18g was no a limi for hman deceleraion. 53. In an early pracice rn while he rocke sled was sopping, a passenger dmmy broke is resraining deice and he window of he rocke sled and sopped afer skidding down he rack. Wha physics principle bes explains his ocome? (a) Newon s firs law (b) Newon s second law (c) Newon s hird law (d) The firs and second laws (e) All hree laws