Scribd
Upload
121 views90 pages

Taller 2

ga

Uploaded by

Dianita Peñarete
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
121 views90 pages

Taller 2

ga

Uploaded by

Dianita Peñarete
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
You are on page 1/ 90
Taller de Autoaprendizaje No 2 Due: 14:59pm on Monday, May 9, 2016 ‘You wi eeiven creditor tama you comple athe assignmentis dus, asin Policy Enhanced EOC: Exercise 4.5 wo do pull horizontally on ropes alached fo post; the angle between the ropes is $5.0°. Dog A exes a force of 278 N and dog B exerts a force of 300 N You may want to review ({ELpaaes 106 08) Forholp with math skis, you may want to rview ‘Vector Macntudes Determining he Angle ofa Vector Vector Adon For general problem-solving tps and stratgis fr this topic, you may want to view a Video Tutor Solution of Superpostin f forces Pata Find the magetude of the resultant fore. Hint 1. How to approach the problem Imagine you were siting in tee directly above the post, so that you were looking down on the dogs and the ropes tying hem othe post. ‘Start by draning a sketch ofthe two dogs pulling on thelr ropes as seen by you trom above, and choose a coordinate system so thatthe post Is atthe origin {and the rope ted to dog Ais along the a-axis In what rection would dog B be seen puting its rope? Now nd tho resultant force. How is the magnitude ofa vector related to its components? ANSWER: P= 519 N Parte Find the angle the resultant force makos with the rope of dag A, Hint 1. How to approach the problem How can you tnd the angl the eb uant foes vector makes wih the xan (he rope of dg A) ftom the components ofthat vector? ANSWER, O= 26° + Two Forces Acting at a Point ‘Two forces, Fy and F. act ata point. F; has a magnitude of 9.60.N and is directed at an angle of 58,0 ° above the negative x axis in the second quadvant. F) has a magnitude of 6.40 N and is directed at an angle of 53.8 ° below ine ragatve x axs in he thir quadrant PartA ‘What athe x component ofthe restart force? Express your answer In newtons. Hint 1 How approaen the posi ‘The estan ec is fr am vctr sumo. Th, x comgoent he sum of thx compares lh ree andi components team te y compart oh ten Hint 2 Find the x component fF Fin tx component ot Fi Express your answer In newtons. epee siya Siesta “IE Tate ce reno? Hint 4. Components of a vector Consider vector A that forms an angle withthe postive x axis. The x and y camponents of are, respectively, A, = Acos® and A, = Asind, were A the magni fhe vector: Nota that A, 0NE<0< 7, A, 0" E ONE 083 This theory is sometimes cll the Animist theory of motion since it envisions a if fre beng associated with tion. Newtons 1st law is often very ficult grasp because it contradcts vaious common-sense ideas of mation that may have been acquit fram experince in everyday Me, For example, unaccounted for forces tke ction might cause a bal roling onthe playground to eventually stop, eventhough no vious forces seem to be acting, When studying Newtonian mechanics, tis best o remember this as two laws: 1. pe nat ora (.e., vector sum of al forces) acting on an object is 20, the object wll kop moving with constant volocty (which may be 260) 2 tan object moving with constant velocity (rot speed). that Is, wth zero acceleration then tho ot force acting on that object must bo zr. Compete th folowing sentences to 80 you can apply these ideas, PartA H¥acaris mouing to the loft wth constant velocity, ane can conch that ANSWER, there must be no forces exerted onthe car the not force exertod onthe care drctos tothe ot 2 net force exerted on the aris zero ‘here is exactly on force exerted onthe cat Parte [An object cannot remain at rest ures ANSWER, there are no forces a all exerted on | the net fore exerted on i fs zero the not force exerod ont is constant ‘here is only one force exorted on it ‘A Gymnast on a Rope A gymnast of mass 83.0 kg hangs trom a vertical ope attached fo he cling, You can ignare the weight of he ope and assume tha he rope does not stretch Use the value 9.Sm/s! forthe acceleration of gravy. openers sanyo ieee “IE Part CCaleate the tension inthe rope if the gymnast hangs motions onthe rope. Express your answer in newton Hint 1. A body in static equilibrium ‘Tho gymnasts hanging al rest, This means thatthe gymnast is in state equim and, according to Newiors {st law the net frce acting on the gymnast Hint 2, Find what forces act on the gymnast What are the forces acting on the gymnast? ANSWER: ‘The tonsion in the rope ony, “The woight of tho gymnast on | The tonsion nthe rope and the weight ofthe gymnast. ‘The gymrast street 80 no forces ae acting on her. ANSWER, PartB ‘Caltato th tension inthe rope tho gymnast climbs th rope at a constant ate Express your answer In newtons. Hint 1. A body in dynamic equilorium ‘The gymnasts moving witha constant velocity, This means that ho gymnast in dynamic egullxum and, accoring to Newtons 1st lw, the not Fores acting onthe gymnast 8260 ANSWER: Ts 520 N Correct eas it surprise you thatthe answors to Parts A are Baro the sao? In both cases, tho gymnasts nt accelerating. Therefor, tho nt fore acting on tho ‘gymnast zero, Sines tha only wo frees ating onthe gymnast are tension and wait, the tanlon inthe ope in each casa is equal in magnitude (and ‘opposite indirection) tothe gyrmrast's weight. Parte CCaleate the tension inthe rope if tho gymnast climbs up the ope wih an upward acceleration of magritud 1.50 m/s? Expres your answer in newions. Hint 4. Newton's 2nd taw of mation Accorting to Newtons 2nd twa body accelerates, the magritud of the net force Fy. acting oni equals the producto the mass rm of the Body athe ‘cesleration a ofthe body Fay = ma. Hint 2. Find an expression forthe net external force The only frees acting onthe gymnast are the tonson in the rope an hor own weight, Which ofthe folowing clans gives the nt force Fue ating onthe ‘gymnast wile aeslerating up the rope? ‘Take the postive crecton ofthe y axis to be upwar. Here, m and ¢ dente, respectwvely, the mass cf the gymnast and the acceleration due to graviy. ANSWER: openness ieee “DIE Fa =-T—mg Fa = OP + mg © Fa =Toma Fag = T+ ma Hint 3. Find the sign of the acceleration IF you take the postive y axe tobe upmard, then isthe aoceleration of he gymnast clmbing up te rope postive or negative? ANSWER: © postive ogatve ANSWER, Ts 599 N art D CCaledate the tension inthe rape if he gymnast sides down the rope wth a downisard acceleration of magnitude 1.50 m/s? Express your answer in newons Hint 4. Newton's 2nd tw of mation -Aooorting te Newton's 2nd law «body accelerate, the magnus of the net force Fx ating anit aqua the product of he mass m ofthe beay an the ‘acceleration a of the body Hint 2, Find an expression forthe net external force ‘The only forces acting onthe gymnast re the tension inthe rope andthe weight of he gymnast Which ofthe following relations gives the net force Fea, acting on te oymnast wile sing down te rope? ‘Toke the postive y axis tobe upward, an let m and 9 denote, respectively the mas ofthe gymnast andthe acceleration due o gravy ANSWER: Hint 3. Find the sign ofthe acceleration If yu take the postive y axs tobe upward, thon isthe acceleration of to gymnast as sho slides down the ope positive or negative? ANSWER: postive © negative T= 40 > Correct In ths problem, the crectons of velocty and acceleration happsned tobe the same, I hay ar diferent, itis the rection ofthe acceleration, not the drecton ‘of volt, thal determines the magritases of he forces, Newton's 2nd lnw has nothing todo wth the abjoct's veloc. Conceptual Questions on Newton's 1st and 2nd Laws Learning Goal openers sanyo ieee “IE ooo come ese mre? “To understand ihe meaning and the basic appcaions of Newtons ‘stand 2nd laws. Inthis problem, you ae given a dlagram representing the motion of an obect—a maton chagram. The dots represent tne object's postion at maments separated by equal erate of ime. The dots are connected by ‘roms reprasontng the ebjects average velocity during the corespanding time interval A B ‘Yur goals to use this motion dlagram to determine the action of tha nat force acting onthe object. You wll then delermine which free aigrams and whch situations may coespend to such a mio. Parta wna isthe aration ofthe net force acting on the abject at position A? Hint 1. Using Nowion's 2nd law ‘According to Newton's 2nd lw, voctors @ and Fux have the same direction, Can you determine the diction of acceleration a postion A by analyzing the esyan? ANSWER: onard couwars tothe ltt to the taht © The net fore is 20, Correct ‘The velocity vectors connecting poston A fo the ajacent postions appear o have the same maghituse and rection. Therefore, the accelerations zore-and S018 the nat fore, Parte \Wnat isthe arecton ofthe nat fore acting en the object at position 8 ANSWER: woward counwars © tothetot to the ight ‘Tho net free fs 200 Correct “Tho velocity is rcted to the ight however, tis decreasing, Therefore, the acceleration is directed lo the let—and sos the net force. Partc What sth cretion ofthe net force acting on the object at position C? Hint 1. Consider the components ofthe velocity ‘The hczontal component af the Vlocty appears fo remain constant. What about the vatel ane? ANSWER: openers sanyo ieee “IE pars tothe ltt tthe igh ‘The nat force fs zero Correct ‘The horzontal component ofthe velecty doesnot change. The verical component af he velelty Increases. Therefore, the aceelcation-and the nt foree—are rected stright downward “Tne not four questions ar relate to the force alagrams numbered 1 1 6. These dagrams represent the {forces acing on a moving object, The number next to each srw epresans the magrtude ol Ine force in L G wo PartD Which of these lagrams may possibly corespond to the situation at point A onthe mation dagram? “Type, in increasing order, the numbers corresponding tothe correct diagrams. Do not use commas. For instance, ifyou think that only diagrams 3 and 4 Correct i = Et te Wich of hese iagrams may possity corespondt the situation al point B on tho motion diagram? rams, Do not use commas, For instance, if you think that only diagrams 3 and 4 “Type in increasing order, the numbers corresponding tothe correct di Part F Which of these diagrams may possibly corespond to the situation at point C onthe mation dagram’? ‘Type, in increasing order, the numbers corresponding tothe correct diagrams. Do net use commas. For instance, ityou think that only diagrams 3 and 4 are correct, PartG Wien of hese diagrams correspond toa situation where the moving object (not nacessarly the one shown inthe motion diagram) is changing is velocity? “Type in increasing order, the numbers corresponding are correct, type 34 the correct diagrams. Do not use commas. For Instance, Ifyou think that only diagrams 3a Hint 1. What doos a change in velocity mean? openers sy anata DIE ooo Irthe velocity ofthe moving object is changing, the net force applied to the bject must be ANSWER: rected tothe ih rected tothe tet rected upward ciracted commer acted the same way a5 the velocity rected opposite to the velacty © of magnitude greater than zero ANSWER: Correct | Consider the fotbing situations: ‘Acaris mowing along a stright road ata constant speed, ‘A cars moving along astralght rad wel slowing dow, ‘aris mowing along a straight road we speeding Up. ‘A hockey puck slides along 2 hotzontal iy (itoness)surace A hockey puck slides along a rough concrete surface. ‘A cockraseh s speeding up fom rest. ‘Arc is thrown horizontally; a res stance is negobe ‘rock's thon horizontally; a resstance is substantia LA tock is cropped vertcaly ar resistance is neglgie JCA tock is cropped vetcaly ar resistance is Substata Part Wien of hese situations describe the mation showin the mation dagram at pot A? “Type the leters corresponding fo all the right answers in siphabetical order. Do not use commas. For instance, if you think that only situations C and D ate correct, type CO ANSWER: I Part! \wnien of hese situations describe the mation shown inthe mation clagram at pot 8? ‘Type the letters corresponding tall the right answers In alphabetical order. De not use commas. For Instance Ifyou think that only situations C and D a1 correct, type c. ANSWER: Correct | PartJ rien of these situitons describe the mation showin the mation dagram at pot ©? “Type the letors corresponding fo llth right answors In alphabstcal order, Do not use commas. For Instance Ifyou think that only situations C and D ate correct, type CO ANSWER: Applying Newton's 2nd Law openers sanyo ieee “IE Learning Goal ‘To lam a systematic approach to solving Newton's Zn law problems using a simple example, (Once you have decided a oWve a problem using Neworis 2nd law, there are stops that Wl ead you to soliton, One such prescription Is the folowng: + Visualize the problem and ident epoca cases + Isolate each Boay ana araw the forces acting on it + Choose a coordinate system foreach body. + Apply Newon's 2a lato each body. + Wete equations for to constrains and other given information Solve the resulting equations symootealy (Check tat your answer has the corect dmansions and saleies special cases. I numbers aro given nthe problem, plug thom in ane chock that the answer makes sense. ‘Think aout generations or simpiltestions of he proce [As an example, we wll apply ths procedure to fin the acceleration ofa lock of mass ms that is pulled up a fctionles pls horizontal by a perfect sting that passes over a peract pulley toa block of mass ra that Is hanging vertally. Inclined at angle 0 wih respect to the block | ‘Visualize the problem and identity spacial cases Fist examine tho problom by dawing a picture and visualizing the motion. Apply Newloris 2nd law. S> F = mai o each body in your mind. Dost worry about which {quanitles are given. Thrk abou the forces on each by: How ae these consistent wth the direction ofthe acceleration for hat body? Gan you thnk of any special Eases that you can solve quckly now and use fo teat your understansng later? ‘one special case inthis problem Is ig =O, n whch case block 1 would simply fal rely under the acceleration of gravity: a Pata ‘Consider another special case in which the inclined plane veal (9 ~ x/2). In this case, for what value of m, would the acceleration of the two blocks be equal tozee? Express your answer In terms of some oral of the variable ANSWER: sms and 9, Isolate each body and draw the forces actng on i [A force dagram should include only ral ores that act onthe body and satisfy Nowons Slaw. One way to check ifthe forces are reais to dermine whether thoy are part ofa Newtons rd law pal, that, whether they rut fm a physieal interaction that alo causes an opposite ferce on some ater body, which may net be part of {he problem. De not decompose the forces into component, and do no nlude restart forces that ar combinations of other rel forces like centripetal force of flettous forces tke the “centitugal force y om r eek folock | block block 2 ym ("2 . my mat mse 8 mse ‘Assign each free symbol, but don stat to solve the problem at this pol art B nen of the four arawings i @ comet force dagram forts problem? y 7 ir bot Me ok ih Fa ae mg EMMA) Ang c a openers sanyo ieee “IE va ANSWER: ‘Choose a coordinate system for each body Nowlons 2nd aw, 32 F= mii, isa vector oquation, To alo sublet vectors i's often oases to docompose each vector into componans, Whereas a particular set of vector componeni i only valid in a paicular coordinate system, th vector equality holds in any coordinate sysiom, giving you trodom to pck a coordina system ‘that most simples the equatons that esut fram the component equations ts generally beso pick a coorinale system where the acceleration ofthe system les drecty on one ofthe coodtnate axes. I her Is no acceleration, then pick a coordinate systom wih as mary unknowns as possible along the coranate axes. Vectors thal le along the axes appear in aly oe ofthe equation fr each component, rather tan nto equations wih iganometicprelacios. Nolo that is sometimes advantagoous to use ferent coordinate systems fr each body in the problem, In this problem, you should use Cartesian coordinates and your ates should be stationary with respect othe inlined plane, Parte Civen the etl ust deserved, what alttin of the coordinate axes would be best to use in ths problem’? er options, “ited” means with the x axis oriented parallel tothe plane (Le. at angle 2 tothe horizontal), and “level” means with the x axis, ANSWER, tad for bon look and block 2 tad for look and level fr block 2 | Jove for black 1 an tite fr block 2 level for both lock 1 and block 2 ‘Apply Newton's 2nd law to each body PartD nats SD Fie the sum ofthe x components ofthe frees acting on block 2? Take fore acting up the incline tobe postive. Express your answer in terms of some oral of the variables tension T, ma, the magnitude of the acceleration of gravity 9, and 8. Hint 1. Decompose the force of gravity on block 2 In this problem, the hardest force vector to expr in terms of ts coordinates isthe force of gravity on black 2. The magetude ofthe weights maa. Find the fre of gravity in terms of ts components, using a ited cooranat system whose x axis paral to and porting up the inlined plane. Express the force of gravity on block 2, Fi, in terms of some oral of the variables ra, unit vectors 3 and j ANSWER: and 8, Express your answar as a vector in terms ofthe | Faq = —mao(sin(@)é +con()3) ANSWER: made = DF = T—mygsind Parte Now doterrine rary = 52 Fy. tho sum ofthe y components ofthe forces acting on block 1. Tako forces acting upward as postive. Express your answer in terms of some oral of the variables 7, rm, and 9 ANSWER, epee sanyo ieee IE ‘100 may = Dy Tomo Part F Wirlte equations forthe constraints and other given information In this robe, the fac that the length of the sting does no! change imposes a constraint on eatve accelerations ofthe tw blocks. Find a elatonship between the x component ofthe acceleration of block 2. ane, and the acceleration of Mack 1. Pay cael atfention fo sigh. Express agg in tonms of a1, andlor ayy, the components ofthe secel Hint 1. Visualize the motion Fr block 2 has an acesleration a2, up te incline, must the accsaratin of block 1 be upward or downsard to keep the sting taut? ANSWER: PartG Solve and check Inthe previous parts, you obtained the folowing uations using Newton's 2nd law andthe constraint on the mation ofthe two Blocks: mada, = T—mzgsin(®), (1) miaiy=T—ma, 2) os axe = —ay. (8) Boforo you enter your answer, make su it satis the special cases you awady dented + ay = gti: = 01nd + ayy =Oif my = mz ans 9/2 [Also make sur that your answor has dimonsions of acceleration. Express ayy in terms of some or all ofthe vara rma, ma, 8, and 9 Hint 1, How to sob the equations Substitute for tom equation (1) nto equation (2) and then use ae from equation (3) inthe now equation (2). This wl yield @ linear equation in ay that ls easy to soho. ANSWER, ay = assind-mg Correct ‘can you see how a simple genecazation of he problem could be solved wth ate extra work or how you could solve @ nana problem tha sa subse of this one? For example, magi that thre i ction inthis problem betwaon the plane an block 2. This would lead to an acitional force on block 2: Fg = aN, where ‘tne nomal force N is gven by NV = m,.9cos(d) “Tis addon orce would load to anew term inthe expression for the acceleration of Bock ©, you have a resut that can be applied wheter the pane is fetloness or nt? Now, by choosing whether of nat Enhanced EOC: Exercise 4.10 ‘A dockwarker applies a constant horzontal ores of 82.0 N toa block of le on smooth horizontal lor The ronal force is naghgible. The block starts frm rest and moves adistance 13.0m ina time of 208 ‘You may want to reviow (hnagss 112. 117) openness Seana IE so For general problem-solving tps and stratgis fr ths topic, you may want to view a Video Tutor Solution of Determining fore from acceleration Part Wat isthe mass ofthe block of ice? Hint 4. How to approach the problem ‘Star by drtnng a sketch ofthe block fle and ts motion across the smooth horizontal lor. Create a standard coordinate system, and daw al the forces onthe Hock. Do you need to wony about the vetcal forces (gravity and the surace's normal force) on the Bock? Why? ‘You know the force applied horizontal on the block. To delermine its mass, what other quantity must you find? How can you use the information provided about the block's motion to help you determine that ther quantity? ANSWER, m= 066 kg Parte the worker stops pushing aftr 5.308, now far des the black move in the next 4.60? Hint 1. How to approach the problem ‘Tofing out how far something maves ina time period. you need te know its nal velocity and acceleration, How can you determine these quant fr the block nthe cond time interval, when the worker fs no longer pushing? During that second interval of meio, there is no fore onthe block af ic fom the deckworker. What canbe sad about the accaleration on the Back In this ima? Use tis information to fing the stance traveled during the second time interval ANSWER, e= 26 m Force and Velocity Conceptual Question [At ts natura esting lengtn, a muscle is close tots optimal ana or producing force. As the muscle contrac, the maximum fore t can delve dsceases. When a ‘muscles at approximately 80% of ts natural length. K cannot eerract much more and the force can produce crops crastialy. Fora muscle slrlched beyond ts ata length, the same is te. At about 120% of nal length, the free thal a muscle can exert again drops drastically is muscle lang to force ralationship can be demonstrated by doing a chino. As you hang tram the bar, your biceps muscle are strehed and can produce only a relatively small fxce. As you gt close to tho bar, you Biceps masclos contract substantially, and you again exzerence dificult. Th Someuhre In Between, when your muscles are else to thar natural length. est part ofthe chip occurs PartA Imagine hanging trom a ehinap bar and begioning @chi-up Which of the ftlowing veloty versus time graphs best represent the fst part of your mation om Boing trest fo being approximately hafivay to tho bar}? Assuma you are tying odo the chim as icky a possile, aly Bry cry Hint 1, Determine the variation in muscle force asad on the deserigion of muscle force, does the force exerted by yourbiceps Increase, decrease, or stay the same dung the fst hal ofa chinup? ANSWER: openness ieee “DIE ‘0 come ese rei? © Ieinreases, It decreases. It stays the same Hint 2. Determine the variation in acceleration ‘Based onthe vatation in muscle force dung the fist half fa chinup, does your acceleration increase, decease, or stay the same duting the ist half of @ chip? ANSWER: © Ieincreases, It docreases. Ie stays the same Hint 3. Determine the variation inte slope ofthe velocity graph ‘axed onthe variation of your acceleration dung the fist hal of a chip, does the slope of your velociy g-aph increase, decrease, oF lay the same during the fst half of a chin-up? Racal hat the acceleration at specific ime is equal tthe slope ofa valocy vs. tme graph at that time. ANSWER: © reineraases. Ie decreases, He stays th ANSWER: Motion from Force Graphing Question For each of the net force versus time graphs in Pats AB, and C, construct a possible coresponding graph of valocty u(t), or postion =(t), versus time, Assume one dimonsioeal moton, PartA Pot vloety varus tine, o or Hint 1, Relating force and kinematics graphs [Newton's 2nd law states thatthe net fores acting on an objct is proporionalto its acceleration. Therefore, graphs of net force versus time and acceleration ors time must have te same general shape, From the graph of acceleration varus ‘ime, you can then canst velocity versus time graph. The velocity under the acceleration curve between tO and = T. tine ete in I velcty pls the aes By the same process, you can construct a poston versus timo graph from the graph of velocity versus time. Tho position ta time T's tho intial positon pls the ata Under the veloc curve between t= 0 ana ¢ = 7 openness ieee “DIE come ese rei? Hint 2. Wit values Knowing the net force that acts onan cbect does nt allow you to determin te intial velocity or position ofthe objct. Therefore, the velocity or position ‘apn ean bogin at any inal value ANSWER: PartB lot velocity versus time o * Hint 1. Relating force and kinematics graphs [Nowor's 2nd law sats thatthe not force acting on an object is proporionalo its acceleration. Therafor, graphs of nt force versus time and acceleration versus time must have the same general shape From the graph of acceleration verus time, you can then const velocity versus time graph. The velocity ‘under the acceleration curve between t — Oand ¢ time 7 is the intial vlocy plus the area By the same process, you can constucta positon versus time graph rom the graph of vlocty versus time. The posiian at atime 7's the inal postion pls the area under tne velocity curve between t= 0 ang t = T. Hint 2. inital vatues Knowing tho nel force that ats onan bjoet doos nol allow you to determin the inal velocity position ofthe object. Therefore, the velocity o position 73pn can begin at any inl vale. ANSWER: openers sanyo ieee “IE 0 woe ‘ae ce reno? Parte tot positon versus tin. oe Hint 1. Relating force and kinematics graphs Nowor's 2nd law stats thatthe nat force acting on an object is proporionalto ts acceleration. Therefore, graphs of nt force versus ime and acceleration ors time mast have te same general shape, From the graph of acceleration versus time, you can then construct velcty versus time graph. The veocty under the acceleration curve between tO and = 7. time Tis the nta veloc plus the area By the same process, you can consucta poston versus time graph from th graph of velocity versus lime, The pasion al atime T's the inal poston pls the area under the veloc curve batwoen t= O ana ¢ = Hint 2. Wit values ‘Knowing the net force that acs onan cbect does nt allow you to determin te inal velocity or position ofthe object. Therefore, the velocity or position ‘pn can bogin at any inal value ANSWER, openers sanyo ieee “IE Newton's 1st and 2nd Laws Leaming Goat ‘To undorstan the meaning and the basic appeaions of Newtons stand 2 ws. Newtons laws re fundamental in mechanes. The mathematical expressions are very simple but conceptual understaning of Newtors laws, whichis necessary for solving nontvlprobloms Is nt simple at all Newtons tatiaw “The common textbook slaloment of Newtons 1st lw may seem rather sraightfoward. Hore tis ‘An object has @ constant vaoety oossibly 22) if and only the et force scting onthe abet 26 In athor werd if the vecter sum of tne forces applet the oboe is zor, the object would bo other at restor at constant velocity (has, the object would nave zoro sceolratin) i sucha sum isnot Zero, the abject cannot possibly be moving ata constant voc Frames of reference ‘Tho slatoment of Nowin’s Tt law Becomes a Bit more complicated in actual applications. Imagine youself in a car. To understand Newtons {st lw fly, we nocd the concept ofa frame of reference. A frame of reference e a set of coordinates used to measure dstances and times. In your frame of reference, any cstance would be measured eative to you. For example the radon the cars 075m to the right of you The raco is at et in your rame of reference, because the radio doesnt change In your tame of reference, the car Is ata’ at rst. only possible thatthe net ote acting an the ar fs net 2r0: The car may (nthe rame of rfernce af an bsarver standing on the ground) be accslratng,tareng, a braking, Yen your fame of referane, the car woud remain at est because, rave to ou, t= not ‘moving at al. So, the cars at rest or accelerating, depending upon who you ask inertial ramos of reference ts tempting to ignore this ticaty by saying tha he frame of reference attached te the cars somehow wrong The observer on the ground, contrast, 1s ht The bsorvarse05 the mation ofthe car asi rely is. Howovar, sucha line of roasoning seams Naned, because it rises tho questo af how fo determine which ramos of feloroce at “igh” and whch ones are “wrong,” isis what Newton's 1 aw gles, Now established the concept of an inertia fame of reference. An neta frame of reference, by dint, one in wth the staterant of Newion'® Tet laws, nfl, te. Newton's 2nd law It is important to krow thatthe frame of reference bsing used is, Infact, inertial. Only than does Newtons 2nd lw wor in a simple and elegant form, Newon's 2nd law establishes the relationship between the net force acting onan object the mass ofthe object, ad ts acceleration: Bae = mn, Note that Newon's 2 aw allows ene o tnd the maghitus of the objects aeceleation. also establishes the fact that the acceleration ofan object has the same sirction a the net orc acting onthe objac. ‘Applying Newton's laws in inertia and noninertal ames Ir ne frame of reference lsat neal, using Newtons 2nd aw to calculate acceleration stil possible but may be far more complicated. Object tat experience zero rol force may accelerate, and objects that move at constant velocity may experence anol force nol equal o zero. The important question i: Which frames of reference 5 inertial ard which anes are net? This also rises the flowing question: Are there any inet frames of erence inthis universe? epee snyder IE sm Newion postulated that intial ames of reference do exist. This statement, coupled with tho definition finial ames of reference, may be considered @ more proper way to state Newton's 8am, Cony an experiment can estabish whether a particular fame of reference i inert (r,t be precise, “ietal enough fr the purposes needed), Let us go back to the car example. Tho tame of reference attached to tha ground, we would usualy says inertial. That i, we got an objet and make sure that al axial frces acting on iad upto ero, wo can then observe that the obec is, in fact, moving at constant velocity or, possibly, remaining at rest. In mest problems that wo willbe solving, the fame of reerence ofthe earth wil be considered an Ineral rae of reference. For al practical pupases, this means that Newtons 2nd law wil work ia Homer, fs Instnactive to understand tat the earth proves a reference ram that i less than “perfectly inal” An observer an the sun, for nstance, woul notice thal the otoct in question does, in fact, have an acceleration: the cenkpeal acceleration associlad wih the oral motion ofthe earth around the sunl The best inertial frame of elerence is the one assocated with stant stars and ary aher rame of reference that ls moving at aconstar velo relative to stant Stars. “The conceptual questions tha ell should help you leam to apply Newton's 1st and 2nd laws propery. Note that, throughout his problem, we wl assume thatthe frame of erence associated wih the eat is perectly net Panta Which aboot provides an inertial frame of roferance? ANSWER: the tp ofthe moving second hand ofa clock ‘eck thrown vertically upward ‘a pendulum swinging wth no a resistance © a skyeiver fang at tominal constas) velocity Correct ‘Assuming that the earh proves an ner rame of reference, an object moving at @ constant vlocty relative fo the earth would 0 provide an intial frame of reference, Parte ‘Yu are conducting an experiment insge an elevator that can move ina veteal shat. A lead is hung vertcaly fram the caling on sting, ands stationary wth respect to you, The tension inthe sting & eased to be 10% less than the free due to gaily on the load, No othe fares ate acting onthe load Wie of he following staements about tne slevator are caret? ‘check al that apply. ANSWER: The elevator isn inertial frame of reference, & The elevators not an neta rams of reference ‘The elevator may beat rest forthe duration ofthe entire experiment ‘The elevator may be moving at a constant velocty upward ‘The elevator may be moving a a constant velocity downward rating Partc & The elevator must be ace ‘You are conducting an experiment inside an elevator that can move ina vertical sha. A load is hung verealy fram the celing on a sting The tension inthe sting & mossured lobe exactly aqua othe free die to gravity on the load, No other frees aro acting on te load, Wah af he folowing slatenonts about the eovator ‘check al that apply. ANSWER: % The elevator isan neta frame of reference, The elevators not an neta frame of reference Y The elevator may be a ret The elevator may be moving at @ constant velocity upward The elevator may be moving a @constat velocity downward The elevator may be accelerating, “The elevator must be accelerating. Panto You are conducting an experiment inside rain carthat may move along evel al racks. loads hung trom the cling ona string. The load is rot swinging, ana openers sanyo ieee “IE a0 ‘ho sting observed to make a constant angle of 45° wih the horizontal, No forces other than tension and gravy are ating onthe load. Which ofthe folowing ‘check a that apply. ANSWER: ‘The tain i an inertial frame of reference. % The tran isnot an neal rameof reference. 4 The tan may be instantaneously at rst, The tain may be moving ata coosiant speed in 8 sight ie % Theta may be moving ata constant speed in a cee The tan must be speeding up. ‘The tran must be slowing down, & The tian must be accelerating, Correct ‘Since the torsion and the fore dus to gravy ate not eected opposite to each otha, the nt fore cannot possibly be 2ero-and yt the load sat rest elatve te the tain ca. Therfore, the car isnot anineial frame of reference It must be accelerating relative tothe earth, although it's not lear exactly how. Parte CConsir the train car described inthe previous part. Another experiment is conducted init Ant force of 20 Nis applied to an object of mass & lg. Can you elermine the acceleration of tho abject wth respect Io the rain, a, 80, what ts vale? Yes: 0.25 m/s? Yes: 4.0 m/s" Yes: 100 m/s. © No; there isnot enough nfrmation. Correct ‘The train car is not an inotial frame of reference, so Figs — mi would not work hero, PartF ‘1000-49 car is moving along a straight road down a 30" slope at constant speed of 20.0 m/s, What is the net force acting onthe ear? ANSWER: ©0N 10000. 17320 220000 N Correct ‘Te ca’ has 260 sccaerton: therfore, experiences 20 net force. Accoring to Newton's 15 aw, no net force is required to maintain @ constant veloc (in ‘an inatial ram of reference, of course). The car has a consta veclocty relative to tho earth; therefore, the cars also an neal rare of efrence Part ‘consis wo cars moving along the same straight readin opposite rections. Car A has a mass of 500 kg and has a constant speed of 20 m/s; car 8 has a mass (of $00 kg and a constant speed of 15 m/s. What can you Say about the net forces onthe cars? ANSWER, (Car A experiences groster net force than ar B (Car B exporences greater net frce than car A 1 Both cars exprince equal nol foros. Correct Each carhas zero acceleration; therefore, the net frce on each car, according to Newtons fat law, is zero, openers sanyo ieee “IE sa Part In an inertial frame of reference, a sees of experiments is conducted. In ach experimert, Wo otras forces are apie o an object. The magnitudes ofthese ‘ezoes ae given. No cher forces are acting on the obec. In which eases may the abject ossay remain at rest? ‘The forces applied ae a follows: ‘check al that apply. Hint 4. Using the net force In an inertial frame of reference, the stale of rests ony possible when the net force acting onthe objet is zero, In which cases can the forces acting on the ‘jet possibly ade up to ror? You may want fo draw same diagrams. ANSWER: 2N2N 200, 200 N 200; 201 N 2N2NAN 2N-2N2N 2N2N3N 2N.2N-5N 200; 20018: 5N Part! In an ner rame of reference, a sees of experiments is conducted. In each experiment, tWo othe forces are applied o an object. The magnitudes ofthese ‘ercas ar gen, No cher frees are acting on the obec. In wnich eases may the objet possiay mave ata constant veloc of 256 m/e? ‘The forces app ae a follows: ‘check al that apply. Hint 4. Using the net force In aninerial ame of reference, moving at @corstat velocity is only possible when the net force acting on he obec 2 era v2 2N 4 200, 200N 200; 201 N 4 2N2N3N 4 200, 200K: N Correct ‘You should have noticed that the sets of forces apple to the abject ae the same asthe ones In the prevous question. Newton's 18 aw and the 2nd tw 100) ‘makes no distinction betwoon the stale of rest and the stats of moving ata constant velocity (oven a high vlozty). I both cases, the net force applied to the ‘object must equal zero ‘Although some of the questions inthis problem may have seomes tcky and una, the sublllios eco are important in inproving conceptual understanding, ‘That understanding, in tum, will rable You te cect salve complex computational problems using Newtons laws. Pulling Three Blocks “Tres identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force FF. The magnitude of the tension in the sting between blocks B and Cis T’= 3.00 N' Assume tha each Kock has mass m= 0400 kg openers sanyo ieee “IE PartA ese rei? Wat isthe magnitude F of the force? Express your answer numereally in newtons. Hint 4. Find the acceleration of block B What isthe magnitude aw of the acceleration of Boek 8 Express your answer numerically in meter per second squared, Hint 1, Consider blocks A and B as a unit, Since blocks A and 8 are nt moving with respect to each ater, you can eat them as one lager object This larger object has the same ‘acceleration ae ether block A or black B alons, The advantage of sun an approach ie that the larger abject has only ene orca acing oni the Tension 3.00 N in the ope) ANSWER: ag = 375 m/s? Hint 2, Find the acceleration of al three blocks Wich ofthe flowing expressions gives the magnitude ofthe acceleration ofthe throe blocks? Hint 4. Consider ll hree blocks as a nit Since the the blocks ae not moving wth respect to one another, you can treat them as one larger “objact of mass equal to the sum ofthe masses of all tree blocks. Ths only horizontal fore acting on this lager boo is FF, s0 you can uss Nowion's 2nd law o determine an expression forts acceleration ANSWER a=k aE = ean oe ANSWER Ps 450 N Parte Wat is lonsion Tan the sting between Block A and block 8? Express your answer numerteally in newton Hint 1. How to approach the question ‘The tension Ty, is the only horizontal force acting on block A. Thus, you can fi the acceleration af block A and hen apply Newtris 2nd aw. Note tht ll epee since OIE three blocks have the same acceleration ANSWER: Tan = 150 N + Motion of a Block with Three Forces ‘The dagram bolow shows a block of mass m = 2.00 kg ona fictonloss horizontal sutace, as seen trom above, Three forces of magnitudes F = 4.00 N, F) = 6.00 N, and F) = 8.00 N are api tothe Bick, inal a res on the surface, at angles shown onthe dlagram. In ths pablem, you wit determine the resuttant (otal force vector rom the combination of he tree individual force vectors. All anges shoul! be ‘ensured counterclockwise rom the postive x axis (all angle ar poste) PartA ‘Caleate the magnitude of he total esutant force Fi: = Fy + Fa + Fy acting on the mass. Express your answer in Newtons to three significant figures. Hint 4, Definition of resultant force \Whon several forces are apotied to an objet, the vector sum is olon called the resultant othe resultant force Hint 2, How to find the resultant When working wth vectors, the general uli to think geometrcal bt to calculate using components. Thus to add vectors one estimates the sum by imagining the tio the sacond vector to be placed a tho po ofthe st the lai ofthe tid to placed at tho socond, et. Bu to calculate tn vector ‘Sum each Vectors represented by components In @ convener coordinate system and these compenents are ae to fia the components ofthe stm. Hint 3. Find the components of FF, ‘What are the x component and y component of 7 Express your answer as an ordered pair of numbers, separated by a comma to three significant figures. bine. xcomponent ot Fy The x comporet ot Fis Fco(0), wher @ eth rl bataen ih piven andthe vcas recto, ansves Fig, Fry * 363,169 N Hint 4. Find the components of Fy Find the x and y components ofthe vector Fy Express your answer as an ordered pa oth significant figures ANSWER: Pax Py 4onoae Hin Find tne components of Now in the 2 andy components of he resutant (sum) vector, (Oot forget to etude Fy.) openness ieee “DIE Express your answer as an ordered pair to three significant igure. ANSWER: Fox, Fey * 05804.75 Hint 6, Magnitude of F, ‘The magnitude of Fin torms of its x and y components Fh, and Fy is gvon by Bil = Fatty? answer Fje ie N Part 8 wnat angle does H, make withthe postive x axe? Express your answer In degrees to two significant figures. Hint 1. Find the angle symboicaly The angle that, makes withthe x axis can be determined if you know its x andy components, which you should have from your ealeulaion for Par A Wat isthe angle that, makes with he positive x axis? Answer symboliealy in ims of Fox and Fy Hint 4. How to approach this problem ‘When develoing a general formula for the angle, you can choose the vector to len any quadrant is easiest io have the vector lis inthe rst quacrart ANSWER: wo() ANSWER, 200 degrees Parte ‘What isthe magnitude of the masss acceleration vector, 7 Express your answer to two significant figures, Hint 1, Newton's 2nd law openness ieee “DIE Recall that F = rn, #0 you shouldbe tte t i [i aity easly here, 092 m/s? PartD \Wnat isthe direction of 2? In ether words, what angle does this vactor make wih respect othe postive x axis? Express your answer in degrees to two significant figures. Hint 4. Relation between the direction of @ and F Is ther any reason why the dracton of shouldbe diferent tom 7 ANSWER: 200 dogroos Parte How arr meter) wil the mass move in 5.0 5? Express the distance d in meters to two significant figures. Hint 1, Displacement with constant acceleration Remember tht we ave constant acceleration hee, 0 you cn use the equation, a(¢) = dy +v9t-+ Sat? hore dt) the displacomont at time & Part F ‘What isthe magnitude of he velocity vector af the block at = 5 os Expres you ewer in meters per second to two significant figures, Hint 1. Velocity with constant acceleration Remember, we have constant acceleration, aw because the obec stats fom rest, the veloc vector le paral othe acceleration vec, Therefore, ort at ANSWER: PartG In what rection isthe mass moving at ime t = 5.0 8? Thats, what angle does the velocity vector make wth respec tothe positive x axis? Express your answer In degrees to two sigifiant figures Hint 1. Relationship between the direction of @ and & openness aie “1 come ese reo? ‘The mass stars at est and is accelerated in one direction. Therefore, i must have veloc inthe dacton ofthe acceleration, and that drecton onl, ANSWER: 290 dogroos Two Hanging Masses “Two blocks wih masses My and Mz hang ono under the other Fortis problem. ak sceeleration due to gray. the postive rection to be upward, and use 9 forthe magnitude of tho ‘Case 1: Blocks at rest For Parts A and @ assume the blocks ar at rt. Parta Find Ty, the tension nthe lower ope. Express your answer in trms of some or all ofthe variables Mj, Mz, and 9. Hint 1. Free-body aiagram Isolate the low block (mass Mz) by considenng ist the forces that act on. Use Newtons 2nd tw while noting tha the aceseration ofthis Beck is 2610 Hint 2. Sum of forces. \Wirte down the sum of he y components of llth forces acting on the lower block. Express your answer in ferms of some of ll ofthe variables Mj, Ms, T and a. ANSWER: Dy = May =0= Ty Mag ANSWER: Parte Find T;, the torsion nthe upper rope. [Express your answer in forms of some oF ll of he variables Mi, Ma, and 9. Hint 4. Sum of forces \Wirte down the sum ofthe y components of ll the frees acting onthe unper block. Express your answer in terms of some or all ofthe variables Mj, Ma, T., Ts, and ANSWER: Dy =0= T-T-Mo openness ieee “DIE ANSWER, T= (Mi + Mo ase 2: Accelerating blocks For Parts and D the blocks are now accelerating upward (ve tothe tension inthe sings) wth acceleration of magnitude a Parte Find 2, the torsion inthe lower rope Express your answor In terms of some or all of tho valables Mj, Mz, a, and 9 Hint 1. Sum of forces. [Apply Newt's 2nd law, 33/F, = Mya, tothe lower block, Wie the sum ofthe y components ofthe forces, Express your answer in terms of some oral of the variables Mi, Moy Ts and 9 ANSWER: TPy= Mas T-Mhg ANSWER, Ty = Mza~ Mzgsin(1.5708) Correct Good! Now natice that acceleration cts inthe tension equation the same way that gravy does. If we lok at a limting case in which the block of mass Mp is Infos fa, accolrating downwars with a ~ —g, thon the tension goes to 20 Panto Find The sion nth upper rope. Expross your answor In terms of some or allo tho varlables Ms, Mz, a, and g Hint 1, Sum of forces: consi the block of ms My 2 an isolates system and apply Newton's 2nd law, 32 Fy = Ma, win the value of T; found inthe previous par. ANSWER: (My + Ma)a-+ (My + Ma)osin( 1.8708) Correct “The force exerted by a rope sa result of he ropes tension and points along the rope. ‘A World-Class Sprinter Wior-class sprinters can accelerate out ofthe staring Blocks wth an acceleration that is nearly horzontal and has magnitude 15 m/s? Part a How much horizontal force F musta sprinter of mass 49, exert onthe starting blocks to proce tis accolration? Express your answer in newtons using two significant figures. Hint 1. Newton's 2nd taw of mation ‘Accorting te Newton's 2nd law of maton, if net extemal force Facts on body, te body accelerates, andthe nat force is equal othe mass m ofthe body times the aeceteration a of the Body Faq =a. openers sanyo ieee “IE ANSWER: F214 N Parte \Which body oxo the force that propos the sprinter, tho Blocks othe sprintar? Hint 1. How to approach the question To start moving forwar, sprinter push backward onthe string blocks with tel fet. Newton's Slow ells you thatthe blacks exer a fore onthe sprinter ofthe same magntuds, but cpposio in dracon. ANSWER: © the bbeks the spiter Correct ‘To stat moving forward, sprinters push backward onthe stating blocks wih thei feet. As a reaction, te Blocks push forward on thi feat wth force ofthe ‘same magnitude, This extemal force accelerates the sprinter forward Enhanced EOC: Exercise 4.24 no upward noma fore exerted by the lors 620 N on an elevater passenger who weighs 650 N. You may want ta review j{ELaaaes 112. 117) For general problem-solving tps and strategies fr this topic, you may want to view a Video Tutor Solution of Determining acceleration from fore. Panta What isthe magnitude of he acceleration? Hint 1. How to approach the problem ‘Start by dating a sketch with an appropiate coordinate system and including al of the forces acting on the elevator passenger. yin this potion s the noma ore na equa othe passenger's weight? What must be happening? Find the esstat net force acting onthe elevator passenger, and using the appropiate equations, calculate the passenger's acceleration, What adational (uanty do you need to fn to calulate the acceleration? ANSWER, a= 0452 m/s? Pane nat isthe dracton ofthe acceleration? Hint 1. How to approach the problem ‘Suppose you were inthis elevator. What would toa Ike i the noma fore (rom the elevator floor) acting on you nthe upward retin were less than the foxes of gravy acting on you inthe wrard rection? Suppose the normal farce was larger than ravi —whien way would you have? In which drection i the resutant force acting on the elevator passenger? ANSWER: upward eyesore saya gmat alaska IE oo woe ‘ate ce reo? Forces on Blocks in an Elevator Conceptual Question “Two blocks are stacked on top of each other on the flora an elevator, Far each ofthe following sustons, sleet the coect relationship between the magetudes af the ‘oo forces given, ‘You wil be asked twa questions about each of thes situations. Each situation is described above the fst in the pairof questions. Do rt assume arytring abut a given situation excepk for whats given in the ‘desertion fr that pateuar st Frstiuation ‘The elevators moving downward ata constant speed. Part Hint 1. Comparing forces that act onthe same object, When comparing fores that act onthe same objet, draw 2 free-body dagram ofthe object being acted on. Then, determine the acceleration af he object. By Newton's 2nd la, the net force must be proportional otha cbjeet's acceleration, Hint 2. Draw a free-body dagram forthe top block [Complete the fee-body diagram forthe top block by drawing the fore onthe top block due tothe earth, This force should act atthe center ofthe block ANSWER: ANSWER: rater than © equalto ‘The magnitude of the fre of the Bom block an the op Blk ie tan tha magnude ofthe force ofthe earth on the top Block. Luneooun compared to Part 8 Hint 1. Comparing forces that do not act an the same abjact openness ieee “DIE 200 come Tate ce reno? Ir two forces 6 not act onthe same object, they wil not appear on the same fee-body clagram. Therefore, Newton's 2nd aw cannot be used Yo determine therrelatve 20s ofthese frees, Cera forces ean, howover, be compared using News 3s am, Hint 2, Newton's 3rd law Newtons Slaw stats that when wo objects exer fores en each othe, these forces are aluays equal in magnitude ard apposite in rection. Ths, if you ‘siting in a char, the force tho char exerts upward on you's exactly th same as tho force you exer dowrward onthe chair, rgarcoss of whether you ‘78a rest nthe char, or have you fet up on your desk, or arn the process of geting up out of he cha, ori the process of andng inthe cha after jumping rom a great neigh. does nt matter ANSWER: greater than © equal to “The magnitude of the force of the bottom block ontop Back IS oon han the magnlude ofthe force ofthe tp black on bottom back. Lunknoan compared to Second stvation ‘The elevator is moving downward at an increasing speed. Parte Hint 1. Determining acceleration HF the elevators moving downward at an incre Ing speed, hat isthe drection ofthe elevato’s aceslaration? ANSWER: wars © dour ANSWER: ster than equal to “Tho magnitude ofthe force of tho bottom block on to top BLOCKS jes than the magnitude ofthe free ofthe eats on the top Block. known compared to art D Hint 1, Newton's rd law in accelerating elevator [Nowtor’s Slaw holds that fores come in pais of equal magnitude and opposite action in all cases. Thus, the accooraton oft alo the lative magnitude of two forces thal fom a Sd aw pa ANSWER: ater han © equalto “Tho magnitude of tho force of tho bottom block on to 19p BLOCKS jeg tan ‘ho magnitude of the force ofthe top block on the Blom block. known compared to Correct, Tried stuation openers sanyo ieee “IE ano “The elevators moving uoward Pate Hint 1. Determining acceleration Ifthe elevators moving upward, whats tho retin of the elevators acceleration? wars downware © unkroun ANSWER: oate: than ‘eal to The magatude of the force ofthe Bttom block onthe op Bleck IS ore than the magnude of the force ofthe earth on he top block 1 unknown compares Correct Eventhough he elevators moving upwards, you do nat knowin which drection iis accelerating, of indeed whether the elevator accelerating at al! Part F ANSWER: rate: han © equal to ‘The magnitude of he force ofthe bottom block onthe top Bock IS oes nan the magntude ofthe force ofthe top Block on the batom block unknown compared to Newton's 3rd Law Discussed Learning Goal fo understand Newtor's a aw, which stats tata phystcal interaction alvays generates a pair forces on the two interacting bodes. In Prince, Newton wrote: To every action thors always opposed an equal action: the mutual actions of two bods upon each thor aro always equal and rected to contrary pats (arstaion by Cajos) ne pirase aftr the colon (often ames from textbooks) makes it clear that this Isa statement abou! the nature of fore. The conta! deals that physical interactions (c.a. dus to gravity, bodies touching, alate forces) cause forces io ase betwoon pas cf bodies. Each palvise intraction produces a pa f opposite forces, one Being an each bod. In sunmary, each pyseal interaction between two bodes generates a pa of forces. Whatever the prysiel cause of the Interaction, the force {on body Arm body is equal in magnitude and opposite in direction to the force on body fom body A Incidentally, Nawion states that he word “acon” danctas both athe fore dus to an interaction ang (b) the changes in momentum that impars te tha two intractng bods. I you havent leamed about momentum, dort wony: for now his is just astlement about the orgin of forces. Mark each ofthe following statements as ve or fale, Ifa statement refers fo "wo bosos” interacting via Some force, you arena fo assume thal these two bodes have Parta Every fore has one and en one Slaw pai force ANSWER, openers sanyo garter “DIE sa Parte “Tho two forces in each pai act in opposite roctions. ANSWER, false Correct Parte “The twa frees n each pair oan ear both act onthe same Body or they can act on etteant bod, ANSWER: PartD “Tho two forces in each pair may have diferent physical origins (forinstance, one ofthe frees coud be due to gravity, an its pa force could be due to freon or lee charge). ANSWER: Parte ‘Tho two forces ofa aw pair almay’s act on dierent boos. ANSWER: Correct Part F Coven that we boss interact va some force, the accelerations of these two bodies have the some magntuds but opposte rections. (Assume no oer forces act oneier body.) Hint 1. P= ma Remember = mdi: tthe fore are equal in magrstas, must the accelerations also be of equal magnitude? © false Correct Newtons 3 law can be summarised as follows: A physical ieraction (e.g, gravity) operates between two interacting boss and generates par of oppose {orcee, ane on each body. It offers you a way to test for rel forces (.e, those that belong on the force side of ZF = mai-thare should bea Sd aw par force ‘operating on some cher body foreach eal force that acts onthe body whose acceleration ls undar consideration, openers sanyo ieee “IE si Part ‘Accortng to Newtons Sa, the force onthe (smaller moon due othe (argo) earth Is tern magnitude and antiparallel to he fore onthe eath due to the moon, gator in magnitude and paral othe force on the eath due to tho moon. "© equal in magritude but ansparall to the fore onthe earth du to the moon ‘aval in magnitude an paral to the force onthe earth duet the moon ‘smaller in magntude and artpaall othe force onthe earth due tothe meen ‘smallor in magnitude and paral fo the force onthe earth dust tho moon Tension Definition “This problem concoms the concept of tension ina rope. Consider a rope subjected fo @ poling force ants two ends es shown in. The rope is stationary, An arbitrary point P eves the ope ina a fe-hand segment L and a rghchand seamen: - - pall pall Part Fer sogmertR and sogmont Lo hold toethor, they must exert frcas on gach other. What isthe rection ofthe free certed on segment R by segment L? Hint 4, Look atthe forces The fores on segment R are 4. te free ve to Land 2 to pl 1 tho right) tthe right end of tho rope, nat must be tra about these two forces the rope isto remain stationary? ANSWER: Parte ‘Assume that segment R exers afrce of magnitude Ton segment L. What Is the magnitude Fy ofthe force exerted en segment R by Segment L? Give your anawer in terms of T and other constants such ao Hint 1. How to approach the problem ‘Apply Newt's 3 aw. ANSWER: A= T openers sanyo ieee “IE sa woe ‘tec reno? Correct ‘The magnitude of the fee exerted by one prt ofa ope on anther ta certain poet scaled the fension at that pnt, Tensions often designated with the symbol. The tension eal the magnitude ofthe free with which the ropa pulls on whatever is attached tots ends Parc "Now imagine two points, @ and P, that evi the rope into Segments LM and R. The rope remains salionary, Assume thal segment L exes force of magrituse Fixe on sgment M. What the ‘magnitude Fhar o the force exerted by segment R on segment M? Give your anewor interme of Fac and constants such as 9. « pull pall Hint 1. How to approach the problem Draw a reo body diagram forthe section M of the rope. Hint 2, Relative magnitudes ofthe two forces. ‘The magnitude of he force exerted by Segment Lon segment Mis the magnitude ofthe force exerted by segment Ron segment M? ANSWER: ANSWER: Foc= Fat Correct ‘This answer implies thal inthe absonce of gravity, th tnsion in a stationary rope may bo taken tobe constart. rope that, unlike those usually studied in mechanics problems, actualy has @ sinficatinrtia m. The tension atthe right end of his rope is T; and tal a the lett ends T. The rope has an acceleration dying 10 the righ ‘Complete the flloning equation forthe force on ection fo be to the Hh. Give your answer in terms of T:, Ts, and constants such as 9 sion of rope of ineria m, taking the postive 7_PPDPIDIPIPIID 7 m n Hint 1. How to approach the problem Use Newton's 2nd law of mation, openers sanyo ieee “IE 0 Parte mien of he flowing phrases, they appear ina problam, alow you to assume tht T; = Tina horizontally rented pe? [A The rope is masstess, 3. The rope moving at constant speed The ope i stoned with negigble sag, ANSWER, only 2 only only © Aor aac RorBorc Correct Having ether negligible mass or deng in uniform mation (constant vlocty) both cause T; =. This an be seen using Newons 2nd law: SF = ma. Tae fel foce F is ven by Ty —T). rm ~ 0 ori =O than the net free wi be zero, Impiing that T} = Ty. Enhanced EOC: Exercise 4.28 [A porson pulls horizontally on block in the figure, causing both blocks to move fogeter as aun You may want to review ({Dkpases #28 25) For general problem-solving tips and strategies forth topic, you may want to view a Video Tutor Salton of A ‘Nawlon's In aw savaoe Pull Horizontal table Parta \Wnil this eystom is moving, make a carefully labeled toe-body lagram of Bleck A ifthe table is Fctoness. Draw all relevant force vectors with thelr tall atthe dot, The orientation of your vectors wil be graded, Th ‘graded, but the relative length of one tothe other wil be graded. act length of your vectors wll not be Hint 1. How to approach the problem Fist, plture what happening. What forces) does black B exert on black A? Ave there ary other forces acting on block A? Ir the tales Hctinless, what happens to block B asi ls pulled? Since block A and lock & mave as un, what canbe sald about ther accelerations? ‘S01 there a nat frce on block A? “Thine aout what ca ths resultant free on look A. In what erection must at? ANSWER: openers sanyo ieee “IE Parte nites aystem is moving, make a careful labeled toe-body dagram of block Ai there's fretion between block B andthe table an th pls equal othe ‘ction force on black Bd tothe ttle Draw all relevant force vectors with ther tall at the dot. The orientation of your vectors will be graded, The exact length of your vectors will not be ‘graded, but tho relative length of one tothe other wil be graded. Hint 1. How to approach the problem How has fiction wih the table changed this problem from par A? What isthe seceleration of Block 8 now? ‘Since block A and black @ rave a a unt, what can be said about thir accelerations? Soe there @ net fore on block A? ANSWER: Free-Body Diagrams and Newton's Laws \wmen solving problems involving orcs and Newtons laws, 1 flloning summary of things to do wil start your mind thinking about ging involved inthe problem at Problem Solving: Free-Body Diagrams and Newion's Laws 2 Consider any one objct (ta time, and draw a reeady cagram for that body, showing ll ne forces acting on that body. Do at show any forces thatthe epee sanyo ieee tang “OIE ss ome Tecate? body exerts on other bodies. If savera bodies are involved daw afree-body Gagram for each body separaely,shoning al he forces acting on thal body 5, Nouns second law volves vectors, and it Is Usual important o resolve vectors io companents, Choose an x andy axe Ina way that simp the caleulavon. 4 For ach body, Nowtors Second law can be applied to the x and y components separately. That isthe x component ofthe nt fore on that ody wil be relates tothe component ofthat body's acceleration: SPs — ma. ang sim for they rection, 5. Salve the equation or aquations fer ho unknowns) ‘Apply these stops Use the stops outed above to find the magnitude ofthe aeceleration a ofa chair and the magatude ofthe normal force Fy acting onthe chair Yusot pushes a eae ‘of mass m = 55.0 kg across a carpeted floor with a force Fy the subscict ‘here is lowerc 196 N cirocted at {= 35.0 degrees below th horizontal. The magnitude of the kinetic tctonal force between the carpet ad the hair's Fy = 107 N Draw the vectors starting atthe black dot. The location and orlentation ofthe vector will be graded. The length of the vectors wil not be graded. ANSWER: Parte Wich set of coortnate axes isthe most convenient to use in this problem’? Hint 1. Determine the direction ofthe acceleration Incicale the cretion ofthe chairs acceleration onthe figue blow, ‘The orientation ofthe vector will be graded. The location and length of th ANSWER: ctor will not be graded. openness ieee “DIE ‘ate ce reno? ANSWER: Correct Now tat you have selected a coordinate system, you should resolve the forces into x and y components so that you can aosly Newtons sacond aw to each ‘coordinate direction independent Parte Use the component form of Newton's second kw fo wrt an expression forth x component ofthe nt force, UF Express your answer in forms of some or all ofthe variables: F's, Fy, Fp, 8, and Fy. Hint 4. Find the x component ofthe pushing force ats Fy thx component oth fre Fy ext by Yost? Joe Fy and Express your answor in trms ofthe vari Hint 1 Right angle tangle teganemetry Keep in ming thatthe cosine ofan angles defined a the length of the adjacent leg vided by the length of he hypoteneuse, The sine ofan angles tha length ofthe opposite log divided by the length of he hypotensuse. Apply these dfiitions to the trangleformad by Fy. 8, Fye and Fry tepals gman Fy ANSWER: jst) ANSWER, BF. = Fyeos(@)— Fk — mas PartD Use the compeneet frm of Newtons second nw fo wite an expression for they component ofthe nel foro, ewer interme of some oral ofthe variables: Fs, Fy, F, 0, and Fy. Express you Hint Find he y component of the pushing frce Ut Fy. thy conpoent tte toe Fi, exo by Ys” Express your answer In terms of the variables F, and 0. Hint 1. Right angle triangle trgonometry ‘oop in ming that th cosine of an angle is dened as the length of he adjacent eg vided by tho length ofthe hypeter the length ofthe opposite eg divided by the length of he hypoteneuse. Apply these definitions to the Wang formed by Fy, 8, Fpx and Foy 1. The sine ofan angles Fre ANSWER: Fy = —Fysin(®} ANSWER, BF, = —Fysin(@)—(Fo~ Fy) = may Correct ‘You have created two equations that describe the mation ofthe chair EF, Fycosd Fy mas ‘and ER, =Fy Fe Fysind may ‘Salve these equations to find Fy and a Parte nat isthe magnitude of the acceleration a ofthe cha? What ls the magnitude ofthe normal force Py acting onthe chai? Express your answers, separated by a comma, in metars per second squared and newtons to three significant figures. ‘You ais not open its fortis pat. epee saya “DIE come ese rei? ANSWER, Fy Incorrect; Try Again 0.277.624 m/s*,N Pushing a Chair along the Floor [A chai of weight 195.N Fos atop a horizontal lor, the floors not tories. You push onthe chair with a force of F'= 37.0 N doce at an angle of 38.0° below the hoizetal andthe chai slides slang the floc. Parta Using Newton's laws, calculate, the magnitude ofthe normal fore thatthe flor exerts onthe cha. Express your answer in newtons. Hint 1. How to approach the problem ‘To atve this problam you neato focus on the forces thal havea veieal component. In fact, because the direction of motion is horzonal the char sos ‘along te floor ath the acceleration ofthe char andthe net force acting on the cha ae purely harzortal. This canbe rue ony if the net vertical force ‘acting on the char is zor, thal, if the noal fore exerted on the chat by the lor balances all he ether vertical frees acting on the cha. [Also in any problem involving forces you should alas 6raw afoe-bdy eagram that shows al the forces acting on the system. To do that, choose a coarse System and identity al the forces acting on the ena Hint 2. Choosing the correct tree-body diagram Lat f be the fiction force, F be the force you exert on the chal, and ui be the weight ofthe chair. If you choose the x axis to be parallel tothe floor, which free-body diagram would corectly represent the situation described inthe reduction ofthis problem? 7 f @ PF, iv F Ls : in te) oo" Hint 4. Direction of the friction force Force of ftion opposes relative mation between sutaces, ANSWER: Hint 3. Find the vertical net force Let the postive y axis point upward, and etn be the magnitude ofthe normal ores exerted onthe chairby the fae, w be the magntude of the weight of he hat and F, be the magnitude othe y component of the force you exert onthe chair whan you push. What f the vertical nat force, thats, the y component ofthe nat force, acting on the char? Hint 4. How to approach the problem From your ree-body dlagram you can eee thatthe normal ore pnts upward, whereas the weight pln ‘exer on th chai has a vertical component which s parallel to th weigh downward, Moreover, the free that you ANSWER: openness ieee “DIE sa n+w+h, en-w-F, Hint 4. Find the vertical component a the force that you exert on the chair Fina F,, the magnitude ofthe verlesl component of he fre tat you exert onthe eh when you push Express your answer in newton Hint 4. Components of @ vector ‘Consider a vector A that forms an angle @ with the positive x axis. The x and the y components of A are, respectively, Az = Acos® and A, = Asind, whore isthe magnitude of the vector. ANSWER: Fy aN PSS 5.1 Newton's First Law: Equilibrium of a Particle Learning Goal ‘To practice Problam-Solving Stiatogy 5.1 Nowon’s Fist Law Equlixium of @ Parco ‘Suppose that you want lo move a heavy box wth mass 30.0 kg across a carpeted lor. You try pushing hard on one ofthe edges, but the box does not move. Suppose that you ae pushing agaist th box rom an angle 90.0" above horzontal wih 2 force of magnitude 240 N, Whats the magnitude of the Fsevon fore acting onthe box? Problem-Solving Strategy: Newton's frst law: Equilibrium of a particle IDENTIFY the reevant concepts: You must use Newors fst 1a or any problem that involves forces acting ona body in equim. the problem involves mor than one body andthe bodies interact lin eacn other, youl alsa need to ure Newton's thd law Be cern hat you lent the torgt variables) ‘SET UP the problem using the flowing steps 1. Draw a simple sketch of th physical stuation, showing dimensions and angles. 2, Draw afroe-body diagram for each body that sn equim. In your ree-b0dy cagram, include only one body 3, On your fee-boy cgram, draw 2 force vector for sach ineracton, and label bach force wh a symbol representing the magne ofthe fore, Hf you know th ang a which aforesis docted, daw the angle accurtoy. 4. nat show in the tee-bodydlagram any Torees exered by the body en ary other body. neue only forces that act onthe body. 5. Choose a sel of coorinalo axes, and incluce them in your rea-boay cagra. (thee Is more than one body inthe problem, choose axes for ach body separately) EXECUTE the soluion 9 flows: 1. Find the components of each free 2 Satta algeerac sum of al x components of force equal o era. In a separate equation, set the algabric sum of lly components equa o zor 31 here are two or mor bodes, repeat al of the above stops foreach body. I the bores interact with eachother, use Newton's tht kw to eat the forcos ‘thay exer on each other. 4. Make sur that you have as many independent equations asthe numb of unknown quantities. Thon, solve tho uations to oblan the target vaabs EVALUATE your answor Look at your osu, and ask whether thy make sense. Whan the result isa symbolic expression o fom, ty to check your formula In spacial cases for which you can guess what the resus ought oe, IDENTIFY the relevant concepis| Since the box sits ina fted poston its in equlloium and Newtons fst law apois. You wll ot need to use Newteris thi law to determine the magritude of any of tho forces, The tage! variable the magnitude ofthe Feo fore, SET UP the problom using the following stops openers sanyo ieee “IE a

You might also like