CHAPTER 4: Dynamics: Newton s Laws of Motion. Answers to Questions. 0 10m s x 10 m. v v a x x a

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1 CHAER 4: Dnaic: ewtn Law f Mtin Anwer t Quetin 1. he child tend t reain at ret (ewtn 1 t Law), unle a ce act n her. he ce i applied t the wagn, nt the child, and the wagn accelerate ut under the child, aing it l lie the child fall bacward relative t the wagn. If the child i tanding in the wagn, the ce f ictin between the child and the btt f the wagn will prduce an acceleratin f the feet, pulling the feet ut under the child, al aing the child fall bacward.. (a) Mar ee the b ta tatinar with repect t the grund. here i n hrizntal ce n the b ince the truc bed i th, and the b cannt accelerate. hu Mar wuld decribe the tin f the b in ter f ewtn 1 t law there i n ce n the b, it de nt accelerate. (b) Chri, hi nn-inertial reference ae, wuld a ething abut the b being thrwn bacward in the truc, and perhap ue ewtn nd law t decribe the effect f that ce. But the urce f that ce wuld be ipible t pecif. 3. If the acceleratin f an bject i zer, then b ewtn ecnd law, the net ce ut be zer. here can be ce acting n the bject a lng a the vectr u f the ce i zer. 4. If nl nce ce act n the bject, then the net ce cannt be zer. hu the bject cannt have zer acceleratin, b ewtn ecnd law. he bject can have zer velcit an intant. r eaple, an bject thrwn traight up under the influence f gravit ha a velcit f zer at the tp f it path, but ha a nn-zer net ce and nn-zer acceleratin thrughut the entire flight. 5. (a) A ce i needed t bunce the ball bac up, becaue the ball change directin, and accelerate. If the ball accelerate, there ut be a ce. (b) he paveent eert the ce n the glf ball. 6. When u tr t wal eat, u puh n the grund (r n the lg in thi cae) with a wetward ce. When u puh wetward n the aive Earth, the Earth ve iperceptibl, but b ewtn 3 rd law there i an eatward ce n u, which prpel u ward. When waling n the lg, the relativel light and unretricted lg i ee t ve, and when u puh it wetward, it ve wetward a u ve eatward. 7. B ewtn 3 rd law, the de r wall eert a ce n ur ft equal in agnitude t the ce with which u hit the de r wall. If u hit the de r wall with a large ce, then there will be a large ce n ur ft, cauing pain. Onl a ce n ur ft caue pain. 8. (a) When u are running, the tpping ce i a ce f ictin between ur feet and the grund. Yu puh ward with ur feet n the grund, and thu the grund puhe bacward n u, lwing ur peed. (b) A fat pern can run abut 1 eter per ecnd, perhap tae a ditance f 5 eter ver which t tp. he 5 eter wuld be abut 5 tride, f 1 eter each. he acceleratin can be fund Eq. -11c. v v 1 v v a a earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 67

2 Chapter 4 Dnaic: ewtn Law f Mtin 9. When giving a harp pull, the e i the uddenne f the applicatin f the ce. When a large, udden ce i applied t the btt tring, the btt tring will have a large tenin in it. Becaue f the tne inertia, the upper tring de nt iediatel eperience the large ce. he btt tring ut have re tenin in it, and will brea firt. If a lw and tead pull i applied, the tenin in the btt tring increae. We appriate that cnditin a cnidering the tne t be in equilibriu until the tring brea. he ee-bd diagra the tne wuld l lie thi diagra. While the tne i in equilibriu, ewtn nd law tate that up dwn. hu the tenin in the upper tring i ging t be larger than the tenin in the lwer tring becaue f the weight f the tne, and the upper tring will brea firt. 1. he acceleratin f bth rc i fund b dividing their weight (the ce f gravit n the) b their a. he -g rc ha a ce f gravit n it that i twice a great a the ce f gravit n the 1-g rc, but al twice a great a a a the 1-g rc, the acceleratin i the ae bth. 11. Onl the pund reading wuld be crrect. he pring cale wr n the fact that a certain ce (the weight f the bject being weighed) will tretch the pring a certain ditance. hat ditance i prprtinal t the prduct f the a and the acceleratin due t gravit. Since the acceleratin due t gravit i aller b a factr f 6 n the n, the weight f the bject i aller b a factr f 6, and the pring will be pulled t nl ne-ith f the ditance that it wa pulled n the Earth. he a itelf den t change when ving t the Mn, and a a reading n the Mn wuld be incrrect. 1. When u pull the rpe at an angle, nl the hrizntal cpnent f the pulling ce will be accelerating the b acr the table. hi i a aller hrizntal ce than riginall ued, and the hrizntal acceleratin f the b will decreae. 13. Let u find the acceleratin f the Earth, auing the a f the eel falling bject i = 1 g. If the a f the Earth i M, then the acceleratin f the Earth wuld be fund uing ewtn 3 rd law and ewtn nd law. Ma a g M Earth bject Earth Earth dwn Since the Earth ha a a that i n the rder f 1 5 g, then the acceleratin f the Earth i n the 5 4 rder f 1 g, r abut 1. hi tin acceleratin i undetectable. 14. (a) lift the bject n the Earth require a ce the ae ize a it weight n Earth, 98. lift the bject n the Mn require a ce the ae ize a it Earth Earth weight n the Mn, Mn Mn Mn (b) he hrizntal accelerating ce wuld be the ae in each cae, becaue the a f the bject i the ae n bth the Earth and the Mn, and bth bject wuld have the ae acceleratin t thrw the with the ae peed. S b ewtn ecnd law, the ce wuld have t be the ae. 15. In a tug f war, the tea that puhe hardet againt the grund win. It i true that bth tea have the ae ce n the due t the tenin in the rpe. But the winning tea puhe harder againt the grund and thu the grund puhe harder n the winning tea, aing a net unbalanced ce. tne up 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 68

3 Giancli hic: rinciple with Applicatin, 6 th Editin he ee bd diagra belw illutrate thi. he ce are grund, G 1, the ce n tea 1 the, the ce n tea the grund, and G R, the ce n each tea the rpe. hu the net ce n the winning tea i in the 1G R winning directin. 16. (a) he agnitude i 4. (b) he directin i dwnward. (c) It i eerted n the pern. (d) It i eerted b the bag f grcerie. G 1 Large ce grund ea # 1 (winner) 17. If u are at ret, the net ce n u i zer. Hence the grund eert a ce n u eactl equal t ur weight. he tw ce acting n u u t zer, and u dn t accelerate. If u quat dwn and then puh with a larger ce againt the grund, the grund then puhe bac n u with a larger ce b ewtn third law, and u can then rie int the air. 18. In a whiplah ituatin, the car i vilentl puhed ward. Since the victi bac i againt the eat f the car, the bac ve ward with the car. But the head ha n direct hrizntal ce t puh it, and it lag behind. he victi bd i literall puhed ward, ut under their head the head i nt thrwn bacward. he nec ucle ut eventuall pull the head ward, and that caue the whiplah. avid thi, ue the car headret. 19. he truc bed eert a ce f tatic ictin n the crate, cauing the crate t accelerate.. On the wa up, there are tw ce n the blc that are parallel t each ther cauing the deceleratin the cpnent f weight parallel t the plane, and the ce f ictin n the blc. Since the ce are parallel t each ther, bth pinting dwn the plane, the add, cauing a larger agnitude ce and a larger acceleratin. On the wa dwn, the ae tw ce are ppite f each ther, becaue the ce f ictin i nw directed up the plane. With thee tw ce being ppite f each ther, their net ce i aller, and the acceleratin i aller. 1. Aue ur weight i W. If u weighed urelf n an inclined plane that i inclined at angle, the bathr cale wuld read the agnitude f the nral ce between u and the plane, which wuld be W c. R R Equal and ppite tenin ce ea # G Sall ce grund Slutin t rble 1. Ue ewtn ecnd law t calculate the ce. a 6. g Ue ewtn ecnd law t calculate the a. 65 a 115 g a.3 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 69

4 Chapter 4 Dnaic: ewtn Law f Mtin 3. Ue ewtn ecnd law t calculate the tenin. a 3 96 g In all cae, W, where g change with lcatin. (a) W (b) W (c) W (d) W 76 g Earth Earth 76 g Mn Mn 76 g Mar Mar Space Space 76 g 5. (a) he. g b reting n the table ha the ee-bd diagra hwn. It weight. g Since the b i at ret, the net ce n i the b ut be, and the nral ce ut al be 196. (b) ree-bd diagra are hwn bth be. 1 i the ce n b 1 (the tp b) due t b (the btt b), and i the nral ce n b 1. 1 i the ce n b due t b 1, and ha the ae agnitude a 1 b ewtn 3 rd law. i the ce f the table n b. hat i the nral ce n b. Since bth be are at ret, the net ce n each b ut be. Write ewtn nd law in the vertical directin each b, taing the upward directin t be pitive. g g 1. g g 1 1 g 98.. g p b (#1) Btt (#) 1 1 1g b 1 6. ind the average acceleratin Eq. -. he average ce n the car i fund ewtn ecnd law..78 v v 6.4 v v 95 h 6.4 a 3.3 avg 1 h t 8. avg avg a 3 11 g he negative ign indicate the directin f the ce, in the ppite directin t the initial velcit. 7. he average ce n the pellet i it a tie it average acceleratin. he average acceleratin i fund Eq. -11c. r the pellet, v, v 15, and.8. a avg avg v v a 7. 1 g avg 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 7

5 Giancli hic: rinciple with Applicatin, 6 th Editin 8. We aue that the fih line i pulling verticall n the fih, and that the fih i nt jering the line. A ee-bd diagra the fih i hwn. Write ewtn nd law the fih in the vertical directin, auing that up i pitive. he tenin i at it aiu. a g a 1.8 g g a hu a a f 1.8 g i the aiu that the fih line will upprt with the given acceleratin. Since the line bre, the fih a ut be greater than 1.8 g (abut 4 lb). 9. he prble a the average ce n the glve, which in a direct calculatin wuld require nwledge abut the a f the glve and the acceleratin f the glve. But n inatin abut the glve i given. B ewtn 3 rd law, the ce eerted b the ball n the glve i equal and ppite t the ce eerted b the glve n the ball. S calculate the average ce n the ball, and then tae the ppite f that reult t find the average ce n the glve. he average ce n the ball i it a tie it average acceleratin. Ue Eq. -11c t find the acceleratin f the ball, with v, v 35., and.11. he initial directin f the ball i the pitive directin. a avg avg v v avg a.14 g hu the average ce n the glve wa 78, in the directin f the initial velcit f the ball. 1. Che up t be the pitive directin. Write ewtn nd law the vertical directin, and lve the tenin ce. a g a 4 1 g Ue Eq. -11b with v t find the acceleratin. t " g " v t at a g ' 9.8 he accelerating ce i fund b ewtn nd law. a g Che up t be the pitive directin. Write ewtn nd law the vertical directin, and lve the acceleratin. a g 9.8 a g Since the acceleratin i pitive, the bucet ha an upward acceleratin. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 71

6 Chapter 4 Dnaic: ewtn Law f Mtin 13. In bth cae, a ee-bd diagra the elevatr wuld l lie the adjacent diagra. Che up t be the pitive directin. find the MAXIMUM tenin, aue that the acceleratin i up. Write ewtn nd law the elevatr. a a a g.68 g g 485 g find the MIIMUM tenin, aue that the acceleratin i dwn. hen ewtn nd law the elevatr bece a a a g.68g g g If the thief were t hang tinle n the heet, r decend at a cntant peed, the heet wuld nt upprt hi, becaue the wuld have t upprt the full 75 g. But if he decend with an acceleratin, the heet will nt have t upprt the ttal a. A eebd diagra f the thief in decent i hwn. If the heet can upprt a a f 58 g, 58 g then the tenin ce that the heet can eert i Aue that i the tenin in the heet. hen write ewtn nd law the thief, taing the upward directin t be pitive g9.8 a a. 75 g he negative ign hw that the acceleratin i dwnward. If the thief decend with an acceleratin f. / r greater, the heet will upprt hi decent. 15. here will be tw ce n the pern their weight, and the nral ce f the cale puhing up n the pern. A ee-bd diagra the pern i hwn. Che up t be the pitive directin, and ue ewtn nd law t find the acceleratin. a.75 a a.5g Due t the ign f the reult, the directin f the acceleratin i dwn. hu the elevatr ut have tarted t ve dwn ince it had been tinle. 16. Che U t be the pitive directin. Write ewtn nd law the elevatr. a a 1,75 15 g g 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 7

7 Giancli hic: rinciple with Applicatin, 6 th Editin 17. (a) here will be tw ce n the diver their cbined weight, and the upward ce f air reitance,. Che up t be the pitive directin. Write A ewtn nd law the diver. a.5 a A a.75g Due t the ign f the reult, the directin f the acceleratin i dwn. (b) If the are decending at cntant peed, then the net ce n the ut be zer, and the ce f air reitance ut be equal t their weight g A A 18. (a) Ue Eq. -11c t find the peed f the pern jut bee triing the grund. ae dwn t be the pitive directin. r the pern, v, 3.9, and a 9.8. v v a v a (b) r the deceleratin, ue Eq. -11c t find the average deceleratin, ching dwn t be pitive. v v.7 v v a v a he average ce n the tr due t the leg i fund ewtn nd law. See the ee bd diagra. Dwn i pitive. a net a g a 3 4 g he ce i upward. 19. ree bd diagra the b and the weight are hwn belw. he tenin eert the ae agnitude f ce n bth bject. (a) If the weight f the hanging weight i le than the weight f the b, the bject will nt ve, and the tenin will be the ae a the weight f the hanging weight. he acceleratin f the b will al be zer, and the u f the ce n it will be zer. r the b, g g g g (b) he ae anali a part (a) applie here. g g (c) Since the hanging weight ha re weight than the b n the table, the b n the table will be lifted up ff the table, and nral ce f the table n the b will be.. 1g. (a) Jut bee the plaer leave the grund n a jup, the ce n the plaer wuld be hi weight and the ce f the flr puhing up the plaer. If the plaer i juping traight up, then the ce f the flr puhing n the plaer will be traight up a nral ce. See the firt diagra. In thi cae, while the are tuching the flr,. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 73

8 Chapter 4 Dnaic: ewtn Law f Mtin (b) While the plaer i in the air, the nl ce n the plaer i their weight. See the ecnd diagra. 1. (a) Jut a the ball i being hit, if we ignre air reitance, there are tw ain ce n the ball the weight f the ball, and the ce f the bat n the ball. (b) A the ball flie tward the utfield, the nl ce n it i it weight, if air reitance i ignred. bat. he tw ce ut be riented that the nrtherl cpnent f the firt ce i eactl equal t the utherl cpnent f the ecnd ce. hu 1 the ecnd ce ut act uthweterl. See the diagra Cnider the pint in the rpe directl belw Arlene. hat pint can be analzed a having three ce n it Arlene weight, the 1 1 tenin in the rpe tward the right pint f cnnectin, and the tenin in the rpe tward the left pint f cnnectin. Auing the rpe i ale, the tw tenin will be f the ae agnitude. Since the pint i nt accelerating the u f the ce ut be zer. In particular, cnider the u f the vertical ce n that pint, with U a the pitive directin. in1. in1. 5. g9.8 in1. in he net ce in each cae i fund b vectr additin with cpnent (a) et 1 et 16. et tan he actual angle the -ai i then et 19. a.73 at g 1 net 1 (b) c in et 1 et 1 a et tan at g et 1 net We draw ee-bd diagra each bucet. (a) Since the bucet are at ret, their acceleratin i. Write ewtn nd law each bucet, calling U the pitive directin. 1 1 p (# ) Btt (# 1) 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 74

9 Giancli hic: rinciple with Applicatin, 6 th Editin g g (b) w repeat the anali, but with a nn-zer acceleratin. he ee-bd diagra are unchanged. a a 3. g a a (a) We aue that the wer i being puhed t the right. i the ictin ce, and i the puhing ce alng the handle. (b) Write ewtn nd law the hrizntal directin. he ce ut u t ince the wer i nt accelerating. c 45. c c (c) Write ewtn nd law the vertical directin. he ce ut u t ince the wer i nt accelerating in the vertical directin. in 45. in g in (d) irt ue Eq. -11a t find the acceleratin. v v 1.5 v v at a.6 t.5 w ue ewtn nd law the directin t find the necear puhing ce. c 45. a f a g.6 f 99.9 c 45. c Che the directin t be the ward directin the tin f the nwcat, and the directin t be t the right n the diagra in the tetb. Since the huing unit ve in the ward directin n a traight line, there i n acceleratin in the directin, and the net ce in the directin ut be. Write ewtn nd law the directin. in 5 in 3 A B A B in 5 45 in 5 A B in 3 in 3 Since the cpnent add t, the agnitude f the vectr u f the tw ce will jut be the u f their cpnent. c 5 c 3 45 c 5 69 c A B A B 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 75

10 Chapter 4 Dnaic: ewtn Law f Mtin 8. Since all ce f interet in thi prble are hrizntal, draw the ee-bd diagra hwing nl the hrizntal ce. 1 i the tenin in the cupling between the lctive and the firt car, and it pull t the right n the firt car. ecnd car. It pull t the right n car, labeled R i the tenin in the cupling between the firt car an the and t the left n car 1, labeled L. Bth car have the ae a and the ae acceleratin a. te that R L b ewtn 3 rd law. 1 Write a ewtn nd law eprein each car. a a 1 1 Subtitute the eprein a the ecnd eprein int the firt ne. a hi can al be dicued in the ene that the tenin between the lctive and the firt car i pulling car, while the tenin between the car i nl pulling ne car. 9. he windw waher pull dwn n the rpe with her hand with a tenin ce, the rpe pull up n her hand with a tenin ce. he tenin in the rpe i al applied at the ther end f the rpe, where it attache t the bucet. hu there i anther ce pulling up n the bucet. he bucet-waher cbinatin thu ha a net ce f upward. See the adjacent ee-bd diagra, hwing nl ce n the bucet-waher cbinatin, nt ce eerted b the cbinatin (the pull dwn n the rpe b the pern) r internal ce (nral ce f bucet n pern). (a) Write ewtn nd law in the vertical directin, with up a pitive. he net ce ut be zer if the bucet and waher have a cntant peed. 65 g9.8 3 (b) w the ce i increaed b 15%, law, but with a nn-zer acceleratin. a a g g Again write ewtn nd Since the printer eert a ce f 7 n the grund at an angle f belw the hrizntal, b ewtn 3 rd law the grund will eert a ce f 7 n the printer at an angle f abve the hrizntal. A ee-bd diagra the printer i hwn. (a) he hrizntal acceleratin will be fund the net 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 76

11 Giancli hic: rinciple with Applicatin, 6 th Editin hrizntal ce. Uing ewtn nd law, we have the fllwing. c 7 c c a a 65 g (b) Eq. -11a i ued t find the final peed. he tarting peed i. v v at v at (a) See the ee-bd diagra included. (b) r blc 1, ince there i n tin in the vertical directin, we have g. We write ewtn nd law the 1 1 directin: a r blc, we nl need t cnider vertical ce: g a. Since the tw blc are cnnected, the agnitude f their acceleratin will be the ae, and let a a a 1. Cbine the tw ce equatin abve, and lve a b ubtitutin. a g a g a a g 1 a a g a g a g Cnider a ee-bd diagra f the dice. he car i ving t the right. he acceleratin f the dice i fund Eq. -11a. v v 8 v v a t a 4.67 t 6. w write ewtn nd law bth the vertical () and hrizntal () directin. c in a c Subtitute the eprein the tenin the equatin int the equatin. a in in tan a g tan c a 4.67 tan tan 5 g (a) In the ee-bd diagra belw, 1 = ce n blc 1 eerted b blc, 1 = ce n blc eerted b blc 1, 3 = ce n blc eerted b blc 3, and 3 = ce n blc 3 eerted b blc. he agnitude f 1 and 1 are equal, and the agnitude f 3 and 3 are equal, b ewtn 3 rd law earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 1g g

12 Chapter 4 Dnaic: ewtn Law f Mtin (b) All f the vertical ce n each blc add up t zer, ince there i n acceleratin in the vertical directin. hu each blc,. r the hrizntal directin, we have a a 1 3 (c) r each blc, the net ce ut be a b ewtn nd law. Each blc ha the ae acceleratin ince the are in cntact with each ther. 1net net 1 3 3net (d) r the ee-bd diagra, we ee that 3, 3 3net 1 3. And b ewtn 3 rd 3 law, 33 3net 1 3 Al the ee-bd diagra, we ee that 1,. Of cure, 3 and 3 are in ppite directin net 1 1. B ewtn 3 rd law, (e) Uing the given value, a g 1 3. Since all three ae are the ae value, the net ce n each a i a net hi i al the value f 3 and 3. he value f 1 and 1 i a 4 g uarize: net 1 net net g he value ae ene in that in rder f agnitude, we huld have, ince i the 1 3 net ce puhing the entire et f blc, 1 i the net ce puhing the right tw blc, and 3 i the net ce puhing the right blc nl. 34. irt, draw a ee-bd diagra each a. tice that the ae tenin ce i applied t each a. Che U t be the pitive directin. Write ewtn nd law each f the ae. g a g a Since the ae are jined tgether b the crd, their acceleratin will have the ae agnitude but ppite directin. hu a1 a. Subtitute thi int the ce eprein and lve the acceleratin b ubtracting the ecnd equatin the firt.. g 1 3. g 1g 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 78

13 Giancli hic: rinciple with Applicatin, 6 th Editin g a g a g a g a g a g g a a a g 1 3. g. g g. g he lighter blc tart with a peed f, and ve a ditance f 1.8 eter with the acceleratin fund abve. Uing Eq. -11c, the velcit f the lighter blc at the end f thi accelerated tin can be fund. v v a v v a w the lighter blc ha different cnditin f tin. Once the heavier blc hit the grund, the tenin ce diappear, and the lighter blc i in ee fall. It ha an initial peed f.556 / upward a fund abve, with an acceleratin f 9.8 / due t gravit. At it highet pint, it peed will be. Eq. -11c can again be ued t find the height t which it rie. v v.556 v v a.33 a 9.8 hu the ttal height abve the grund i = leae refer t the ee-bd diagra given in the tetb thi prble. Initiall, treat the tw be and the rpe a a ingle te. hen the nl accelerating ce n the te i. he a f the te i 3. g, and uing ewtn nd law, the acceleratin f the te i a. hi i the acceleratin f each piece f the te. 3. g w cnider the left b alne. he nl ce n it i B, and it ha the acceleratin fund abve. hu can be fund ewtn nd law. B a 1. g B B. w cnider the rpe alne. he net ce n it i A B, and it al ha the acceleratin fund abve. hu can be fund ewtn nd law. A a a.9 1. g A B C A B C 36. A ee-bd diagra the crate i hwn. he crate de nt accelerate verticall, and. he crate de nt accelerate hrizntall, and. utting thi tgether, we have.3 35 g If the cefficient f inetic ictin i zer, then the hrizntal ce required i, ince there i n ictin t cunteract. Of cure, it wuld tae a ce t SAR the crate ving, but nce it wa ving, n further hrizntal ce wuld be necear t aintain the tin. 37. A ee-bd diagra the b i hwn. Since the b de nt accelerate verticall, 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 79

14 Chapter 4 Dnaic: ewtn Law f Mtin (a) tart the b ving, the pulling ce ut jut verce the ce f tatic ictin, and that ean the ce f tatic ictin will reach it aiu value. hu we have the tarting tin, f g9.8 (b) he ae ce diagra applie, but nw the ictin i inetic ictin, and the pulling ce i O equal t the ictinal ce, ince the b i accelerating t the right. a a a a 5. g g A ee-bd diagra u a u tand n the train i hwn. Yu d nt accelerate verticall, and. he aiu tatic ictinal ce i, and that ut be greater than r equal t the ce needed t accelerate u. a a a a g.g g. he tatic cefficient f ictin ut be at leat. u t nt lide. 39. A ee-bd diagra the accelerating car i hwn. he car de nt accelerate verticall, and. he tatic ictinal ce i the accelerating ce, and a. If we aue the aiu acceleratin, then we need the aiu ce, and the tatic ictinal ce wuld be it aiu value f. hu we have a a a a g See the included ee-bd diagra. find the aiu angle, aue that the car i jut read t lide, that the ce f tatic ictin i a aiu. Write ewtn nd law bth directin. te that bth directin, the net ce ut be zer ince the car i nt accelerating. c c in in c in c 1 tan.8 tan ig fig 41. Start with a ee-bd diagra. Write ewtn nd law each directin. in a c a tice that the u in the directin i, ince there i n tin (and hence n acceleratin) in the directin. Slve the ce f ictin. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 8

15 Giancli hic: rinciple with Applicatin, 6 th Editin in a in a 15. g 9.8 in w lve the cefficient f inetic ictin. te that the eprein the nral ce ce the directin ce equatin abve c.59 c 15. g 9.8 c3 4. he directin f travel the car i t the right, and that i al the pitive hrizntal directin. Uing the ee-bd diagra, write ewtn nd law in the directin the car n the level rad. We aue that the car i jut n the verge f idding, that the agnitude f the ictin ce i. a 4.8 a a.4898 g 9.8 w put the car n an inclined plane. ewtn nd law in the -directin the car n the plane i ued t find the acceleratin. We again aue the car i n the verge f lipping, the tatic ictinal ce i at it aiu. in a a in c in g c c13 in in 43. (a) Here i a ee-bd diagra the b at ret n the plane. he ce f ictin i a SAIC ictinal ce, ince the b i at ret. (b) If the b were liding dwn the plane, the nl change i that the ce f ictin wuld be a KIEIC ictinal ce. (c) If the b were liding up the plane, the ce f ictin wuld be a KIEIC ictinal ce, and it wuld pint dwn the plane, in the ppite directin t that hwn in the diagra. 44. Aue that the tatic ictinal ce i the nl ce accelerating the racer. hen cnider the ee-bd diagra the racer a hwn. It i apparent that the nral i equal t the weight, ince there i n vertical acceleratin. It i al aued that the tatic ictinal ce i at it aiu. hu a a a g f he acceleratin f the racer can be calculated Eq. -11b, with an initial peed f. 1 v t at a t gt ec a g 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 81

16 Chapter 4 Dnaic: ewtn Law f Mtin 45. A ee-bd diagra the bbled i hwn. he acceleratin f the led i fund Eq. -11c. he final velcit al need t be cnverted t /. 1 v 6 h h v v a a v v w write ewtn nd law bth directin. Since the led de nt accelerate in the directin, the net ce n the directin ut be. hen lve the puhing ce. c c in a a in a in a in c a g c in g c 6. in he anali f the blc at ret can be dne eactl the ae a that preented in Eaple 4-, up g II t the equatin the acceleratin, a. w, the tatinar cae, the ce f ictin i tatic ictin. find the iniu value f hu II I I II I 1 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 8 II I, we aue the aiu tatic ictinal ce. g g a. inall, the te t ta at ret, the acceleratin ut be zer. hu g g. g g II I I II 47. A ee-bd diagra the b i hwn, auing that it i ving t the right. he puh i nt hwn n the ee-bd diagra becaue a n a the b ve awa the urce f the puhing ce, the puh i n lnger applied t the b. It i apparent the diagra that the vertical directin. We write ewtn nd law the hrizntal directin, with pitive t the right, t find the acceleratin f the b. a a a g Eq. -11c can be ued t find the ditance that the b ve bee tpping. he initial peed i 4. /, and the final peed will be. v v 4. v v a 4.1 a (a) Since the tw blc are in cntact, the can be treated a a ingle bject a lng a n inatin i needed abut internal ce (lie the ce f ne blc puhing n the ther blc). Since there i n tin in the vertical directin, it i apparent that 1 + g

17 Giancli hic: rinciple with Applicatin, 6 th Editin, and g g. Write ewtn nd law the 1 1 hrizntal directin. a a g9.8 g g (b) lve the cntact ce between the blc, an individual blc ut be analzed. L at the ee-bd diagra the ecnd blc. i the ce f the firt blc puhing n the ecnd blc. Again, it 1 i apparent that g and g. Write ewtn nd law the hrizntal directin. a 1 g a g g B ewtn 3 rd law, there will al be a 37 ce t the left n blc # 1 due t blc #. (c) If the crate are revered, the acceleratin f the te will reain the ae the anali part (a) till applie. We can al repeat the anali part (b) t find the ce f ne blc n the ther, if we ipl change 1 t in the ee-bd diagra and the reulting equatin. he reult wuld be a g a g g he ce f tatic ictin i what decelerate the crate if it i nt liding n the truc bed. If the crate i nt t lide, but the aiu deceleratin i deired, then the aiu tatic ictinal ce ut be eerted, and. he directin f travel i t the right. It i apparent that ince there i n acceleratin in the directin. Write ewtn nd law the truc in the hrizntal directin. a a a g he negative ign indicate the directin f the acceleratin ppite t the directin f tin g 5. Cnider a ee-bd diagra f the car n the ic inclined drivewa. Aue that the car i nt ving, but jut read t lip, that the tatic ictinal ce ha it aiu value f. Write ewtn nd law in each directin the car, with a net ce f in each cae. c c in in c 1 1 in c tan tan tan he car will nt be able t ta at ret n an lpe teeper than 8.5. Onl the drivewa acr the treet i afe paring. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 83

18 Chapter 4 Dnaic: ewtn Law f Mtin 51. We aue that the child tart ret at the tp f the lide, and then lide a ditance alng the lide. A ce diagra i hwn the child n the lide. irt, ignre the ictinal ce and cnider the n-ictin cae. All f the tin i in the directin, we will nl cnider ewtn nd law the directin. in a a g in Ue Eq. -11c t calculate the peed at the btt f the lide. v v a v v a g in ictin w include inetic ictin. We ut cnider ewtn nd law in bth the and directin nw. he net ce in the directin ut be ince there i n acceleratin in the directin. c c a in in in c in c a gin c With thi acceleratin, we can again ue Eq. -11c t find the peed after liding a certain ditance. v v a v v a g in c ictin w let the peed with ictin be half the peed withut ictin, and lve the cefficient f ictin. Square the reulting equatin and divide b g c t get the reult. v v g g 1 1 in c ictin ictin in 1 g g in c in 3 3 tan tan (a) Cnider the ee-bd diagra the cartn n the urface. here i n tin in the directin and thu n acceleratin in the directin. Write ewtn nd law bth directin. c c in a a in in c a g in c 9.8 in..1c (b) w ue Eq. -11c, with an initial velcit f, t find the final velcit. v v a v a (a) Cnider the ee-bd diagra the cartn n the ictinle urface. here i n acceleratin in the directin. Write ewtn nd law the directin. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the currentl eit. prtin f thi aterial a be reprduced, in an r b an ean, withut periin in writing the 84

19 Giancli hic: rinciple with Applicatin, 6 th Editin in a a g in Ue Eq. -11c with v 3. and v t find the ditance that it lide bee tpping. v v a v v a 9.8 in. he negative ign ean that the blc i diplaced up the plane, which i the negative directin. (b) he tie a rund trip can be fund Eq. -11a. he ee-bd diagra (and thu the acceleratin) i the ae whether the blc i riing r falling. r the entire trip, v 3. and v v v v v at t 1.6 a 9.8 in 54. See the ee-bd diagra the decending rller cater. It tart it 1 decent with v 6. h he ttal 3.6 h diplaceent in the directin i 45.. Write ewtn ecnd law bth the and directin. c c a in in in c in c a gin c w ue Eq. -11c t lve the final velcit. v v a v v a v g in c in45.18 c h 55. Cnider a ee-bd diagra f the b. Write ewtn nd law bth directin. he net ce in the directin i becaue there i n acceleratin in the directin. c c in a w lve the ce f ictin and the cefficient f ictin. c c in a 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 85

20 Chapter 4 Dnaic: ewtn Law f Mtin in a g in a 18. g 9.8 in c.719 c 18. g 9.8 c Cnider a ee-bd diagra the b, hwing ce n the b. When 13, the blc de nt ve. hu in that cae, the ce f ictin i tatic ictin, and ut be at it aiu value, given b. Write ewtn nd law in bth the and directin. he net ce in each cae ut be, ince the blc i at ret. c c in in in c in 13 c in.4 c 8 in g 9.8 g 57. (a) Cnider the ee-bd diagra the nw n the rf. If the nw i jut read t lip, then the tatic ictinal ce i at it aiu value,. Write ewtn nd law in bth directin, with the net ce equal t zer ince the nw i nt accelerating. c c in in c tan tan 3.58 If.58, then the nw wuld nt be n the verge f lipping. (b) he ae ee-bd diagra applie the liding nw. But nw the ce f ictin i inetic,, and the net ce in the directin i nt zer. Write ewtn nd law the directin again, and lve the acceleratin. in a a in in c c v t find the peed at the end f the rf. g in Ue Eq. -11c with i v v a v v a g in c 9.8 in 3. c (c) w the prble bece a prjectile tin prble. he prjectile ha an initial peed f 5.7 /, directed at an angle f 3 belw the hrizntal. he hrizntal cpnent f the peed, (5.66 /) c 3 = 4.9 /, will ta cntant. he vertical cpnent will change due t gravit. Define the pitive directin t be dwnward. hen the tarting 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 86 3

21 Giancli hic: rinciple with Applicatin, 6 th Editin vertical velcit i (5.66 /) in 3 =.83 /, the vertical acceleratin i 9.8 /, and the vertical diplaceent i 1.. Ue Eq. -11c t find the final vertical peed. v v a v v a / find the peed when it hit the grund, the hrizntal and vertical cpnent f velcit ut again be cbined, accrding t the thagrean there. v v v / (a) A ee-bd diagra the car i hwn, auing that it i ving t the right. It i apparent the diagra that = the vertical directin. Write ewtn nd law the hrizntal directin, with pitive t the right, t find the acceleratin f the car. Since the car i aued t O be liding, ue the aiu ce f tatic ictin. a a a g Eq. -11c can be ued t find the ditance that the car ve bee tpping. he initial peed i given a v, and the final peed will be. v v v v v v a (b) Uing the given value: a g g 1 v 6.38 v 95 h h g A ee-bd diagra the cffee cup i hwn. Aue that the car i ving t the right, and the acceleratin f the car (and cup) will be t the left. he deceleratin f the cup i caued b ictin between the cup and the dahbard. r the cup t nt lide n the dah, and t have the iniu deceleratin tie ean the larget pible tatic ictinal ce i acting,. he nral ce n the cup i equal t it weight, ince there i n vertical acceleratin. he hrizntal acceleratin f the cup i fund Eq. -11a, with a final velcit f zer. 1 v 45 h h v v 1.5 v v at a 3.57 t 3.5 Write ewtn nd law the hrizntal ce, cnidering t the right t be pitive. a 3.57 a a.36 g We derive tw eprein acceleratin ne the ineatic, and ne the dnaic. r Eq. -11c with a tarting peed f v up the plane and a final peed f zer, we have v v v v a a d 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 87

22 Chapter 4 Dnaic: ewtn Law f Mtin Write ewtn nd law bth the and directin. te that the net ce in the directin i zer, ince the blc de nt accelerate in the directin. c c in in a a w equate the tw eprein the acceleratin, ubtitute in the relatinhip between the ictinal ce and the nral ce, and lve the cefficient f ictin. in v in c v a d d v tan gd c 61. Since the wall are vertical, the nral ce are hrizntal, awa the wall face. We aue that the ictinal ce are at their aiu value, applie at each wall. We aue that the rpe in the diagra i nt under an tenin and de nt eert an ce. Cnider the ee-bd diagra the cliber. i the nral ce n the cliber the right R wall, and i the nral ce n the cliber the left wall. he tatic ictinal ce are L and. Write ewtn nd law bth the and directin. he net L L L R R R ce in each directin ut be zer if the cliber i tatinar. L R L R L R Subtitute the inatin the equatin int the equatin. L R L L R R L R L L L R 75 g And 55. hee nral ce arie a ewtn 3 rd law reactin ce t the L R cliber puhing n the wall. hu the cliber ut eert a ce f at leat each wall. 6. tice the etr f thi prble in the firt half f the tin, the bject accelerate with a cntant acceleratin t a certain peed, and then in the ecnd half f the tin, the bject decelerate with the ae agnitude f acceleratin bac t a peed f. Half the tie elape during the firt egent f the tin, and half the ditance i traveled during the firt egent f the tin. hu we analze half f the tin, and then duble the tie fund t get the ttal tie. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 88 cliber againt rictin i the accelerating and decelerating ce. We aue that the be d nt lip n the belt ince lippage wuld increae the travel tie. have the larget pible acceleratin, and hence the larget pible ce, that the travel tie can be a iniu, the b ut be ved b the aiu value f the tatic ictinal ce, and. See the ee-bd diagra the b n the firt half f the trip, auing that the cnver belt i level. Since there i n vertical L L R R

23 Giancli hic: rinciple with Applicatin, 6 th Editin acceleratin f the b, it i apparent that, and. Ue ewtn nd law in the hrizntal directin t find the acceleratin. a a g w ue Eq. -11b t deterine the tie taen t ve half the ditance with the calculated acceleratin, tarting ret. 1 d v t at t d a. hu the ttal tie the trip will be t d a 63. (a) Draw a ee-bd diagra each blc. Write ewtn nd law each blc. tice that the acceleratin f blc # 1 in the 1 directin will be zer, ince it ha n tin in the 1 directin. g c g c g in a g a g a ttal Since the blc are cnnected b the crd, a a a 1. Subtitute the eprein the tenin ce the lat equatin int the directin equatin blc 1, and lve the acceleratin. g in g a a g in g a a a g in 1 1 (b) If the acceleratin i t be dwn the plane, it ut be pitive. hat will happen if 1 in dwn the plane 1. he acceleratin will be up the plane (negative) if in up the plane. If in, then the te will nt accelerate. It will 1 ve with a cntant peed if et in tin b a puh. 64. (a) Given that i ving dwn, 1 ut be ving up the incline, and the ce f inetic ictin n 1 will be directed dwn the incline. Since the blc are tied tgether, the will bth have the ae acceleratin, and a a a 1. Write ewtn nd law each a. a a in a 1 c c 1 ae the inatin the tw equatin and ubtitute int the equatin t lve the acceleratin. a in c a 1 1 1g earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 89

24 Chapter 4 Dnaic: ewtn Law f Mtin 1 in 5.15c 5 1in c a g 9.8. (b) have an acceleratin f zer, the eprein the acceleratin ut be zer. 1in c a g 1 in c 1in 1in 5.64 c c Cnider a ee-bd diagra the cclit cating dwnhill at a cntant peed. Since there i n acceleratin, the net ce in each directin ut be zer. Write ewtn nd law the directin. in in hi etablihe the ize f the air ictin ce at 6. /h, and can be ued in the net part. w cnider a ee-bd diagra the cclit clibing the hill. i the ce puhing the cclit uphill. Again, write ewtn nd law the directin, with a net ce f. in in in 65 g 9.8 in v v he average acceleratin f the bld i given b a t.1 hu the net ce n the bld, eerted b the heart, wuld be 3 a 1 g he acceleratin f a pern having a 3 g deceleratin i a g 1.. he average ce cauing that acceleratin i a 9.8 3" " 9 " g " 4 7 g Since the pern i underging a deceleratin, the acceleratin and ce wuld bth be directed ppite t the directin f tin. Ue Eq. -11c t find the ditance traveled during the deceleratin. ae the initial velcit t be in the pitive directin, that the acceleratin will have a negative value, and the final velcit will be. 1 v 1 h h v v 7.78 v v a 1.3 a 9. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 9

25 Giancli hic: rinciple with Applicatin, 6 th Editin 68. (a) Aue that the earthquae i ving the Earth t the right. If an bject i t hld it place, then the bject ut al be accelerating t the right with the Earth. he ce that will accelerate that bject will be the tatic ictinal ce, which wuld al have t be t the right. If the ce were nt large enugh, the Earth wuld ve ut under the chair ewhat, giving the appearance that the chair were being thrwn t the left. Cnider the eebd diagra hwn a chair n the flr. It i apparent that the nral ce i equal t the weight ince there i n tin in the vertical directin. ewtn nd law a that a. We al aue that the chair i jut n the verge f lipping, which ean that the tatic ictinal ce ha it aiu value f. Equate the tw eprein the ictinal ce t find the cefficient f ictin. a a g If the tatic cefficient i larger than thi, then there will be a larger aiu ictinal ce, and the tatic ictinal ce will be re than ufficient t hld the chair in place n the flr. (b) r the 1989 quae, a Since.5, the chair wuld lide. g We draw three ee-bd diagra ne the car, ne the trailer, and then add the the cbinatin f car and trailer. te that ince the car puhe againt the grund, the grund will puh againt the car with an equal but ppitel directed ce. i the ce n the car due t the grund, C i the ce n the trailer due t the car, and C i the ce n the car due t the trailer. te that b ewtn 3 rd law, C C. r cnideratin f the vertical ce in the individual ee-bd diagra, it i apparent that the nral ce n each bject i equal t it weight. hi lead t the cncluin that CG g g w cnider the cbined ee-bd diagra. Write ewtn nd law the hrizntal directin, hi allw the calculatin f the acceleratin f the te. a a CG C CG C g inall, cnider the ee-bd diagra the trailer alne. Again write ewtn nd law the hrizntal directin, and lve. C a a C g C C C C Cg C CG C g CG g 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 91

26 Chapter 4 Dnaic: ewtn Law f Mtin 7. Aue that inetic ictin i the net ce cauing the deceleratin. See the ee-bd diagra the car, auing that the right i the pitive directin, and the directin f tin f the idding car. Since there i n acceleratin in the vertical directin, and. Appling ewtn nd law t the directin give a a a g f. Ue Eq. -11c t deterine the initial peed f the car, with the final peed f the car being zer. v v a v v a g We include ictin the tart, and then the n-ictin reult, et the cefficient f ictin equal t. Cnider a ee-bd diagra the car n the hill. Write ewtn nd law bth directin. te that the net ce n the directin will be zer, ince there i n acceleratin in the directin. c c in a c a g in g in g in c Ue Eq. -11c t deterine the final velcit, auing that the car tart ret. v v a v a g in c he angle i given b in 1 4 in (a) v g in in (b) v in14.5.1c See the ee-bd diagra the falling pure. Aue that dwn i the pitive directin, and that the air reitance ce i cntant. Write ewtn nd law the vertical directin. a g a w btain an eprein the acceleratin Eq. -11c with v, and ubtitute bac int the ictin ce. v v a a f v 9 g v. g earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 9

27 Giancli hic: rinciple with Applicatin, 6 th Editin 73. Cnider the ee-bd diagra the cclit in the ud, auing that the cclit i traveling t the right. It i apparent that ince there i n vertical acceleratin. Write ewtn nd law the hrizntal directin, pitive t the right. a a a g Ue Eq. -11c t deterine the ditance the cclit culd travel in the ud bee cing t ret. v v v 1 a g v v a 1 Since there i nl 11 f ud, the cclit will eerge the ud. he peed upn eerging i fund Eq. -11c. v v a v v a v g i he given data can be ued t calculate the ce with which the rad puhe againt the car, which in turn i equal in agnitude t the ce the car puhe againt the rad. he acceleratin f the car n level grund i fund Eq. -11a. v v 1 v v at a 1.5 t 14. he ce puhing the car in rder t have thi acceleratin i fund ewtn nd law. a 11 g We aue that thi i the ce puhing the car n the incline a well. Cnider a ee-bd diagra the car clibing the hill. We aue that the car will have a cntant peed n the aiu incline. Write ewtn nd law the directin, with a net ce f zer ince the car i nt accelerating. in in in in g Cnider the ee-bd diagra the watch. Write ewtn nd law bth the and directin. te that the net ce in the directin i becaue there i n acceleratin in the directin. c c in a in a c a gtan 9.8 tan earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 93

28 Chapter 4 Dnaic: ewtn Law f Mtin Ue Eq. -11a with v t find the final velcit (taeff peed). v v at v v at (a) Cnider the ee-bd diagra bth bject, initiall tatinar. A and i added, the tenin will increae, and the ce f tatic ictin n the blc will increae until it reache it aiu f. hen the te will tart t ve. Write ewtn nd law each bject, when the tatic ictinal ce i at it aiu, but the bject are till tatinar. g g bucet 1 1 g g blc blc Equate the tw eprein tenin, and ubtitute in the eprein the nral ce t find the ae. g g g g 1.6 g 1 hu 1.6 g 1.35 g g f and wa added. 1 1g (b) he ae ee-bd diagra can be ued, but nw the bject will accelerate. Since the are tied tgether, a a a. he ictinal ce i nw inetic ictin, given b 1 g. Write ewtn nd law the bject in the directin f their acceleratin. g a g a bucet a a blc Equate the tw eprein tenin, and lve the acceleratin. g a g a a g 1 g g.3 8.g 1.6g 77. Cnider a ee-bd diagra a grcer cart being puhed up an incline. Auing that the cart i nt accelerating, we write ewtn nd law the directin. in in in in g9.8 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 94

29 Giancli hic: rinciple with Applicatin, 6 th Editin 78. (a) find the iniu ce, aue that the pian i ving with a cntant velcit. Since the pian i nt accelerating, Mg. r the lwer pulle, 4 ince the tenin in a rpe i the ae thrughut, and ince the pulle i nt accelerating, it i een that Mg Mg It al can be een that ince, that Mg. (b) Draw a ee-bd diagra the upper pulle. r that diagra, we ee that 3Mg 3 1 uarize: Mg 3Mg Mg Lwer ulle Upper ulle 1 4 Mg he acceleratin f the pilt will be the ae a that f the plane, ince the pilt i at ret with repect t the plane. Cnider firt a ee-bd diagra f the pilt, hwing nl the net ce. B ewtn nd law, the net ce MUS pint in the directin f the acceleratin, and it agnitude i a. hat net ce i the u f ALL ce n the pilt. If we aue that the ce f gravit and the ce f the ccpit eat n the pilt are the nl ce n the pilt, then in ter f vectr, a. Slve thi equatin the ce f the eat t find net eat a eat net. A vectr diagra f that equatin i a hwn. Slve the ce f the eat n the pilt uing cpnent. a c g 3.5 c eat net a in 45 eat net 75 g g 3.5 c 45 9 he agnitude f the ccpit eat ce i eat eat he angle f the ccpit eat ce i 1 eat 1 9 tan tan 79 abve the hrizntal. 18 eat 45 net 45 net eat i. Ue Eq. -11a t find the deceleratin 3.6 h f the child. v v 1.5 v v at a 6.5. t. he net ce n the child i given b ewtn nd law. 8. he initial peed i v 45 h a 1 g , ppite t the velcit net We al aued that ictin between the eat and child i zer, and we aued that the btt f the eat i hrizntal. If ictin eited r if the eat wa tilted bac, then the ce that the trap wuld have t appl wuld be le. 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 95

30 Chapter 4 Dnaic: ewtn Law f Mtin 81 (a) he helicpter and ae will bth have the ae acceleratin, and can be treated a ne bject if n inatin abut internal ce (lie the cable tenin) i needed. A ee-bd diagra the helicpter-ae cbinatin i hwn. Write ewtn nd law the cbinatin, calling U the pitive directin. g a lift H H 765 g 15 g9.8.8 g a lift H (b) w draw a ee-bd diagra the ae alne, in rder t find the tenin in the cable. Again ue ewtn nd law. g a g a 4 15 g (c) he tenin in the cable i the ae at bth end, and the cable eert a ce f dwnward n the helicpter. H lift g g 8. (a) We aue that the aiu hrizntal ce ccur when the train i ving ver lwl, and the air reitance i negligible. hu the aiu acceleratin i given b 5 a 4.1 a.61 a g (b) At tp peed, we aue that the train i ving at cntant velcit. heree the net ce n the train i, and the air reitance ut be f the ae agnitude a the hrizntal puhing ce, which i Cnider the ee-bd diagra the decelerating ater, ving t the right. It i apparent that ince there i n acceleratin in the vertical directin. r ewtn nd law in the hrizntal directin, we have a a a g w ue Eq. -11c t find the tarting peed. v v a v v a g irt calculate Karen peed falling. Let the dwnward directin be pitive, and ue Eq. -11c with v. v v a v a w calculate the average acceleratin a the rpe tp Karen, again uing Eq. -11c, with dwn a pitive. v v v v a a 1. rpe 5 earn Educatin, Inc., Upper Saddle River, J. All right reerved. hi aterial i prtected under all cpright law a the 96