v. The same amount of work was done on the

Transcription

1 CHATER 6: r and Energ Answers Quesins. Sme pes f phsical labr, paricularl if i inles lifing bjecs, such as sheling dir r carring shingles up a rf, are wr in he phsics sense f he wrd. Or, pushing a lawn mwer wuld be wr crrespnding he phsics definiin. hen we use he wrd wr fr emplmen, such as g wr r schl wr, here is fen n sense f phsical labr r f ming smehing hrugh a disance b a frce.. Since cenripeal means pining he cener f curaure, hen a cenripeal frce will n d wr n an bjec, because if an bjec is ming in a cured pah, b definiin he direcin wards he cener f curaure is alwas perpendicular he direcin f min. Fr a frce d wr, he frce mus hae a cmpnen in he direcin f displacemen. S he cenripeal frce des n wr.. The nrmal frce can d wr n an bjec if he nrmal frce has a cmpnen in he direcin f displacemen f an bjec. If smene were jump up in he air, hen he flr pushing upward n he persn (he nrmal frce) wuld d psiie wr and increase he persn s ineic energ. Liewise when he hi he flr cming bac dwn, he frce f he flr pushing upwards (he nrmal frce) wuld d negaie wr and decrease he persn s ineic energ. 4. The wman des wr b ming he waer wih her hands and fee, because she mus eer a frce me he waer sme disance. As she sps swimming and begins fla in he curren, he curren des wr n her because she gains ineic energ. Once she is flaing he same speed as he waer, her ineic energ des n change, and s n ne wr is being dne n her. 5. The ineic frce f fricin ppses he relaie min beween w bjecs. As in he eample suggesed, as he ableclh is pulled frm under he dishes, he relaie min is fr he dishes be lef behind as he ableclh is pulled, and s he ineic fricin ppses ha and mes he dishes in he same direcin as he ableclh. This is a frce ha is in he direcin f displacemen, and s psiie wr is dne. Als ne ha he clh is ming faser han he dishes in his case, s ha he fricin is ineic, n saic. 6. hile i is rue ha n wr is being dne n he wall b u, here is wr being dne inside ur arm muscles. Eering a frce ia a muscle causes small cninual mins in ur muscles, which is wr, and which causes u ire. An eample f his is hlding a hea lad a arm s lengh. hile a firs u ma hld he lad sead, afer a ime ur arm will begin shae, which indicaes he min f muscles in ur arm. 7. (a) In his case, he same frce is applied bh springs. Spring will srech less, and s mre wr is dne n spring. (b) In his case, bh springs are sreched he same disance. I aes mre frce srech spring, and s mre wr is dne n spring. 8. A pin C he blc s speed will be less han B. The same amun f wr was dne n he blc in ging frm A B as frm B C since he frce and he displacemen are he same fr each segmen. Thus he change in ineic energ will be he same fr each segmen. Frm A B, he 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 4

2 Giancli hsics: rinciples wih Applicains, 6 h Ediin blc gained m f ineic energ. If he same amun is gained frm B C, hen he al B ineic energ a C is m m which resuls in, r.4 C B C B C B 9. Yur graiainal E will change accrding E. If we chse sme pical alues f m 80 g and 0.75 m, hen E 80 g 9.8 m s 0.75 m 590 J 0. Since each balln has he same iniial ineic energ, and each balln underges he same erall change in graiainal E, each balln will hae he same ineic energ a he grund, and s each ne has he same speed a impac.. The w launches will resul in he same larges angle. Appling cnserain f energ beween he launching pin and he highes pin, we hae E E m h h. The direcin ma f he launching elci des n maer, and s he same maimum heigh (and hence maimum angle) will resuls frm bh launches. Als, fr he firs launch, he ball will rise sme maimum heigh and hen cme bac he launch pin wih he same speed as when launched. Tha hen eacl duplicaes he secnd launch.. The spring can leae he able if i is cmpressed enugh. If he spring is cmpressed an amun 0, hen he gain in elasic E is. As he spring is cmpressed, is cener f mass is lwered b 0 sme amun. If he spring is unifrm, hen he cener f mass is lwered b, and he amun 0 f decrease in graiainal E is. If he gain in elasic E is mre han he lss in 0 graiainal E, s ha r, hen he released spring shuld rise up ff f he able, because here is mre han enugh elasic E resre he spring is riginal psiin. Tha era elasic energ will enable he spring jump ff he able i can raise is cener f mass a higher pin and hus rise up ff he able. here des ha era energ cme frm? Frm he wr u did in cmpressing he spring.. If he insrucr releases he ball wihu pushing i, he ball shuld reurn eacl he same heigh (barring an dissipaie frces) and jus uch he insrucr s nse as i sps. Bu if he insrucr pushes he ball, giing i era ineic energ and hence a larger al energ, he ball will hen swing a higher pin befre spping, and hi he insrucr in he face when i reurns. 4. hen waer a he p f a waerfall falls he pl belw, iniiall he waer s graiainal E is urned in ineic energ. Tha ineic energ hen can d wr n he pl waer when i his i, and s sme f he pl waer is gien energ, which maes i splash upwards and uwards and creaes uging waer waes, which carr energ. Sme f he energ will becme hea, due iscus fricin beween he falling waer and he pl waer. Sme f he energ will becme ineic energ f air mlecules, maing sund waes ha gie he waerfall is rar. 5. Sar he descripin wih he child suspended in mid-air, a he p f a hp. All f he energ is graiainal E a ha pin. Then, he child falls, and gains ineic energ. hen he child reaches he grund, ms f he energ is ineic. As he spring begins cmpress, he ineic energ is changed in elasic E. The child als ges dwn a lile bi furher as he spring cmpresses, and s mre graiainal E is als changed in elasic E. A he er bm f a hp, he energ is all elasic E. Then as he child rebunds, he elasic E is urned in ineic energ and graiainal E. hen he child reaches he p f he bunce, all f he elasic E has 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 5

3 Chaper 6 r and Energ been changed in graiainal E, because he child has a speed f 0 a he p. Then he ccle sars er again. Due fricin, he child mus als add energ he ssem b pushing dwn n he pg sic while i is n he grund, geing a mre frceful reacin frm he grund. 6. As he sier ges dwn he hill, he graiainal E is ransfrmed msl in ineic energ, and small amun is ransfrmed in hea energ due he fricin beween he sis and he snw and air fricin. As he sier sries he snwdrif, he ineic energ f he sier urns in ineic energ f he snw (b maing he snw me), and als in sme hea frm he fricin in ming hrugh he snwdrif. 7. (a) If here is n fricin dissipae an f he energ, hen he graiainal E ha he child has a he p f he hill all urns in ineic energ a he bm f he hill. The same ineic energ will be presen regardless f he slpe he final speed is cmpleel deermined b he heigh. The ime i aes reach he bm f he hill will be lnger fr a smaller slpe. (b) If here is fricin, hen he lnger he pah is, he mre wr ha fricin will d, and s he slwer he speed will be a he bm. S fr a seep hill, he sled will hae a greaer speed a he bm han fr a shallw hill. 8. Sepping n he lg requires ha he enire bd mass be raised up he heigh f he lg, requiring wr (ha is n recerable) prprinal he enire bd mass. Sepping er he lg nl requires he raising f he legs, maing fr a small mass being raised and hus less wr. Als, when jumping dwn, energ is epended sp he fall frm he lg. The penial energ ha u had a he p f he lg is ls when cming dwn frm he lg. 9. If we assume ha all f he arrw s ineic energ is cnered in wr dne agains fricin, hen he fllwing relainship eiss: KE KE KE F d cs80 m m F d m f i fr f 0 fr 0 m0 d Ffr Thus he disance is prprinal he square f he iniial elci. S if he iniial elci is dubled, he disance will be muliplied b a facr f 4. Thus he faser arrw peneraes 4 imes furher han he slwer arrw. 0. (a) Cnsider ha here is n fricin dissipae an energ. Sar he pendulum a he p f a swing, and define he lwes pin f he swing as he zer lcain fr graiainal E. The pendulum has maimum graiainal E a he p f a swing. Then as i falls, he graiainal E is changed ineic energ. A he bm f he swing, he energ is all ineic energ. Then he pendulum sars rise, and ineic energ is changed graiainal E. Since here is n dissipain, all f he riginal graiainal E is cnered ineic energ, and all f he ineic energ is cnered graiainal E. The pendulum rises he same heigh n bh sides f eer swing, and reaches he same maimum speed a he bm n eer swing. (b) If here is fricin dissipae he energ, hen n each dwnward swing, he pendulum will hae less ineic energ a he bm han i had graiainal E a he p. And hen n each swing up, he pendulum will n rise as high as he preius swing, because energ is being ls fricinal dissipain an ime he pendulum is ming. S each ime i swings, i has a smaller maimum displacemen. hen a grandfaher clc is wund up, a weigh is eleaed s ha i has sme E. Tha weigh hen falls a he prper rae pu energ bac in he pendulum replace he energ ha was ls dissipain. 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 6

4 Giancli hsics: rinciples wih Applicains, 6 h Ediin. The superball cann rebund a heigh greaer han is riginal heigh when drpped. If i did, i wuld ilae cnserain f energ. hen a ball cllides wih he flr, he KE f he ball is cnered in elasic E b defrming he ball, much lie cmpressing a spring. Then as he ball springs bac is riginal shape, ha elasic E is cnered bac KE. Bu ha prcess is lss n all f he elasic E ges cnered bac KE. Sme f he E is ls, primaril fricin. The superball rebunds higher han man her balls because i is less lss in is rebund han man her maerials.. The wr dne lif he suicase is equal he change in E f he suicase, which is he weigh f he suicase imes he change in heigh (he heigh f he able). (a) r des OT depend n he pah, as lng as here are n nn-cnseraie frces ding wr. (b) r des OT depend n he ime aen. (c) r DOES depend n he heigh f he able he higher he able, he mre wr i aes lif he suicase. (d) r DOES depend n he weigh f he suicase he mre he suicase weighs, he mre wr i aes lif he suicase.. The pwer needed lif he suicase is he wr required lif he suicase, diided b he ime ha i aes. (a) Since wr des OT depend n he pah, he pwer will n depend n he pah eiher, assuming he ime is he same fr all pahs. (b) The pwer DOES depend n he ime aen. The mre ime aen, he lwer he pwer needed. (c) The pwer needed DOES depend n he heigh f he able. A higher able requires mre wr lif he suicase. If we assume ha he ime lif he suicase is he same in bh cases, hen lif he higher able aes mre pwer. (d) The pwer DOES depend n he weigh f he suicase. A heaier suicase requires mre frce lif, and s requires mre wr. Thus he heaier he suicase, he mre pwer is needed lif i (in he same amun f ime). 4. The climber des he same amun f wr wheher climbing sraigh up r ia a zigzag pah, ignring dissipaie frces. Bu if a lnger zigzag pah is aen, i aes mre ime d he wr, and s he pwer upu needed frm he climber is less. Tha will mae he climb easier. I is easier fr he human bd generae a small amun f pwer fr lng perids f ime raher han generae a large pwer fr a small perid f ime. 5. Assuming ha here are n dissipaie frces cnsider, fr eer meer ha he lad is raised, w meers f rpe mus be pulled up. This is due he rpe passing er he bm pulle. The wr dne b he persn pulling mus be equal he wr dne n he pian. Since he frce n he pian is wice ha eered b he persn pulling, and since wr is frce imes disance, he persn mus eer heir smaller frce er wice he disance ha he larger pulle frce mes he pian. Sluins rblems. The frce and he displacemen are bh dwnwards, s he angle beween hem is 0. d cs 65 g 9.80 m s.80 m cs J G 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 7

5 Chaper 6 r and Energ. The minimum frce required lif he firefigher is equal his weigh. The frce and he displacemen are bh upwards, s he angle beween hem is 0. 4 F d cs d cs 65.0 g 9.80 m s 0.0m cs J climb climb. (a) See he free-bd diagram fr he crae as i is being pulled. Since he crae is n acceleraing hriznall, F F 0. The wr dne fr me i acrss he flr is he wr dne b he pulling frce. The angle beween he pulling frce and he direcin f min is 0. F d cs m 9. 0 J F fr F F (b) See he free-bd diagram fr he crae as i is being lifed. Since he crae is n acceleraing ericall, he pulling frce is he same magniude as he weigh. The angle beween he pulling frce and he direcin f min is 0. F d cs 0 d m 5. 0 J F 4. Draw a free-bd diagram fr he crae as i is being pushed acrss he flr. Since i is n acceleraing ericall, F. Since i is n acceleraing F hriznall, F F F. The wr dne me i acrss he fr flr is he wr dne b he pushing frce. The angle beween he pushing frce and he direcin f min is 0. F d d push push cs g 9.80 m s 0. m F fr F 8. 0 J 5. Since he accelerain f he b is cnsan, use Eq. -b find he disance med. Assume ha he b sars frm res. a 0 0 Then he wr dne in ming he crae is 0.0 m s 7 s 49 m F cs 0 ma 5 g.0 m s 49 m J 6. The firs b is alread in psiin, s n wr is required psiin i. The secnd b mus be med upwards b a disance d, b a frce equal is weigh,. The frce and he displacemen are in he same direcin, s he wr is d. The hird b will need be med a disance f d b he same size frce, s he wr is d, This cninues hrugh all seen bs, wih each needing be raised b an addiinal amun f d b a frce f. The al wr dne is d d d 4d 5d 6d 7d 8d 8.7 g 9.8 m s 0.04 m.0 0 J. 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 8

6 Giancli hsics: rinciples wih Applicains, 6 h Ediin 7. Cnsider he diagram shwn. If we assume ha he man pushes sraigh dwn n he end f he leer, hen he wr dne b he man (he inpu wr) is gien b F h. The bjec mes a I I I F I shrer disance, as seen frm he diagram, and s F h. O O O Equae he w amuns f wr. F h O I F h F h O O I I F h I O h I l I l O h O Bu b similar riangles, we see ha h h I O l l I O, and s F O F I l l I O. F O 8. The pian is ming wih a cnsan elci dwn he plane. F is he frce f he man pushing n he pian. (a) rie ewn s nd law n each direcin fr he pian, wih an accelerain f 0. F F cs 0 F cs F fr F F F sin F F 0 fr F sin F sin cs fr 0 g 9.80 m s sin cs (b) The wr dne b he man is he wr dne b F. The angle beween F and he direcin f min is 80. F d cs m.4 0 J. (c) The angle beween F fr and he direcin f min is 80. F d cs80 d cs g 9.8 m s.6 m cs 8 fr fr J (d) The angle beween he frce f grai and he direcin f min is 6. S he wr dne b grai is F d cs 6 d cs 6 0 g 9.8 m s.6 m cs J. G G (e) Since he pian is unacceleraed, he ne frce n he pian is 0, and s he ne wr dne n he pian is als 0. This can als be seen b adding he hree wr amuns calculaed. 400 J 400 J 5500 J 0 J e fr G 9. (a) rie ewn s nd law fr he erical direcin, wih up as psiie. F F Mg Ma M 0.0 g F.0 Mg L (b) The lifing frce and he displacemen are in he same direcin, s he wr dne b he lifing frce in lifing he helicper a erical disance h is F h cs 0.0 Mgh L L. L F L M g 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 9

7 Chaper 6 r and Energ 0. Draw a free-bd diagram f he car n he incline. Include a fricinal frce, bu ignre i in par (a) f he prblem. The minimum wr will ccur when he car is med a a cnsan elci. (a) rie ewn s nd law in bh he and direcins, ning ha he car is unacceleraed. F F cs 0 F cs F F sin 0 F sin The wr dne b F in ming he car a disance d alng he plane (parallel F ) is gien b 6 F d cs 0 d sin 950 g 9.80 m s 80 m sin J (b) w include he fricinal frce, gien b F F. e sill assume ha he car is n fr acceleraed. e again wrie ewn s nd law fr each direcin. The -frces are unchanged b he addiin f fricin, and s we sill hae F cs. F F F sin 0 F F sin cs sin. fr fr The wr dne b F in ming he car a disance d alng he plane (parallel F ) is gien b F d d cs 0 sin cs g 9.80 m s 80 m sin cs J F F fr F. The wr dne is equal he area under he graph. The area is rughl rapezidal, and s he area f he regin is fund as fllws. F F d d m 0.0 m J ma min B A. The wr dne will be he area under he F s. graph. (a) Frm m, he shape under he graph is rapezidal. The area is 0 m 4 m a J (b) Frm 0.0 m 5.0 m, he frce is in he ppsie direcin frm he direcin f min, and s he wr will be negaie. Again, since he shape is rapezidal, we find 5 m m J. a Thus he al wr frm m is 800 J 700 J. 0 J. The frce eered srech a spring is gien b F srech (he ppsie f he frce eered b he spring, which is gien b F. A graph f F s. will be a srech sraigh line f slpe hrugh he rigin. The srech frm, as shwn n he graph, ulines a rapezidal area. This area represens he wr, and is calculaed b 88 m m 0.00 m J. Frce F = Srech disance 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 40

8 Giancli hsics: rinciples wih Applicains, 6 h Ediin 4. See he graph f frce s. disance. The wr dne is he area under he graph. I can be fund frm he frmula fr a rapezid..0 m 5.0 m J F () (m) 5. Find he elci frm he ineic energ, using Eq. 6-. KE 6. 0 J KE m 6 m m s 6. (a) Since KE m, hen KE m and s KE. Thus if he ineic energ is dubled, he speed will be muliplied b a facr f. (b) Since KE m, hen KE muliplied b a facr f 4.. Thus if he speed is dubled, he ineic energ will be 7. The wr dne n he elecrn is equal he change in is ineic energ. 6 8 KE m m g.90 0 m s.64 0 J 8. The wr dne n he car is equal he change in is ineic energ, and s KE m m m s 0 50 g 05 m h 5. 0 J.6 m h 5 9. The frce eered b he bw n he arrw is in he same direcin as he displacemen f he arrw. Thus Fd cs 0 Fd m 85.8 J. Bu ha wr changes he KE f he arrw, b he wr-energ herem. Thus Fd Fd KE KE m m m 85.8 J g 0 44 m s 0. The wr dne b he ball n he gle will be he ppsie f he wr dne b he gle n he ball. The wr dne n he ball is equal he change in he ineic energ f he ball. KE KE m m g m s 7 J n ball ball F d, because he frce n he gle is in he same S 7 J. Bu cs 0 n gle n gle n gle direcin as he min f he gle. 7 J 7 J F 0.5 m F.9 0. n gle n gle 0.5 m 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 4

9 Chaper 6 r and Energ. The wr needed sp he car is equal he change in he car s ineic energ. Tha wr cmes frm he frce f fricin n he car. Assume he maimum pssible fricinal frce, which resuls in he minimum braing disance. Thus F F. The nrmal frce fr s is equal he car s weigh if i is n a leel surface, and s F. In he diagram, he car is raeling fr s he righ. Since f cs80 fr s KE F d m m d m d d, if increases b 50%, r is muliplied b.5, hen d will be muliplied b a facr.5, r.5.. The wr needed sp he car is equal he change in he car s ineic energ. Tha wr cmes frm he frce f fricin n he car, which is assumed be saic fricin since he drier lced he braes. Thus F F. Since he car is n a leel surface, he fr nrmal frce is equal he car s weigh, and s F if i is n a leel surface. See he diagram fr fr he car. The car is raeling he righ. KE F d cs80 m m d 0 m fr gd m s 88 m 7 m s The mass des n affec he prblem, since bh he change in ineic energ and he wr dne b fricin are prprinal he mass. The mass cancels u f he equain. F fr F fr F F d = spping disance g d = spping disance s m s. The riginal speed f he sfball is 95 m h 6.9 m s. The final speed is 90% f.6 m h his, r.75 m/s. The wr dne b air fricin causes a change in he ineic energ f he ball, and hus he speed change. In calculaing he wr, nice ha he frce f fricin is direced ppsiel he direcin f min f he ball. F d cs80 KE KE m fr fr F fr m m g 6.9 m s 0.9 d d 5 m. 4. If he rc has 80.0 J f wr dne i, and i lses all 80.0 J b spping, hen he frce f grai mus hae dne 80.0 J f wr n he rc. The frce is sraigh dwn, and he displacemen is sraigh up, s he angle beween he frce and he displacemen is 80. The wr dne b he grai frce can be used find he disance he rc rises. F d cs d cs J G G 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 4

10 Giancli hsics: rinciples wih Applicains, 6 h Ediin d G 80.0 J.85 g 9.80 m s 4.4 m 5. (a) Frm he free-bd diagram fr he lad being lifed, wrie ewn s nd law fr he erical direcin, wih up being psiie. F F ma 0.60 F T T g 9.80 m s.4 0 (b) The ne wr dne n he lad is fund frm he ne frce. F d d ne ne cs g 9.80 m s.0 m F T J (c) The wr dne b he cable n he lad is 4 F d cs 0.60 d.6 85 g 9.80 m s.0 m 7. 0 J cable T (d) The wr dne b grai n he lad is 4 d cs80 d 85 g 9.80 m s.0 m J G (e) Use he wr-energ her find he final speed, wih an iniial speed f 0. KE KE m m ne ne m J 85 g 0 8.m s 6. The elasic E is gien b spring frm is naural lengh. E elasic E where is he disance f sreching r cmpressing f he elasic 5 J 440 m 0.4 m 7. Subrac he iniial graiainal E frm he final graiainal E. E 7.0 g 9.8 m s. m 8 J G 8. Subrac he iniial graiainal E frm he final graiainal E. E 64 g 9.8 m s 4.0 m.5 0 J gra 9. Assume ha all f he ineic energ f he car becmes E f he cmpressed spring. m 00 g 65 m h m s.6 m h 4 m 0. (a) Relaie he grund, he E is gien b. m E.0 g 9.80 m s.0 m 45. J G b grund 8. 0 m 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 4

11 Chaper 6 r and Energ (b) Relaie he p f he persn s head, he E is gien b E h.0 g 9.80 m s 0.60 m J G b head (c) The wr dne b he persn in lifing he b frm he grund he final heigh is he same as he answer par (a), 45. J. In par (a), he E is calculaed relaie he saring lcain f he applicain f he frce n he b. The wr dne b he persn is n relaed he answer par (b).. (a) The change in E is gien b 5 E 55 g 9.80 m s 00 m 600 m 9. 0 J G 5 (b) The minimum wr required b he hier wuld equal he change in E, which is 9. 0 J. (c) Yes. The acual wr ma be mre han his, because he climber alms cerainl had ercme sme dissipaie frces such as air fricin. Als, as he persn seps up and dwn, he d n ge he full amun f wr bac frm each up-dwn een. Fr eample, here will be fricin in heir jins and muscles.. The spring will srech enugh hld up he mass. The frce eered b he spring will be equal he weigh f he mass..5 g 9.80 m s 5 m Thus he ruler reading will be 46 cm 5cm 6cm m. The nl frces acing n Jane are grai and he ine ensin. The ensin pulls in a cenripeal direcin, and s can d n wr he ensin frce is perpendicular a all imes her min. S Jane s mechanical energ is cnsered. Subscrip represens Jane a he pin where she grabs he ine, and subscrip represens Jane a he highes pin f her swing. The grund is he zer lcain fr E 0. e hae 5.m s, 0, and 0 (p f swing). Sle fr, he heigh f her swing. m m m m s g 9.8 m s.4 m,, he lengh f he ine des n ener in he calculain, unless he ine is less han 0.7 m lng. If ha were he case, she culd n rise.4 m high. Insead she wuld wrap he ine arund he ree branch., 4. The frces n he sier are grai and he nrmal frce. The nrmal frce is perpendicular he direcin f min, and s des n wr. Thus he sier s mechanical energ is cnsered. Subscrip represens he sier a he p f he hill, and subscrip represens he sier a he bm f he hill. The grund is he zer lcain fr E 0. e hae 0, 85 m, and 0 (bm f he hill). Sle fr, he speed a he bm. m m 0 m 0 F 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 44

12 Giancli hsics: rinciples wih Applicains, 6 h Ediin g 9.80 m s 85 m 60. m s 5 mi h 5. The frces n he sled are grai and he nrmal frce. The nrmal frce is perpendicular he direcin f min, and s des n wr. Thus he sled s mechanical energ is cnsered. Subscrip represens he sled a he bm f he hill, and subscrip represens he sled a he p f he hill. The grund is he zer lcain fr E 0. e hae 0, 0, and.5 m. Sle fr, he speed a he bm. m m m 0 0 F g 9.80 m s.5 m 5.4 m s ice ha he angle is n used in he calculain. 6. e assume ha all he frces n he jumper are cnseraie, s ha he mechanical energ f he jumper is cnsered. Subscrip represens he jumper a he bm f he jump, and subscrip represens he jumper a he p f he jump. Call he grund he zer lcain fr E 0. e hae 0, 0.70 m s, and.0 m m m m 0 m. Sle fr, he speed a he bm. g 0.70 m s 9.80 m s.0 m 6.45 m s 7. (a) Since here are n dissipaie frces presen, he mechanical energ f he persn rampline Earh cmbinain will be cnsered. The leel f he unsreched rampline is he zer leel fr bh he elasic and graiainal E. Call up he psiie direcin. Subscrip represens he jumper a he p f he jump, and subscrip represens he jumper upn arriing a he rampline. There is n elasic E inled in his par f he prblem. e hae 5.0 m s,.0 m, and 0. Sle fr, he speed upn arriing a he rampline. E E m m m m g 5.0 m s 9.8 m s.0 m 9.54 m s 9. m s The speed is he abslue alue f. (b) w le subscrip represen he jumper a he maimum srech f he rampline. e hae 9.54 m s, 0, 0, 0, and. There is n elasic energ a psiin, bu here is elasic energ a psiin. Als, he graiainal E a psiin is negaie, and s 0. A quadraic relainship resuls frm he cnserain f energ cndiin. E E m m m m 0 m g 4 m m g m 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he g 9.8m s 65 g 9.8m s 6. 0 m 65 g 9.54 m s m 0

13 Chaper 6 r and Energ 0.07 m, 0.86 m Since 0, 0. m. The firs erm under he quadraic is abu 000 imes smaller han he secnd erm, indicaing ha he prblem culd hae been apprimaed b n een including graiainal E fr he final psiin. If ha apprimain wuld hae been made, he resul wuld hae been fund b aing he negaie resul frm he fllwing sluin. E E m 65 g 9. m s 0.0 m 6. 0 m 4 8. Use cnserain f energ. Subscrip represens he prjecile a he launch pin, and subscrip represens he prjecile as i reaches he grund. The grund is he zer lcain fr E 0. e hae 85 m s, 65 m, and 0. Sle fr. E E m m m m g 85m s 9.80 m s 65 m 99 m s e ha he angle f launch des n ener in he prblem. m 0 9. Use cnserain f energ. The leel f he ball n he uncmpressed spring aen as he zer lcain fr bh graiainal E 0 and elasic E 0. Tae up be psiie fr bh. (a) Subscrip represens he ball a he launch pin, and subscrip represens he ball a he lcain where i jus leaes he spring, a he uncmpressed lengh. e hae 0, 0.50 m, and 0. Sle fr. E E m m 0, 0 0 m 0 0 m 950 m 0.50 m 0.0 g 9.80 m s 0.50 m 0.0 g 8.m s (b) Subscrip represens he ball a is highes pin. e hae 0, 0.50 m, 0, and 0. Sle fr. E E m m 950 m 0.50 m m 0.0 g 9.80 m s 40. Draw a free-bd diagram fr he blc a he p f he cure. Since he blc is ming in a circle, he ne frce is cenripeal. rie ewn s nd law fr he blc, wih dwn as psiie. If he blc is be n he erge f falling ff he rac, hen F 0. F 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 46

14 Giancli hsics: rinciples wih Applicains, 6 h Ediin F F m r m r gr R p p w use cnserain f energ fr he blc. Since he rac is fricinless, here are n nncnseraie frces, and mechanical energ will be cnsered. Subscrip represens he blc a he release pin, and subscrip represens he blc a he p f he lp. The grund is he zer lcain fr E 0. e hae 0, h, gr, and r. Sle fr h. E E m m 0 h r r h.5 r 4. The blc-spring cmbinain is assumed iniiall be a equilibrium, s he spring is neiher sreched nr unsreched. A he release pin, he speed f he mass is 0, and s he iniial energ is all E, gien b. Tha is he al energ f he ssem. Thus he energ f he ssem when 0 he blc is a a general lcain wih sme nn-zer speed will sill hae his same al energ alue. This is epressed b E m. al 0 4. Cnsider his diagram fr he jumper s fall. (a) The mechanical energ f he jumper is cnsered. Use fr he disance frm he 0 f graiainal E and fr he amun f bungee crd srech frm is unsreched lengh. Subscrip represens he jumper a he sar f he fall, and subscrip represens he jumper a he lwes pin f he fall. The bm f he fall is he zer lcain fr graiainal E 0, and he lcain where he bungee crd jus sars be sreched is he zer lcain fr elasic E 0. e hae 0, m, 0, 0, 0, and 9 m. Appl cnserain f energ. E E m m 6 g 9.8m s m 9 m 04.4 m.0 0 m (b) The maimum accelerain ccurs a he lcain f he maimum frce, which ccurs when he bungee crd has is maimum srech, a he bm f he fall. rie ewn s nd law fr he frce n he jumper, wih upward as psiie. F F ma a ne crd 04.4 m 9 m g 9.8 m s. m s m s m 6 g 4. Since here are n dissipaie frces presen, he mechanical energ f he rller caser will be cnsered. Subscrip represens he caser a pin, ec. The heigh f pin is he zer lcain fr graiainal E. e hae 0 and 5 m. in : m m ; 0 m g 9.80 m s 5 m 6 m s m 9 m Sar f fall Cnac wih bungee crd, 0 fr elasic E Bm f fall, 0 fr graiainal E F crd 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 47

15 Chaper 6 r and Energ in : in 4: m m ; 8 m m g 9.80 m s 7 m m s m m ; 5 m m g 9.80 m s 0 m 0 m s (a) See he diagram fr he hrwn ball. The speed a he p f he pah will be he hriznal cmpnen f he riginal elci. cs m s cs 0 m s p 0 (b) Since here are n dissipaie frces in he prblem, he mechanical energ f he ball is cnsered. Subscrip represens he ball a he release pin, and subscrip represens he ball a he p f he pah. The grund is he zer lcain fr E 0. e hae m s, 0, and cs. Sle fr. E E m m m 0 m cs cs m s cs g 9.8 m s. m 45. The maimum accelerain f 5.0 g ccurs where he frce is a a maimum. The maimum frce ccurs a he bm f he min, where he spring is a is maimum cmpressin. rie ewn s nd law fr he elear a he bm f he min, wih up as he psiie direcin. F F Mg Ma 5.0 Mg F 6.0Mg ne spring spring w cnsider he diagram fr he elear a arius pins in is min. If here are n nn-cnseraie frces, hen mechanical energ is cnsered. Subscrip represens he elear a he sar f is fall, and subscrip represens he elear a he bm f is fall. The bm f he fall is he zer lcain fr graiainal E 0. There is als a pin a he p f he spring ha we will define as he zer lcain fr elasic E ( = 0). e hae 0, h, =0 0, 0, and cnserain f energ.. Appl E E M Mg M Mg 0 Mg h Mg h 6.0Mg 6Mg 6Mg Mg F 6.0 Mg Mg h spring h h Sar f fall Cnac wih spring, F spring Bm f fall, 0 fr graiainal E 46. (a) The wr dne agains grai is he change in E. E agains grai 5 75 g 9.8 m s 50 m. 0 J 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 48

16 Giancli hsics: rinciples wih Applicains, 6 h Ediin (b) The wr dne b he frce n he pedals in ne reluin is equal he angenial frce imes he circumference f he circular pah f he pedals. Tha wr is als equal he energ change f he biccle during ha reluin. e ha a erical rise n he incline is relaed he disance alng he incline b rise disance sin. F r E d sin F pedal an re re re frce an d re sin 75 g 9.8 m s 5. m sin 7.8 r 0.8 m Use cnserain f energ, where all f he ineic energ is ransfrmed hermal energ. E E m E 0.8m s 7650 g 95m h 5. 0 J m h 6 iniial final hermal 48. Appl he cnserain f energ he child, cnsidering wr dne b grai and wr changed in hermal energ. Subscrip represens he child a he p f he slide, and subscrip represens he child a he bm f he slide. The grund is he zer lcain fr E 0. e hae 0,.5 m,. m s, and 0. Sle fr he wr changed in hermal energ. E E m m hermal hermal m.7 g 9.8m s.5 m.7 g. m s J 49. (a) See he free-bd diagram fr he si. rie ewn s nd law fr frces perpendicular he direcin f min, ning ha here is n accelerain perpendicular he plane. F F cs F cs fr F F cs w use cnserain f energ, including he nn-cnseraie fricin frce. Subscrip represens he si a he p f he slpe, and subscrip represens he si a he bm f he slpe. The lcain f he si a he bm f he incline is he zer lcain fr graiainal E 0. e hae 0, d sin, and 0. rie he cnserain f energ cndiin, and sle fr he final speed. e ha F F cs fr KE E m m E E C C F d cs80 m m d cs d sin m fr F fr F d gd sin cs 9.80 m s 75 m sin 0.090cs 0.69 m s m s (b) w, n he leel grund, F, and here is n change in E. Le us again f use cnserain f energ, including he nn-cnseraie fricin frce, relae psiin wih psiin. Subscrip represens he si a he end f he rael n he leel, haing raeled a disance d n he leel. e hae 0.69 m s, 0, 0, and earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 49

17 Chaper 6 r and Energ E E F d cs80 m m C f 0.69 m s d m 0 d 4.7 m.4 0 m g 9.80 m s (a) Appl energ cnserain wih n nn-cnseraie wr. Subscrip represens he ball as i is drpped, and subscrip represens he ball as i reaches he grund. The grund is he zer lcain fr graiainal E. e hae 0,.0 m, and 0. Sle fr. E E m m m g 9.80 m s.0 m 6.0 m s (b) Appl energ cnserain, bu wih nn-cnseraie wr due fricin included. The wr dne b fricin will be gien b F d cs80, since he frce f fricin is in he C fr ppsie direcin as he min. The disance d er which he fricinal frce acs will be he.0 m disance f fall. ih he same parameers as abe, and 8.00 m s, sle fr he frce f fricin. E E F d m m F d m nc fr fr F m g fr d d 8.00 m s 0.45 g 9.80 m s.06.0 m 5. (a) Calculae he energ f he ball a he w maimum heighs, and subrac find he amun f energ ls. The energ a he w heighs is all graiainal E, since he ball has n KE a hse maimum heighs. E E E ls iniial final iniial final E.0 m.5 m ls iniial final iniial final 0.5 5% E.0 m iniial iniial iniial (b) Due energ cnserain, he KE f he ball jus as i leaes he grund is equal is final E. E KE m final grund final grund grund g 9.8m s.5 m 5.4 m s final (c) The energ ls was changed primaril in hea energ he emperaure f he ball and he grund wuld hae increased slighl afer he bunce. Sme f he energ ma hae been changed in acusic energ (sund waes). Sme ma hae been ls due nn-elasic defrmain f he ball r grund. 5. Since he crae mes alng he flr, here is n change in graiainal E, s use he wr-energ herem: KE KE. There are w frces ne ding wr: F, he pulling frce, and F F, he fricinal fr frce. KE 0 since he crae sars frm res. e ha he w frces ding wr d wr er differen disances. F d cs 0 F d cs80 d fr fr fr fr F fr F F 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 50

18 Giancli hsics: rinciples wih Applicains, 6 h Ediin KE KE m ne fr F d d m m fr fr 0 g m g 9.8 m s 5 m 0 m s 5. Since here is a nn-cnseraie frce, cnsider energ cnserain wih nn-cnseraie wr included. Subscrip represens he rller caser a pin, and subscrip represens he rller caser a pin. in is aen as he zer lcain fr graiainal E. e hae.70 m s, 5 m, and 0. Sle fr. The wr dne b he nn-cnseraie fricin frce is gien b F d cs80 0.0d, since he frce is ne-fifh f, and he frce is direced C fr eacl ppsie he direcin f min. E E 0. d m m C 0.4gd g m s 45.0 m.70 m s 9.80 m s 5 m.64 m s m s 54. Cnsider he free-bd diagram fr he sier in he mids f he min. rie ewn s nd law fr he direcin perpendicular he plane, wih an accelerain f 0. F F cs 0 F cs F F cs fr Appl cnserain f energ he sier, including he nncnseraie fricin frce. Subscrip represens he sier a he bm f he slpe, and subscrip represens he sier a he pin furhes up he slpe. The lcain f he sier a he bm f he incline is he zer lcain fr graiainal E 0. e hae.0 m s, 0, 0, and d sin. E E F d cs80 m m C fr d cs m 0 0 d sin gd sin.0 m s an gd cs gd cs 9.80 m s. m cs earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 5 an Use cnserain f energ, including he nn-cnseraie fricinal frce. The blc is n a leel surface, s here is n graiainal E change cnsider. The fricinal frce is gien b F F, since he nrmal frce is equal he weigh. Subscrip represens he blc a fr he cmpressed lcain, and subscrip represens he blc a he maimum sreched psiin. The lcain f he blc when he spring is neiher sreched nr cmpressed is he zer lcain fr elasic E ( = 0). Tae righ be he psiie direcin. e hae 0, m, 0, and 0.0 m. F d F fr

19 Chaper 6 r and Energ E E F cs80 m m C fr 80 m 0.050m 0.0m 0.60 g 9.80 m s 0.07 m Use cnserain f energ, including he nn-cnseraie fricinal frce. The blc is n a leel surface, s here is n graiainal E change cnsider. Since he nrmal frce is equal he weigh, he fricinal frce is F F. Subscrip represens he blc a he cmpressed fr lcain, and subscrip represens he blc a he maimum sreched psiin. The lcain f he blc when he spring is neiher sreched nr cmpressed is he zer lcain fr elasic E ( = 0). Tae righ be he psiie direcin. e hae 0, 0.8 m, and 0. The alue f he spring cnsan is fund frm he fac ha a - frce cmpresses he spring 8 cm, and s F 0.8 m. m. The alue f mus be psiie. E E F cs80 m m C fr m, 0.800m 0.7 m 57. (a) If here is n air resisance, hen cnserain f mechanical energ can be used. Subscrip represens he glider when a launch, a subscrip represens he glider a landing. The landing lcain is he zer lcain fr elasic E ( = 0). e hae 500 m, 0, and m s 500 m h 8.9 m s.6 m h. Sle fr E E m m g 8.9 m s 9.80 m s 500 m 96 m s 067 m h. 0 m h.6 m h m s (b) w include he wr dne b he nn-cnseraie fricinal frce. Cnsider he diagram f he glider m Calculae he wr dne b fricin. d 500 m F d cs80 F d F C fr fr fr sin0 Use he same subscrip represenains as abe, wih,, and as befre, and m s 00 m h m s. rie he energ cnserain equain and sle fr.6 m h he fricinal frce. 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 5

20 Giancli hsics: rinciples wih Applicains, 6 h Ediin E E F d m m F C fr 980 g 8.9 m s m s 9.80 m s 500 m 500 m sin0 f m g d The wr necessar lif he pian is he wr dne b an upward frce, equal in magniude he weigh f he pian. Thus Fd cs 0 h. The aerage pwer upu required lif he pian is he wr dne diided b he ime lif he pian. h h 5 g 9.80 m s 6.0 m s 59. The 8 hp is he pwer generaed b he engine in creaing a frce n he grund prpel he car Fd d frward. The relainship beween he pwer and he frce is gien b F F. Thus he frce prpel he car frward is fund b F. If he car has a cnsan elci, hen he al resisie frce mus be f he same magniude as he engine frce, s ha he ne frce is zer. Thus he al resisie frce is als fund b F. F 8 hp 746 hp 88m h m s.6 m h The pwer is gien b Eq The energ ransfrmed is he change in ineic energ f he car. energ ransfrmed ime hp KE m 400 g 95 m h 7.4 s m s.6 m h 6. (a) (b) 6. (a) (b) 550f lb s 4.45 m hp hp 746 m s 746 hp lb.8 f hp hp s J/s 6 h h.6 0 J h 0 d 4 h 50 mnh 50 mnh 74 h 000 mnh d 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 5

21 Chaper 6 r and Energ (c) 70 h J 9 74 h 74 h. 0 J h $0. (d) 74 h $44.88 $45 h Kilwa-hurs is a measure f energ, n pwer, and s n, he acual rae a which he energ is used des n figure in he bill. The culd use he energ a a cnsan rae, r a a widel aring rae, and as lng as he al used is 70 ilwa-hurs, he price wuld be $ The energ ransfer frm he engine mus replace he ls ineic energ. Frm he w speeds, calculae he aerage rae f lss in ineic energ while in neural. m s m s 85 m h.6m s 65 m h 8.06 m s.6 m h.6 m h 5 KE m m 50 g 8.06 m s.6m s.0 0 J S J 4 4 hp.6 0, r hp 6.0 s r.0 0 hp is needed frm he engine. 64. Since, we hae s 6.0 hp hr 8. 0 J hp h 65. The wr dne in acceleraing he sh pu is gien b is change in ineic energ: The pwer is he energ change per uni ime. KE KE m 7. g 4 m s 0.5 s The frce lif he waer is equal is weigh, and s he wr lif he waer is equal he weigh imes he disance. The pwer is he wr dne per uni ime. h 8.0 g 9.80 m s.60 m 60 sec The minimum frce needed lif he fball plaer ericall is equal his weigh,. The disance er which ha frce wuld d wr wuld be he change in heigh, 40 m sin 74. m. S he wr dne in raising he plaer is and he pwer upu required is he wr dne per uni ime. 95 g 9.80 m s 74. m sec. 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 54

22 Giancli hsics: rinciples wih Applicains, 6 h Ediin 68. See he free-bd diagram fr he biccle n he hill. rie ewn s nd law fr he direcin, ning ha he accelerain is 0. Sle fr he magniude f F. The pwer upu relaed ha frce is gien b Eq. 6-7, F. Use ha relainship find he elci. F F F F sin 0 F sin F F 0.5 hp 746 hp sin 68 g 9.8 m s sin m s 69. Cnsider he free-bd diagram fr he car. The car has a cnsan elci, s he ne frce n he car is zer. F is he fricin frce, and fr F is he car frce f he rad pushing n he car. I is equal in magniude he frce f he car pushing n he rad, and s we can hin f F as he frce he car car is able generae b he engine. rie ewn s nd law in he direcin. F F F sin F F sin car fr car fr Use Eq. 6-7 epress he pwer upu f he car, and hen calculae he angle frm ha epressin. F sin fr F fr F F car 0hp 746 hp sin F sin 650 fr 00 g 9.80 m s m s 75 m h.6 m h Draw a free-bd diagram fr he b being dragged alng he flr. The b has a cnsan speed, s he accelerain is 0 in all direcins. rie ewn s nd law fr bh he (hriznal) and (erical) direcins. F F 0 F F F F 0 F F F fr fr The wr dne b F in ming he crae a disance The pwer required is he wr dne per uni ime. hp 64. hp 746 is gien b F fr F F cs g 9.80 m s.0 m s 64 F 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 55

23 Chaper 6 r and Energ 7. Firs, cnsider a free-bd diagram fr he cclis ging dwn hill. rie ewn s nd law fr he direcin, wih an accelerain f 0 since he cclis has a cnsan speed. F sin F 0 F sin fr w cnsider he diagram fr he cclis ging up he hill. Again, wrie ewn s nd law fr he direcin, wih an accelerain f 0. F F F sin 0 F F sin fr fr Assume ha he fricin frce is he same when he speed is he same, s he fricin frce when ging uphill is he same magniude as when ging dwnhill. F F sin sin fr The pwer upu due his frce is gien b Eq F sin 75 g 9.8 m s 5.0 m s sin fr F fr F F F F fr 7. The ineic energ f he ming car is changed in he elasic E f he bumper, befre i defrms. m 00 g 8m h m s.6 m h 7 m 0.05 m.9 0 m 7. The minimum wr required shele a b is equal he rd shelf weigh f he b imes he erical disance he b is med is increase in E. See he diagram. Each b ha is placed n he lwes shelf has is cener f mass med upwards b 0.5 cm. S he wr dne me 5 bs he lwes shelf is rd shelf 50.5 cm m. Each b ha is placed n he secnd s shelf shelf has is cener f mass med upwards b 50.5 cm, s he 0.5 cm flr wr dne me 5 bs he secnd shelf is m. Similarl, m, m, and m. The al wr dne is he sum f he fie wr epressins m.505 m.805 m.05 m.405 m 5.5 g 9.80 m s 4.05 m 479 J.5 0 J 74. Assume ha here are n nn-cnseraie frces ding wr, s he mechanical energ f he jumper will be cnsered. Subscrip represens he jumper a he launch pin f he jump, and subscrip represens he jumper a he highes pin. The saring heigh f he jump is he zer lcain fr E 0. e hae 0,. m, and 6.5m s. Sle fr. E E m m g 6.5 m s 9.8 m s. m 8.0 m s 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 56

24 Giancli hsics: rinciples wih Applicains, 6 h Ediin 75. (a) Cnsider a free-bd diagram fr he blc a he p f he cure. Since he blc is ming in a circle, he ne frce is cenripeal. rie ewn s nd law fr he blc, wih dwn as erical. If he blc is be n he erge f falling ff he rac, hen F 0. F F m r m r gr R p p p w use cnserain f energ fr he blc. Since he rac is fricinless, here are n nncnseraie frces, and mechanical energ will be cnsered. Subscrip represens he blc a he release pin, and subscrip represens he blc a he p f he lp. The grund is he zer lcain fr E 0. e hae 0, h, gr, and r. p Sle fr h. E E m m h r r h.5 r (b) w he release heigh is h 5 r. Use cnserain f energ again. Subscrip represens he blc a he (new) release pin, and subscrip represens he blc a he bm f he lp. e hae 0, 5r, and 0. Sle fr. E E m m rg. 0 w cnsider he free-bd diagram fr he blc a he bm f he lp. The ne frce mus be upward and radial. rie ewn s nd law fr he erical direcin, wih up as psiie. F F m r R m0rg F m r r (c) Use cnserain f energ again. Subscrip is as in par (b) abe, and subscrip represens he blc a he p f he lp. e hae 0, 0rg, and E E m m 5mrg 0 m r 6rg Refer he free-bd diagram and analsis f par (a) find he nrmal frce. 6 r F F m r F m r 5 R p r r. Sle fr (d) hen ming n he leel, he nrmal frce is he same as he weigh, F. 76. (a) Use cnserain f energ, including he wr dne b he nn-cnseraie frce f he snw n he pil. Subscrip represens he pil a he p f he snwban, and subscrip represens he pil a he bm f he craer. The bm f he craer is he zer lcain fr E 0. e hae = 5 m/s, =. m, = 0, and = 0. Sle fr he nncnseraie wr. E E m m C C C m J J 78 g 5 m s 78 g 9.8 m s. m (b) The wr dne b he snwban is dne b an upward frce, while he pil mes dwn. F d cs80 F d C snw snw F F. 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 57

25 Chaper 6 r and Energ F snw C J d. m (c) T find he wr dne b air fricin, anher nn-cnseraie frce, use energ cnserain including he wr dne b he nn-cnseraie frce f air fricin. Subscrip represens he pil a he sar f he descen, and subscrip represens he pil a he p f he snwban. The p f he snwban is he zer lcain fr E 0. e hae = 0 m/s, = 70 m, = 5 m/s, and = 0. Sle fr he nn-cnseraie wr. E E m m C C C m J.4 0 J 78 g 5 m s 78 g 9.8 m s 70 m 77. (a) The ensin in he crd is perpendicular he pah a all imes, and s he ensin in he crd des n d an wr n he ball. Thus he mechanical energ f he ball is cnsered. Subscrip represens he ball when i is hriznal, and subscrip represens he ball a he lwes pin n is pah. The lwes pin n he pah is he zer lcain fr E 0. e hae 0, L, and 0. Sle fr. E E m m L m gl (b) Use cnserain f energ, relae pins and. in is as described abe. Subscrip represens he ball a he p f is circular pah arund he peg. The lwes pin n he pah is he zer lcain fr E 0. e hae gl, 0, and L h L 0.80L 0.40L. Sle fr. E E m m m gl m 0.40 L.gL 78. (a) The wr dne b he hier agains grai is he change in graiainal E g 9.8 m s 700 m 00 m J J G (b) The aerage pwer upu is fund b diiding he wr b he ime aen. 5 gra J upu 5 h 600 s h hp hp 746 (c) The upu pwer is he efficienc imes he inpu pwer. upu hp upu inpu inpu (a) The wr dne b grai as he elear falls is he ppsie f he change in graiainal E. E E E 90 g 9.8 m s 8 m G J.5 0 J 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 58

26 Giancli hsics: rinciples wih Applicains, 6 h Ediin Grai is he nl frce ding wr n he elear as i falls (ignring fricin), s his resul is als he ne wr dne n he elear as i falls. (b) The ne wr dne n he elear is equal is change in ineic energ. The ne wr dne jus befre sriing he spring is he wr dne b grai fund abe. KE KE m 0 G g 9.8m s 8 m.4m s m s (c) Use cnserain f energ. Subscrip represens he elear jus befre sriing he spring, and subscrip represens he elear a he bm f is min. The leel f he elear jus befre sriing he spring is he zer lcain fr bh graiainal E and elasic E. e hae.4m s, 0, and 0. e assume ha 0. E E m m 4m g m 4 m m g m 0 e mus chse he negaie r s ha is negaie. Thus 5 90 g 9.8 m s 90 g 9.8 m s 90 g. 0 m.4m s 5.56 m. 0 m 80. The frce lif a persn is equal he persn s weigh, s he wr lif a persn up a erical disance h is equal h. The wr needed lif peple is h, and s he pwer needed is he al wr diided b he al ime. e assume he mass f he aerage persn be 70 g, h g 9.80 m s 00 m s 8. (a) Use cnserain f mechanical energ, assuming here are n nn-cnseraie frces. Subscrip represens he waer a he p f he dam, and subscrip represens he waer as i sries he urbine blades. The leel f he urbine blades is he zer lcain fr E 0. e hae 0, 80 m, and 0. Sle fr. E E m m m g 9.8 m s 8 m 9.84 m s m s (b) The energ f he waer a he leel f he urbine blades is all ineic energ, and s is gien b m. 58% f ha energ ges ransferred he urbine blades. The rae f energ ransfer he urbine blades is he pwer deelped b he waer. m g s 9.84 m s earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 59

27 Chaper 6 r and Energ 8. Cnsider he free-bd diagram fr he caser a he bm f he lp. The ne frce mus be an upward cenripeal frce. F F m R F m R bm bm bm bm bm w cnsider he frce diagram a he p f he lp. Again, he ne frce mus be cenripeal, and s mus be dwnward. F F m R F m R. p p p p p Assume ha he speed a he p is large enugh ha p F p 0, and s Rg. w appl he cnserain f mechanical energ. Subscrip represens he caser a he bm f he lp, and subscrip represens he caser a he p f he lp. The leel f he bm f he lp is he zer lcain fr E 0. e hae = 0 and = R. E E m m gr. 4 bm p The difference in apparen weighs is he difference in he nrmal frces. F F m R m R m R bm p bm p bm p m 4gR R 6 ice ha he resul des n depend n eiher r R. 8. (a) Assume ha he energ f he cand bar is cmpleel cnered in a change f E: Ecand 6 bar. 0 J E E.4 0 m. cand bar 8 g 9.8m s (b) If he persn jumped he grund, he same energ is all cnered in ineic energ. E m cand bar E cand 6. 0 J bar m 8 g.6 0 m s 84. Since here are n nn-cnseraie frces, he mechanical energ f he prjecile will be cnsered. Subscrip represens he prjecile a launch and subscrip represens he prjecile as i sries he grund. The grund is he zer lcain fr E 0. e hae 75 m s, 65 m, and 0. Sle fr. E E m m m m g 75 m s 9.8 m s 65 m 84 m s ice ha he launch angle des n ener he prblem, and s des n influence he final speed. 85. The spring cnsan fr he scale can be fund frm he 0.6 mm cmpressin due he 70 frce. F m. Use cnserain f energ fr he jump. Subscrip m represens he iniial lcain, and subscrip represens he lcain a maimum cmpressin f he scale spring. Assume ha he lcain f he uncmpressed scale spring is he 0 lcain fr graiainal E. e hae 0 and.0 m. Sle fr, which mus be negaie. F p F bm 005 earsn Educain, Inc., Upper Saddle Rier, J. All righs resered. This maerial is preced under all cprigh laws as he 60