Energy, Work, and Simple Machines

Transcription

1 CHAPTER 10 Engy, Wok, and Simpl Machins Pacic Poblms 10.1 Engy and Wok pags pag Rf o Exampl Poblm 1 o solv h following poblm. a. If h hocky play xd wic as much foc, 9.00 N, on h puck, how would h puck s chang in kinic ngy b affcd? Bcaus W Fd and KE W, doubling h foc would doubl h wok, which would doubl h chang in kinic ngy o 1.35 J. b. If h play xd a 9.00 N-foc, bu h sick was in conac wih h puck fo only half h disanc, m, wha would b h chang in kinic ngy? Bcaus W Fd, halving h disanc would cu h wok in half, which also would cu h chang in kinic ngy in half, o 0.68 J. 2. Togh, wo sudns x a foc of 825 N in pushing a ca a disanc of 35 m. a. How much wok do h sudns do on h ca? W Fd (825 N)(35 m) J b. If h foc was doubld, how much wok would hy do pushing h ca h sam disanc? W Fd (2)(825 N)(35 m) J which is wic as much wok 3. A ock climb was a 7.5-kg backpack whil scaling a cliff. Af 30.0 min, h climb is 8.2 m abov h saing poin. a. How much wok dos h climb do on h backpack? W Fd mgd (7.5 kg)(9.80 m/s 2 )(8.2 m) J b. If h climb wighs 645 N, how much wok dos sh do lifing hslf and h backpack? W Fd J (645 N)(8.2 m) J J c. Wha is h avag pow dvlopd by h climb? P W minj 1 min 6 0s 3.3 W pag If h sailo in Exampl Poblm 2 pulld wih h sam foc, and along h sam disanc, bu a an angl of 50.0, how much wok would h do? W Fd cos (255 N)(30.0 m)(cos 50.0 ) J 5. Two popl lif a havy box a disanc of 15 m. Thy us ops, ach of which maks an angl of 15 wih h vical. Each pson xs a foc of 225 N. How much wok do hy do? W Fd cos (2)(225 N)(15 m)(cos 15 ) J Physics: Pincipls and Poblms Soluions Manual 225

2 Chap 10 coninud 6. An aiplan passng cais a 215-N suicas up h sais, a displacmn of 4.20 m vically, and 4.60 m hoizonally. a. How much wok dos h passng do? Sinc gaviy acs vically, only h vical displacmn nds o b considd. W Fd (215 N)(4.20 m) 903 J b. Th sam passng cais h sam suicas back down h sam s of sais. How much wok dos h passng do now? Foc is upwad, bu vical displacmn is downwad, so W Fd cos (215 N)(4.20 m)(cos ) 903 J 7. A op is usd o pull a mal box a disanc of 15.0 m acoss h floo. Th op is hld a an angl of 46.0 wih h floo, and a foc of 628 N is applid o h op. How much wok dos h foc on h op do? W Fd cos (628 N)(15.0 m)(cos 46.0 ) J 8. A bicycl id pushs a bicycl ha has a mass of 13 kg up a sp hill. Th inclin is 25 and h oad is 275 m long, as shown in Figu Th id pushs h bik paalll o h oad wih a foc of 25 N. 25 N 275 m 25 Figu 10-4 (No o scal) a. How much wok dos h id do on h bik? Foc and displacmn a in h sam dicion. W Fd (25 N)(275 m) J b. How much wok is don by h foc of gaviy on h bik? Th foc is downwad (90 ), and h displacmn is 25 abov h hoizonal o 115 fom h foc. W Fd cos mgd cos (13 kg)(9.80 m/s 2 )(275 m) (cos 115 ) J pag A box ha wighs 575 N is lifd a disanc of 20.0 m saigh up by a cabl aachd o a moo. Th job is don in 10.0 s. Wha pow is dvlopd by h moo in W and kw? P W F d (575 N) ( 20.0 m) s W 1.15 kw 10. You push a whlbaow a disanc of 60.0 m a a consan spd fo 25.0 s, by xing a 145-N foc hoizonally. a. Wha pow do you dvlop? P W F d (145 N) ( 60.0 m) 348 W s b. If you mov h whlbaow wic as fas, how much pow is dvlopd? is halvd, so P is doubld o 696 W. 11. Wha pow dos a pump dvlop o lif 35 L of wa p minu fom a dph of 110 m? (1 L of wa has a mass of 1.00 kg.) P W mg d m gd wh m (35 L /min)(1.00 kg/l) Thus, P m gd (35 L /min)(1.00 kg/l)(9.80 m/s 2 ) (110 m)(1 min/60s) 0.63 kw 226 Soluions Manual Physics: Pincipls and Poblms

3 Chap 10 coninud 12. An lcic moo dvlops 65 kw of pow as i lifs a loadd lvao 17.5 m in 35 s. How much foc dos h moo x? P W F d F P ( W)(35 s) d 17.5 m N 13. A winch dsignd o b mound on a uck, as shown in Figu 10-7, is advisd as bing abl o x a N foc and o dvlop a pow of 0.30 kw. How long would i ak h uck and h winch o pull an objc 15 m? 1 (15 m)(210.0 N 40.0 N) J Foc (N) Scion Rviw 10.1 Engy and Wok pags pag Wok Muimi pushs a 20-kg mass 10 m acoss a floo wih a hoizonal foc of 80 N. Calcula h amoun of wok don by Muimi. 15 Displacmn (m) W Fd (80 N)(10 m) J Th mass is no impoan o his poblm. Figu 10-7 P W F d F d P ( N)(15 m) ( W) 5.7 min 340 s 14. You ca has salld and you nd o push i. You noic as h ca gs going ha you nd lss and lss foc o kp i going. Suppos ha fo h fis 15 m, you foc dcasd a a consan a fom N o 40.0 N. How much wok did you do on h ca? Daw a foc-displacmn gaph o psn h wok don duing his piod. Th wok don is h aa of h apzoid und h solid lin: W 1 2 d(f 1 F 2 ) 16. Wok A mov loads a 185-kg figao ino a moving van by pushing i up a 10.0-m, ficion-f amp a an angl of inclinaion of How much wok is don by h mov? y (10.0 m)(sin 11.0 ) 1.91 m W Fd mgd sin (185 kg)(9.80 m/s 2 )(10.0 m)(sin 11.0 ) J 17. Wok and Pow Dos h wok quid o lif a book o a high shlf dpnd on how fas you ais i? Dos h pow quid o lif h book dpnd on how fas you ais i? Explain. No, wok is no a funcion of im. Howv, pow is a funcion of im, so h pow quid o lif h book dos dpnd on how fas you ais i. Physics: Pincipls and Poblms Soluions Manual 227

4 Chap 10 coninud 18. Pow An lvao lifs a oal mass of kg a disanc of 40.0 m in 12.5 s. How much pow dos h lvao gna? P W F d mg d ( kg)(9.80 m/s 2 )(40.0 m) 12.5 s W 19. Wok A kg ball falls 2.5 m. How much wok dos h foc of gaviy do on h ball? W F g d mgd (0.180 kg)(9.80 m/s 2 )(2.5 m) 4.4 J 20. Mass A foklif aiss a box 1.2 m and dos 7.0 kj of wok on i. Wha is h mass of h box? W Fd mgd W so m g d J (9.80 m/s 2 )(1.2 m) kg 21. Wok You and a find ach cay idnical boxs fom h fis floo of a building o a oom locad on h scond floo, fah down h hall. You choos o cay h box fis up h sais, and hn down h hall o h oom. You find cais i down h hall on h fis floo, hn up a diffn saiwll o h scond floo. Who dos mo wok? Boh do h sam amoun of wok. Only h high lifd and h vical foc xd coun. 22. Wok and Kinic Engy If h wok don on an objc doubls is kinic ngy, dos i doubl is vlociy? If no, by wha aio dos i chang h vlociy? Kinic ngy is popoional o h squa of h vlociy, so doubling h ngy doubls h squa of h vlociy. Th vlociy incass by a faco of h squa oo of 2, o Ciical Thinking Explain how o find h chang in ngy of a sysm if h agns x focs on h sysm a onc. Sinc wok is h chang in kinic ngy, calcula h wok don by ach foc. Th wok can b posiiv, ngaiv, o zo, dpnding on h laiv angls of h foc and displacmn of h objc. Th sum of h h woks is h chang in ngy of h sysm. Pacic Poblms 10.2 Machins pags pag If h ga adius in h bicycl in Exampl Poblm 4 is doubld, whil h foc xd on h chain and h disanc h whl im movs main h sam, wha quaniis chang, and by how much? IMA cm (doubld) cm MA 100 IMA (0.225) (doubld) F MA so F F (MA)(F ) (0.214)(155 N) 33.2 N IMA d d so d (IMA)(d ) (0.225)(14.0 cm) 3.15 cm 25. A sldghamm is usd o div a wdg ino a log o spli i. Whn h wdg is divn 0.20 m ino h log, h log is spaad a disanc of 5.0 cm. A foc of N is ndd o spli h log, and h sldghamm xs a foc of N. a. Wha is h IMA of h wdg? IMA d ( 0.20 m) 4.0 d ( m) 228 Soluions Manual Physics: Pincipls and Poblms

5 Chap 10 coninud b. Wha is h MA of h wdg? F MA F ( N) 1.5 ( N) c. Calcula h fficincy of h wdg as a machin. MA 100 I MA % You x a foc of 225 N on a lv o ais a N ock a disanc of 13 cm. If h fficincy of h lv is 88.7 pcn, how fa did you mov you nd of h lv? fficincy W 100 W So d o i F d 100 F d F d (100) F (fficincy) 26. A wok uss a pully sysm o ais a 24.0-kg caon 16.5 m, as shown in Figu A foc of 129 N is xd, and h op is pulld 33.0 m. Figu a. Wha is h MA of h pully sysm? F MA m g F F 33.0 m N b. Wha is h fficincy of h sysm? fficincy MA IM 100 A 16.5 m 24.0 kg (24.0 kg)(9.80 m/s 2 ) 129 N (MA)(100) d d (MA)(d )(100) d 0.81 m 28. A winch has a cank wih a 45-cm adius. A op is wappd aound a dum wih a 7.5-cm adius. On voluion of h cank uns h dum on voluion. a. Wha is h idal mchanical advanag of his machin? Compa ffo and sisanc disancs fo 1 v: IMA d ( 2) 45 cm 6.0 d ( 2) 7. 5 cm b. If, du o ficion, h machin is only 75 pcn fficin, how much foc would hav o b xd on h handl of h cank o x 750 N of foc on h op? fficincy MA IM 100 A so F ( N)(0.13 m)(100) (225 N)(88.7) F 100 (F )(IMA) (F )(100) (fficincy)(ima) (75 0 N) ( 100) (75)( 6. 0) N (1.82)(16.5 m)(100) 33.0 m 91.0% Physics: Pincipls and Poblms Soluions Manual 229

6 Chap 10 coninud Scion Rviw 10.2 Machins pags pag Simpl Machins Classify h ools blow as a lv, a whl and axl, an inclind plan, a wdg, o a pully. a. scwdiv whl and axl b. plis lv c. chisl wdg d. nail pull lv 30. IMA A wok is sing a mulipl pully sysm o sima h havis objc ha h could lif. Th lags downwad foc h could x is qual o his wigh, 875 N. Whn h wok movs h op 1.5 m, h objc movs 0.25 m. Wha is h havis objc ha h could lif? F MA F so F (MA)(F ) Assuming h fficincy is 100%, MA IMA d (F d ) ( 1.5 m) (875 N) ( 0.25 m) N 31. Compound Machins A winch has a cank on a 45-cm am ha uns a dum wih a 7.5-cm adius hough a s of gas. I aks h voluions of h cank o oa h dum hough on voluion. Wha is h IMA of his compound machin? Th IMA of h sysm is h poduc of h IMA of ach machin. Fo h cank and dum, h aio of disancs is 2( 45 cm) ( 7. 5 cm) IMA d (3) ( 2) d 2 (3)(2)(45 cm) (2)(7.5 cm) Efficincy Suppos you incas h fficincy of a simpl machin. Do h MA and IMA incas, dcas, o main h sam? Eih MA incass whil IMA mains h sam, o IMA dcass whil MA mains h sam, o MA incass whil IMA dcass. 33. Ciical Thinking Th mchanical advanag of a muli-ga bicycl is changd by moving h chain o a suiabl a ga. a. To sa ou, you mus accla h bicycl, so you wan o hav h bicycl x h gas possibl foc. Should you choos a small o lag ga? lag, o incas IMA ga whl b. As you ach you avling spd, you wan o oa h pdals as fw ims as possibl. Should you choos a small o lag ga? Small, bcaus lss chain avl, hnc fw pdal voluions, will b quid p whl voluion. c. Many bicycls also l you choos h siz of h fon ga. If you wan vn mo foc o accla whil climbing a hill, would you mov o a lag o small fon ga? small, o incas pdal-fon ga IMA bcaus IMA f pdal on ga 230 Soluions Manual Physics: Pincipls and Poblms

7 Chap 10 coninud Chap Assssmn Concp Mapping pag Ca a concp map using h following ms: foc, displacmn, dicion of moion, wok, chang in kinic ngy. Foc Displacmn Dicion of moion 39. Wha is a wa quivaln o in ms of kilogams, ms, and sconds? (10.1) W J/s Nm/s (kgm/s 2 )m/s kgm 2 /s Is i possibl o g mo wok ou of a machin han you pu ino i? (10.2) no, 100% Masing Concps pag In wha unis is wok masud? (10.1) jouls Wok Chang in kinic ngy 36. Suppos a salli volvs aound Eah in a cicula obi. Dos Eah s gaviy do any wok on h salli? (10.1) No, h foc of gaviy is dicd owad Eah and is ppndicula o h dicion of displacmn of h salli. 37. An objc slids a consan spd on a ficionlss sufac. Wha focs ac on h objc? Wha wok is don by ach foc? (10.1) Only gaviy and an upwad, nomal foc ac on h objc. No wok is don bcaus h displacmn is ppndicula o hs focs. Th is no foc in h dicion of displacmn bcaus h objc is sliding a a consan spd. 38. Dfin wok and pow. (10.1) Wok is h poduc of foc and h disanc ov which an objc is movd in h dicion of h foc. Pow is h im a a which wok is don. 41. Explain how h pdals of a bicycl a a simpl machin. (10.2) Pdals ansf foc fom h id o h bik hough a whl and axl. Applying Concps pag Which quis mo wok, caying a 420-N backpack up a 200-m-high hill o caying a 210-N backpack up a 400-m-high hill? Why? Each quis h sam amoun of wok bcaus foc ims disanc is h sam. 43. Lifing You slowly lif a box of books fom h floo and pu i on a abl. Eah s gaviy xs a foc, magniud mg, downwad, and you x a foc, magniud mg, upwad. Th wo focs hav qual magniuds and opposi dicions. I appas ha no wok is don, bu you know ha you did wok. Explain wha wok was don. You do posiiv wok on h box bcaus h foc and moion a in h sam dicion. Gaviy dos ngaiv wok on h box bcaus h foc of gaviy is opposi o h dicion of moion. Th wok don by you and by gaviy a spaa and do no cancl ach oh. 44. You hav an af-school job caying caons of nw copy pap up a fligh of sais, and hn caying cycld pap back down h sais. Th mass of h pap dos no Physics: Pincipls and Poblms Soluions Manual 231

8 Chap 10 coninud chang. You physics ach says ha you do no wok all day, so you should no b paid. In wha sns is h physics ach coc? Wha aangmn of paymns migh you mak o nsu ha you a poply compnsad? Th n wok is zo. Caying h caon upsais quis posiiv wok; caying i back down is ngaiv wok. Th wok don in boh cass is qual and opposi bcaus h disancs a qual and opposi. Th sudn migh aang h paymns on h basis of h im i aks o cay pap, whh up o down, no on h basis of wok don. 45. You cay h caons of copy pap down h sais, and hn along a 15-m-long hallway. A you woking now? Explain. No, h foc on h box is up and h displacmn is down h hall. Thy a ppndicula and no wok is don. 46. Climbing Sais Two popl of h sam mass climb h sam fligh of sais. Th fis pson climbs h sais in 25 s; h scond pson dos so in 35 s. a. Which pson dos mo wok? Explain you answ. Boh popl a doing h sam amoun of wok bcaus hy boh a climbing h sam fligh of sais and hy hav h sam mass. b. Which pson poducs mo pow? Explain you answ. Th pson who climbs in 25 s xpnds mo pow, as lss im is ndd o cov h disanc. 47. Show ha pow dlivd can b win as P Fv cos. P W,bu W Fd cos so, P Fd c os bcaus v d, P Fv cos 48. How can you incas h idal mchanical advanag of a machin? Incas h aio of d /d o incas h IMA of a machin. 49. Wdg How can you incas h mchanical advanag of a wdg wihou changing is idal mchanical advanag? Rduc ficion as much as possibl o duc h sisanc foc. 50. Obis Explain why a plan obiing h Sun dos no viola h wok-ngy hom. Assuming a cicula obi, h foc du o gaviy is ppndicula o h dicion of moion. This mans h wok don is zo. Hnc, h is no chang in kinic ngy of h plan, so i dos no spd up o slow down. This is u fo a cicula obi. 51. Claw Hamm A claw hamm is usd o pull a nail fom a pic of wood, as shown in Figu Wh should you plac you hand on h handl and wh should h nail b locad in h claw o mak h ffo foc as small as possibl? Figu You hand should b as fa fom h had as possibl o mak d as lag as possibl. Th nail should b as clos o h had as possibl o mak d as small as possibl. 232 Soluions Manual Physics: Pincipls and Poblms

9 Chap 10 coninud Masing Poblms 10.1 Engy and Wok pags Lvl Th hid floo of a hous is 8 m abov s lvl. How much wok is ndd o mov a 150-kg figao o h hid floo? W Fd mgd (150 kg)(9.80 m/s 2 )(8 m) J 53. Halok dos 176 J of wok lifing himslf m. Wha is Halok s mass? W Fd mgd; hfo, W m g d 176 J (9.80 m/s 2 )(0.300 m) 59.9 kg 54. Fooball Af scoing a ouchdown, an 84.0-kg wid civ clbas by laping 1.20 m off h gound. How much wok was don by h wid civ in h clbaion? W Fd mgd (84.0 kg)(9.80 m/s 2 )(1.20 m) 988 J 55. Tug-of-Wa Duing a ug-of-wa, am A dos J of wok in pulling am B 8.00 m. Wha foc was am A xing? W Fd, so F W d J m 4 N 56. To kp a ca avling a a consan vlociy, a 551-N foc is ndd o balanc ficional focs. How much wok is don agains ficion by h ca as i avls fom Columbus o Cincinnai, a disanc of 161 km? W Fd (551 N)( m) P W F d (15.0 N) ( m) s 126 W 58. A sudn libaian lifs a 2.2-kg book fom h floo o a high of 1.25 m. H cais h book 8.0 m o h sacks and placs h book on a shlf ha is 0.35 m abov h floo. How much wok dos h do on h book? Only h n vical displacmn couns. W Fd mgd (2.2 kg)(9.80 m/s 2 )(0.35 m) 7.5 J 59. A foc of N is usd o push a 145-kg mass 30.0 m hoizonally in 3.00 s. a. Calcula h wok don on h mass. W Fd (300.0 N)(30.0 m) J 9.00 kj b. Calcula h pow dvlopd. 3 J P W s W 3.00 kw Lvl Wagon A wagon is pulld by a foc of 38.0 N xd on h handl a an angl of 42.0 wih h hoizonal. If h wagon is pulld in a cicl of adius 25.0 m, how much wok is don? W Fd cos (F)(2) cos (38.0 N)(2)(25.0 m)(cos 42.0 ) J J 57. Cycling A cyclis xs a foc of 15.0 N as h ids a bik 251 m in 30.0 s. How much pow dos h cyclis dvlop? 61. Lawn Mow Shani is pushing a lawn mow wih a foc of 88.0 N along a handl ha maks an angl of 41.0 wih h hoizonal. How much wok is don by Physics: Pincipls and Poblms Soluions Manual 233

10 Chap 10 coninud Shani in moving h lawn mow 1.2 km o mow h yad? W Fd cos (88.0 N)( m)(cos 41.0 ) J 62. A 17.0-kg ca is o b pulld a disanc of 20.0 m, quiing 1210 J of wok o b don. If h job is don by aaching a op and pulling wih a foc of 75.0 N, a wha angl is h op hld? W Fd cos cos 1 W Fd cos J (75.0 N)( 20.0 m) Lawn Taco A 120-kg lawn aco, shown in Figu 10-17, gos up a 21 inclin ha is 12.0 m long in 2.5 s. Calcula h pow ha is dvlopd by h aco kg (225 N)(1.15 m) sin J 65. Piano A N piano is o b slid up a 3.5-m ficionlss plank a a consan spd. Th plank maks an angl of 30.0 wih h hoizonal. Calcula h wok don by h pson sliding h piano up h plank. Th foc paalll o h plan is givn by F F sin so W F d Fd sin W (4200 N)(3.5 m)(sin 30.0 ) J 66. Sld Digo pulls a 4.5-kg sld acoss lvl snow wih a foc of 225 N on a op ha is 35.0 abov h hoizonal, as shown in Figu If h sld movs a disanc of 65.3 m, how much wok dos Digo do? 4.5 kg 225 N 35.0 Figu P W Fd s in mgd sin W 2.0 kw 64. You slid a ca up a amp a an angl of 30.0 by xing a 225-N foc paalll o h amp. Th ca movs a a consan spd. Th cofficin of ficion is How much wok did you do on h ca as i was aisd a vical disanc of 1.15 m? F and d a paalll so W Fd F h sin 12.0 m (120 kg)(9.80 m/s 2 )(12.0 m)(sin 21 ) 2.5 s W Fd cos (225 N)(65.3 m)(cos 35.0 ) J Figu Escalao Sau-Lan has a mass of 52 kg. Sh ids up h scalao a Ocan Pak in Hong Kong. This is h wold s longs scalao, wih a lngh of 227 m and an avag inclinaion of 31. How much wok dos h scalao do on Sau-Lan? W Fd sin mgd sin (52 kg)(9.80 m/s 2 )(227 m)(sin 31 ) J 68. Lawn Roll A lawn oll is pushd acoss a lawn by a foc of 115 N along h dicion of h handl, which is Soluions Manual Physics: Pincipls and Poblms

11 Chap 10 coninud abov h hoizonal. If 64.6 W of pow is dvlopd fo 90.0 s, wha disanc is h oll pushd? P W Fd c os so, P d F c os (64.6 W)(90.0 s) (115 N)(cos 22.5 ) 54.7 m 69. John pushs a ca acoss h floo of a facoy wih a hoizonal foc. Th oughnss of h floo changs, and John mus x a foc of 20 N fo 5 m, hn 35 N fo 12 m, and hn 10 N fo 8 m. a. Daw a gaph of foc as a funcion of disanc. Foc (N) b. Find h wok John dos pushing h ca. W F 1 d 1 F 2 d 2 F 3 d 3 (20 N)(5 m) (35 N)(12 m) 600 J 5 (10 N)(8 m) Displacmn (m) 70. Maicuz slids a 60.0-kg ca up an inclind amp ha is 2.0-m long and aachd o a plafom 1.0 m abov floo lvl, as shown in Figu A N foc, paalll o h amp, is ndd o slid h ca up h amp a a consan spd. 25 Figu a. How much wok dos Maicuz do in sliding h ca up h amp? W Fd (400.0 N)(2.0 m) J b. How much wok would b don if Maicuz simply lifd h ca saigh up fom h floo o h plafom? W Fd mgd (60.0 kg)(9.80 m/s 2 )(1.0 m) J 71. Boa Engin An ngin movs a boa hough h wa a a consan spd of 15 m/s. Th ngin mus x a foc of 6.0 kn o balanc h foc ha h wa xs agains h hull. Wha pow dos h ngin dvlop? P W F d Fv ( N)(15 m/s) W kw Lvl In Figu 10-20, h magniud of h foc ncssay o sch a sping is plod agains h disanc h sping is schd. Foc (N) N kg 2.0 m 1.0 m Figu Physics: Pincipls and Poblms Soluions Manual 235

12 Chap 10 coninud a. Calcula h slop of h gaph, k, and show ha F kd, wh k 25 N/m. k y N 0 x m. 00 N m 74. A wok pushs a ca wighing 93 N up an inclind plan. Th wok pushs h ca hoizonally, paalll o h gound, as illusad in Figu F 1 kd 1 L d m Fom h gaph, F 1 is 5.00 N. 1 So k F d N 25 N/m m b. Find h amoun of wok don in sching h sping fom 0.00 m o 0.20 m by calculaing h aa und h gaph fom 0.00 m o 0.20 m. A 1 2 (bas)(high) 1 2 (0.20 m)(5.00 N) 0.50 J c. Show ha h answ o pa b can b calculad using h fomula W 1 2 kd2, wh W is h wok, k 25 N/m (h slop of h gaph), and d is h disanc h sping is schd (0.20 m). W 1 2 kd2 1 2 (25 N/m)(0.20 m) J 73. Us h gaph in Figu o find h wok ndd o sch h sping fom 0.12 m o 0.28 m. Add h aas of h iangl and cangl. Th aa of h iangl is: 1 2 bh 1 (0.28 m 0.12 m)(7.00 N 3.00 N) J Th aa of h cangl is: bh (0.28 m 0.12 m)(3.00 N 0.00 N) 0.48 J Toal wok is 0.32 J 0.48 J 0.80 J 5.0 m 4.0 m 93 N Figu a. Th wok xs a foc of 85 N. How much wok dos h do? Displacmn in dicion of foc is 4.0 m, so W Fd (85 N)(4.0 m) J b. How much wok is don by gaviy? (B caful wih h signs you us.) Displacmn in dicion of foc is 3.0 m, so W Fd (93 N)(3.0 m) J c. Th cofficin of ficion is How much wok is don by ficion? (B caful wih h signs you us.) W F N d (F you, F g, )d 0.20(85 N)(sin ) (93 N)(cos )(5.0 m) 0.20(85 N) m (93 N) 4. 0 ( 5.0 m) N J (wok don agains ficion) 75. Oil Pump In 35.0 s, a pump dlivs m 3 of oil ino bals on a plafom 25.0 m abov h inak pip. Th oil s dnsiy is g/cm Soluions Manual Physics: Pincipls and Poblms

13 Chap 10 coninud a. Calcula h wok don by h pump. Th wok don is W F g d mgh 78. Th gaph in Figu shows h foc and displacmn of an objc bing pulld. (volum)(dnsiy)gh (0.550 m 3 )(0.820 g/cm 3 ) 1 kg 1000 g ( cm 3 /m 3 )(9.80 m/s 2 ) (25.0 m) Foc (N) J b. Calcula h pow poducd by h pump. 5 J P W s W 3.14 kw 76. Convyo Bl A 12.0-m-long convyo bl, inclind a 30.0, is usd o anspo bundls of nwspaps fom h mail oom up o h cago bay o b loadd ono dlivy ucks. Each nwspap has a mass of 1.0 kg, and h a 25 nwspaps p bundl. Dmin h pow ha h convyo dvlops if i dlivs 15 bundls p minu. P W F d mg d (25 nwspaps)(15 bundls/min) (1.0 kg/nwspap)(9.80 m/s 2 ) (12.0 m)(sin 30.0 )(1 min/60 s) W 77. A ca is divn a a consan spd of 76 km/h down a oad. Th ca s ngin dlivs 48 kw of pow. Calcula h avag foc ha is sising h moion of h ca. P W F d Fv so F P v 0.0 a. Calcula h wok don o pull h objc 7.0 m. Find h aa und h cuv (s gaph): 0.0 o 2.0 m: 1 2 (20.0 N)(2.0 m) J 2.0 m o 3.0 m: 1 (30.0 N)(1.0 m) (20 N)(1.0 m) 35 J m o 7.0 m: (50.0 N)(4.0 m) J Toal wok: J 35 J J J Displacmn (m) Figu b. Calcula h pow ha would b dvlopd if h wok was don in 2.0 s. 2 J P W s 2 W N 48,000 W 76 k 1 m h m km 1 h s Physics: Pincipls and Poblms Soluions Manual 237

14 Chap 10 coninud 10.2 Machins pags Lvl Piano Takshi aiss a 1200-N piano a disanc of 5.00 m using a s of pullys. H pulls in 20.0 m of op. a. How much ffo foc would Takshi apply if his w an idal machin? F d F d so F F d d (1200 N) (5.00 m) m N b. Wha foc is usd o balanc h ficion foc if h acual ffo is 340 N? F F f F, idal F f F F, idal 340 N N 40 N c. Wha is h oupu wok? W o F d (1200 N)(5.00 m) J d. Wha is h inpu wok? W i F d (340 N)(20.0 m) J. Wha is h mchanical advanag? F MA N 3.5 F 340 N 80. Lv Bcaus h is vy lil ficion, h lv is an xmly fficin simpl machin. Using a 90.0-pcn-fficin lv, wha inpu wok is quid o lif an 18.0-kg mass hough a disanc of 0.50 m? fficincy W 100 W (Wo)( W i ffici 100) ncy (mg d) ( 100) J o i (18.0 kg)(9.80 m/s 2 )(0.50 m)(100) A pully sysm lifs a 1345-N wigh a disanc of m. Paul pulls h op a disanc of 3.90 m, xing a foc of 375 N. a. Wha is h idal mchanical advanag of h sysm? IMA d 3.90 m 4.00 d m b. Wha is h mchanical advanag? MA N 3.59 F 375 N c. How fficin is h sysm? MA fficincy 100 I MA % 82. A foc of 1.4 N is xd hough a disanc of 40.0 cm on a op in a pully sysm o lif a 0.50-kg mass 10.0 cm. Calcula h following. a. h MA F MA m g F F 3.5 b. h IMA F IMA d cm 4.00 d cm c. h fficincy MA fficincy 100 I MA % A sudn xs a foc of 250 N on a lv, hough a disanc of 1.6 m, as h lifs a 150-kg ca. If h fficincy of h lv is 90.0 pcn, how fa is h ca lifd? MA I MA F d 100 F d (0.50 kg)(9.80 m/s 2 ) 1.4 N F F d d Soluions Manual Physics: Pincipls and Poblms

15 Chap 10 coninud so, d F d F 100F 1 00 d mg 0.24 m Lvl Wha wok is quid o lif a 215-kg mass a disanc of 5.65 m, using a machin ha is 72.5 pcn fficin? o W 100 W i F d 100 Wi m gd 100 Wi d W i mg 100 (90.0)(250 N)(1.6 m) (100)(150 kg)(9.80 m/s 2 ) (215 kg)(9.80 m/s 2 )(5.65 m)(100) J 85. Th amp in Figu is 18 m long and 4.5 m high. b. Wha is h IMA of h amp? IMA d 18 m 4.0 d 4. 5 m f c. Wha a h al MA and h fficincy of h amp if a paalll foc of 75 N is acually quid? F MA F m g F 3.3 MA fficincy 100 I MA % Bicycl Luisa pdals a bicycl wih a ga adius of 5.00 cm and a whl adius of 38.6 cm, as shown in Figu If h whl volvs onc, wha is h lngh of h chain ha was usd? 5.00 cm (25 kg)(9.80 m/s 2 ) 75 N 38.6 cm Figu a. Wha foc, paalll o h amp (F A ), is quid o slid a 25-kg box a consan spd o h op of h amp if ficion is disgadd? W F g d mgh so F F g m gh d 61 N 18 m F g F A 4.5 m (25 kg)(9.80 m/s 2 )(4.5 m) 18 m Figu d 2 2(5.00 cm) 31.4 cm Lvl Can A moo wih an fficincy of 88 pcn opas a can wih an fficincy of 42 pcn. If h pow supplid o h moo is 5.5 kw, wih wha consan spd dos h can lif a 410-kg ca of machin pas? Toal fficincy (88%)(42%) 37% Usful Pow (5.5 kw)(37%) 2.0 kw W Physics: Pincipls and Poblms Soluions Manual 239

16 Chap 10 coninud P W F d F d Fv P P v 3 W F g m g (410 kg)(9.80 m/s 2 ) 0.50 m/s 88. A compound machin is consucd by aaching a lv o a pully sysm. Consid an idal compound machin consising of a lv wih an IMA of 3.0 and a pully sysm wih an IMA of 2.0. a. Show ha h IMA of his compound machin is 6.0. W i1 W o1 W i2 W o2 W i1 W o2 F 1 d 1 F 2 d 2 Fo h compound machin 1 IMA c d d 2 d 1 IMA d 1 and d 2 IMA 1 d 2 2 d 1 d 2 d 1 d IM A 1 d 2 (IMA 2 )(d 2 ) 1 d 1 (IMA 1 )(IMA 2 )(d 2 ) d 1 IMA d c (IMA 1 )(IMA 2 ) 2 (3.0)(2.0) 6.0 b. If h compound machin is 60.0 pcn fficin, how much ffo mus b applid o h lv o lif a 540-N box? MA I MA IMA ( F) ( 100) ( F) ( IMA) so F ( F) ( 100) ( ) ( IMA) F F (5 40 N) ( 100) 150 N (60.0)( 6. 0) c. If you mov h ffo sid of h lv 12.0 cm, how fa is h box lifd? d 1 IMA d c 2 d 1 d cm 2.0 cm IM A 6.0 Mixd Rviw pags c Lvl Ramps Isa has o g a piano ono a 2.0-m-high plafom. Sh can us a 3.0-m-long ficionlss amp o a 4.0-m-long ficionlss amp. Which amp should Isa us if sh wans o do h las amoun of wok? Eih amp: only h vical disanc is impoan. If Isa usd a long amp, sh would qui lss foc. Th wok don would b h sam. 90. Buus, a champion wighlif, aiss 240 kg of wighs a disanc of 2.35 m. a. How much wok is don by Buus lifing h wighs? W Fd mgd (240 kg)(9.80 m/s 2 )(2.35 m) J b. How much wok is don by Buus holding h wighs abov his had? d 0, so no wok c. How much wok is don by Buus lowing hm back o h gound? d is opposi of moion in pa a, so W is also h opposi, J. d. Dos Buus do wok if h ls go of h wighs and hy fall back o h gound? No. H xs no foc, so h dos no wok, posiiv o ngaiv.. If Buus compls h lif in 2.5 s, how much pow is dvlopd? 3 J P W kw 2.5 s 240 Soluions Manual Physics: Pincipls and Poblms

17 Chap 10 coninud Lvl A hoizonal foc of 805 N is ndd o dag a ca acoss a hoizonal floo wih a consan spd. You dag h ca using a op hld a an angl of 32. a. Wha foc do you x on h op? F x F cos Fx 805 N so F co s c os N b. How much wok do you do on h ca if you mov i 22 m? W F x d (805 N)(22 m) J c. If you compl h job in 8.0 s, wha pow is dvlopd? 4 J P W kw 8.0 s 92. Dolly and Ramp A mov s dolly is usd o anspo a figao up a amp ino a hous. Th figao has a mass of 115 kg. Th amp is 2.10 m long and iss m. Th mov pulls h dolly wih a foc of 496 N up h amp. Th dolly and amp consiu a machin. a. Wha wok dos h mov do? W i Fd (496 N)(2.10 m) J b. Wha is h wok don on h figao by h machin? d high aisd m W o F g d mgd (115 kg)(9.80 m/s 2 )(0.850 m) 958 J c. Wha is h fficincy of h machin? fficincy W 100 W o i 958 J J 92.1% 93. Sally dos 11.4 kj of wok dagging a woodn ca 25.0 m acoss a floo a a consan spd. Th op maks an angl of 48.0 wih h hoizonal. a. How much foc dos h op x on h ca? W Fd cos W 11,400 J so F d c os (25.0 m)(cos 48.0 ) 681 N b. Wha is h foc of ficion acing on h ca? Th ca movs wih consan spd, so h foc of ficion quals h hoizonal componn of h foc of h op. F f F x F cos (681 N)(cos 48.0 ) 456 N, opposi o h dicion of moion c. Wha wok is don by h floo hough h foc of ficion bwn h floo and h ca? Foc and displacmn a in opposi dicions, so W Fd (456 N)(25.0 m) J (Bcaus no n focs ac on h ca, h wok don on h ca mus b qual in magniud bu opposi in sign o h ngy Sally xpands: J) 94. Sldding An 845-N sld is pulld a disanc of 185 m. Th ask quis J of wok and is don by pulling on a op wih a foc of 125 N. A wha angl is h op hld? W Fd cos, so cos 1 W F 58.7 d cos J (125 N)(185 m) Physics: Pincipls and Poblms Soluions Manual 241

18 Chap 10 coninud Lvl An lcic winch pulls a 875-N ca up a 15 inclin a 0.25 m/s. Th cofficin of ficion bwn h ca and inclin is a. Wha pow dos h winch dvlop? Wok is don on h ca by h winch, gaviy, and ficion. Bcaus h kinic ngy of h ca dos no chang, h sum of h h woks is qual o zo. Thfo, W winch W ficion W gaviy o, P winch P ficion P gaviy F N d F gd F N d F g d F N v F g v (F g )(cos )(v) F g v (0.45)(875 N)(cos 15 ) (0.25 m/s) (875 N)(0.25 m/s) W b. If h winch is 85 pcn fficin, wha is h lcical pow ha mus b dlivd o h winch? o W P W P so, P i P o i o i W W Thinking Ciically pag Analyz and Conclud You wok a a so, caying boxs o a soag lof ha is 12 m abov h gound. You hav 30 boxs wih a oal mass of 150 kg ha mus b movd as quickly as possibl, so you consid caying mo han on up a a im. If you y o mov oo many a onc, you know ha you will go vy slowly, sing ofn. If you cay only on box a a im, mos of h ngy will go ino aising you own body. Th pow (in was) ha you body can dvlop ov a long im dpnds on h mass ha you cay, as shown in Figu This is an xampl of a pow cuv ha applis o machins as wll as o popl. Find h numb of boxs o cay on ach ip ha would minimiz h im quid. Wha im would you spnd doing h job? Igno h im ndd o go back down h sais and o lif and low ach box. Pow (W) Figu Th wok has o b don h sam, W F g d mgd (150 kg)(9.80 m/s 2 )(12 m) J. Fom h gaph, h maximum pow is 25 W a 15 kg. Sinc h mass p box is 150 kg 5 kg, his psns h 30 boxs boxs. P W so W J 25 W s 12 min 10 Pow v. Mass Mass (kg) 97. Apply Concps A spin of mass 75 kg uns h 50.0-m dash in 8.50 s. Assum ha h spin s acclaion is consan houghou h ac a. Wha is h avag pow of h spin ov h 50.0 m? 242 Soluions Manual Physics: Pincipls and Poblms

19 Chap 10 coninud Assum consan acclaion, hfo consan foc d d i v i 1 2 a2 bu d i v i 0 P W F d m ad 2md W b. Wha is h maximum pow gnad by h spin? Pow incass linaly fom zo, sinc h vlociy incass linaly as shown by P W F d F d Fv. Thfo m 2 d 2 d (2)(75 kg)(50.0 m) (8.50 s) 3 P max 2P av W c. Mak a quaniaiv gaph of pow vsus im fo h ni ac. Final vlociy: v f v i a v i 0 so v f a a( 1 ) Thfo, d f 1 2 a 1 2 a 1 2 a a d f m 1 2 (1.00 s) 2 (1.00 s)(7.50 s) 6.25 m/s 2 Fo h fis scond: d 1 2 a2 1 2 (6.25 m/s 2 )(1.00 s) m Fom Poblm 97, Pow (W) 1.2x Apply Concps Th spin in h pvious poblm uns h 50.0-m dash in h sam im, 8.50 s. Howv, his im h spin acclas in h fis scond and uns h s of h ac a a consan vlociy. a. Calcula h avag pow poducd fo ha fis scond. Disanc fis scond Disanc s of ac 50.0 m d f d i v i 1 2 a2 d i v i 0 so Tim (s) d f 1 2 a( 1 )2 v f ( 2 ) 50.0 m 8.50 P m ad P av (75 kg)(6.25 m/s 2 )(3.12 m) 1.00 s W b. Wha is h maximum pow ha h spin now gnas? P max 2P av W Wiing in Physics pag Jus as a bicycl is a compound machin, so is an auomobil. Find h fficincis of h componn pas of h pow ain (ngin, ansmission, whls, and is). Explo possibl impovmns in ach of hs fficincis. Th ovall fficincy is pcn. Th ansmission s fficincy is abou 90 pcn. Rolling ficion in h is is abou 1 pcn (aio of pushing foc o wigh movd). Th lags gain is possibl in h ngin. Physics: Pincipls and Poblms Soluions Manual 243

20 Chap 10 coninud 100. Th ms foc, wok, pow, and ngy ofn man h sam hing in vyday us. Obain xampls fom advismns, pin mdia, adio, and lvision ha illusa manings fo hs ms ha diff fom hos usd in physics. Answs will vay. Som xampls includ, h company Consums Pow changd is nam o Consums Engy wihou changing is poduc, naual gas. I s no jus ngy, i s pow! has appad in h popula pss. Cumulaiv Rviw pag You a hlping you gandmoh wih som gadning and hav filld a gabag can wih wds and soil. Now you hav o mov h gabag can acoss h yad and aliz i is so havy ha you will nd o push i, ah han lif i. If h can has a mass of 24 kg, h cofficin of kinic ficion bwn h can s boom and h muddy gass is 0.27, and h saic cofficin of ficion bwn hos sam sufacs is 0.35, how had do you hav o push hoizonally o g h can o jus sa moving? (Chap 5) F you on can F ficion s F N s mg (0.35)(24 kg)(9.80 m/s 2 ) 82 N 102. Basball If a majo lagu pich hows a fasball hoizonally a a spd of 40.3 m/s (90 mph) and i avls 18.4 m (60 f, 6 in), how fa has i doppd by h im i cosss hom pla? (Chap 6) d fx d ix v x so d fx d ix v x 18.4 m 0.0 m s 40.3 m/s d fy d iy v iy 1 2 g2 d iy v iy 0 so d fy 1 2 g2 1 2 (9.80 m/s 2 )(0.457 s) m 103. Popl somims say ha h Moon says in is obi bcaus h cnifugal foc jus balancs h cnipal foc, giving no n foc. Explain why his ida is wong. (Chap 8) Th is only on foc on h moon, h gaviaional foc of Eah s mass on i. This n foc givs i an acclaion which is is cnipal acclaion owad Eah s cn. Challng Poblm pag 268 An lcic pump pulls wa a a a of 0.25 m 3 /s fom a wll ha is 25 m dp. Th wa lavs h pump a a spd of 8.5 m/s. 25 m 8.5 m/s 244 Soluions Manual Physics: Pincipls and Poblms

21 Chap 10 coninud 1. Wha pow is ndd o lif h wa o h sufac? Th wok don in lifing is F g d mgd.thfo, h pow is P lif W F gd mg d (0.25 m 3 )( kg/m 3 )(9.80 m/s 2 )(25 m) 1.0 s W 61 kw 2. Wha pow is ndd o incas h pump s kinic ngy? Th wok don in incasing h pump s kinic ngy is 1 2 mv2. Thfo, P W K E 1 2 mv2 mv W 9.0 kw 3. If h pump s fficincy is 80 pcn, how much pow mus b dlivd o h pump? o W 100 W i (0.25 m 3 )( kg/m 3 )(8.5 m/s) 2 (2)(1.0 s) W o W i o 100 P 100 so, P i P i P o W W 11 kw Physics: Pincipls and Poblms Soluions Manual 245