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phsx205_hw06_solutions

phsx205_hw06_solutions - Chapter 6 Answers to suggested...

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Unformatted text preview: Chapter 6 - Answers to suggested homework problems 5. A crate of mass 24 kg is pushed up a frictionless ramp by a person as shown in Figure P6.5. Calculate the work done by the person in pushing the crate a distance of 20 m as measured along the ramp. Assume the crate moves at a constant velocity. (mm/(warm f o’l’kg Lara l5 lnl’ch Jame. AWCC‘HIDV‘ m! {LC (lispl 010m“); WC V\€€Cl *0 Know Wt‘ql’ Val WC 0" a) [fadj +0 (awquf ZQI‘Q—MjsanOO ;: Mao: -? pp: MjSiWZOO: ”g N 9W: EPA: (HAN) mom): 913503 6. Consider again the crate in Problem 5, but now include friction. Assume the coefficient of kinetic friction between the crate and the ramp is pk: O. 25. What Is the work done by the person as he pushes the crate up the ramp? We. («cu/t1 aflOfker {one If\ «Plate X'dlrec’t‘cc)’\dfld ax»: O , 0 5%: p~~mj(0330°: mg: 0 9 L: Ell/13605309 5&3 Bvr‘jfisimKOO— Eff :Mflzp: O "‘9 E3: i’V‘jJ'NAZOQAl-‘MKFM '9 G): mjii‘ngoaf/erf(mj(o‘r 30‘? I: ’66] N aw?) :Oewmom): 33803 7. Find the work done bv gravity on the crate in Problem 6. of law" w'H/ln gal/Lac (,l isplctcfmfm h Gran/1'9 make; an [Li/17R ‘5 V\/ 5 "(135013' *Nvtc nfjwtiwe work 8. A block of mass m = 5.0 kg is lled along a rough horizontal surface by a rope as sketched in figure P6.8. The tension in the rope is 40 N, and the coefficient of kinetic friction between the block and surface is pk = 0.25. (a) If the block travels a distance of 4.5 m along the surface, what is the work done by the rope? (b) Find the work done by friction on the block. (a) For WOi’K dent [:7 +enjion/ Laue law/fl F7] cl, 2/ 9.: \’\/T : FT cl(059 :: (WONMHCQMJ [05(300) ‘3sz ‘gé j *MD’h’, it”; Posr‘flwe {>6me 7+ 7! (toward ”the. dl‘H’C’l'iom of ((islolanmm'l' ., W5: (3 am; (We); perky)(4—X%)(aom)zo_<(l&o‘i) (1)) H04 9,1;ch mew/11 Flt/3M5 3 fFfi‘C‘l’iOn is (appal/l'e ”(4“ CifSP/f‘fwh+r SO “Him work is r’lf’j(it"H’V’t’flixew 9‘: M700) I ’9 : * cl 2: — m ' , .. — WP FF MK.3(’( 9W.(— SSJJ 10. A snowboarder of mass 80 kg slides down the trail shown in Figure P6.10. The first part of the trail is a ramp that makes an angle of 20° with the horizontal, and the final portion of the trail is flat. Find the work done by gravity on the snowboarder as she travels from the beginning totheendofthistrail. We 4094+ («am/é +0 Sue-P UP V‘o’fk’lf’ck X anAfl 606357 ‘l’hc, (/05er ((0,143 57 firm/i3 TL jug‘f’ Pb ‘HW‘LC ‘HAC (Wily-{i in [\(ifll’xf', I‘Hc Pori‘d'z‘wc, bEMsz +lnc, (are: aml cl‘t'I/Dlaccnqm—l’ are [m the $ amt cl i‘rec-Ha n C 12. A person pushes a broom at an angle of 60° with respect to the floor (Fig. P6.12). If the person exerts a force of 30 N directed along the broom handle, what is the work done by the person on the broom as he pushes it a distance of 5.0m? FEM: We, wan/f "(’0 ULSC 5‘ 600/ Lame/1e WC 6 i, €O>§ Wélh’k kLC COMPOnfm+ a4 +L‘c “\[orCC +1001!” 0 r l9 m ‘i’k‘C Jame. irffitiofl (11 A M3 germs 9 : (30M)(£0M)zos(507 9 WP: 75: 16. Two objects have the same kinetic energy. One has a speed that is 2.5 times greater than . . . a ‘ w the speed of the other. What is the ratio of their masses. I! we (re [00 (’C ' ”j . _ 1:7 49L“: kid/w" We Know Kg! : K5} and \/,~: ,1 5V ‘ , ' 9. «for 5L (WHO, we‘ll divide one eiv‘kfion " “(a K5: J‘MU'Z [I “sf-“13% / A ix K g l 3t t __ M \/ 51 ‘ i753” - * " 7» l;- LV: 2 m, (4%? 64% W A 9x "” V 9‘ I . I MM. .1 a “1 V1 m w j - m C" " l _‘ > MA 5 ,% M; __ OJé *HO‘i’C 7:“ «- éAS Balm [orral‘ l 18. A rock of mass 0.050 kg is thrown upward with an initial speed of 25 m/s. Find the work done by gravity on the rock from the time it leaves the thrower’s hand until it reaches the highest point on its trajectory. Hint: You do not have the calculate the rock’s maximum height. The. {one clue. to you/Hy i: joSnj +0 Make «Hm: rock's .— ’ k I ‘ ’ ‘ K O KEJZ at “\f— top, \Aé: 6K5: %-Kéf v ' a . gm ”9%:dKézz’ MV’Q‘: ( , 5 i —- amosoigflgsg % \/\{j z " l 5.6.: *Nv‘ke, +145 WO(K (Kent, (,2? {flu/pg }; ngja—h‘l/C Lean/1'8 F3 VJ“! Ola/wnlte 4’0"? placemm ’l f, dowel ’i’Lxe. rock (lawn. 19. A horizontal force of 15 N pulls a block of mass 3.9 kg across a level floor. The coefficient of kinetic friction between the block and the floor is pk: 0.25. lfthe block begins with a speed of 8.0 m/s and Is pulled for a distance of 12 m, what IS the final speed of the block? TLC WUrK 6(906 bu +L\Q__ Pal/”1AA? {ofce t5 W’Wfiptfll 9 Tlni y “)0le l>€ ‘FJLIQQLW '/ +140. W0((/\ C(Ofle by {(.(f[‘0n \A/ :_Q ‘9 W4: —Il‘i’j This +0124 wofK is equal {a Hm: clncm C, in K5. :. WTDT: Ol(é:‘l‘ T MV": --—-m\/LED‘ 9 VF:;;} AXTOT+VFQ :- (1,3611%. 23 A softball pitcher can exert a force of 100 N on a softball. if the mass of the ball IS 0.19 kg 5 and the pitcher has it in her hand over a distance of 1.5 m, what Is the speed of the ball when it leavesherhand? \A/ : (136‘ .2 (ICON)(LS.M): ‘50: 25. Consider a small car of mass 1200 kg and a large sport utility vehicle (SUV) of mass 4000 kg. The SUV is traveling at the speed limit (v = 35 m/s). The driver of the small car travels so as to have the same kinetic energy as the SUV. Find the speed of the small car. Left: 'Flmél {lag (<5 04 %%5 SUV 6&le +L‘CV‘ 740A Wleot’l’ fpt'fcl "l’lnej'flacdlcar need; (0K 'l’lxe, same Kg: '9 K€$uv Z imfuv‘éuI/J‘; 9x. Lf/leoéj a Kécaf Mm..- _) KCcu(:J—‘ E M‘flv Va «A ‘9 war; I ‘9 View: ézfi ”Z 33. Consider a roller coaster that moves along the track shown in Figure P6.33. Assume all friction is negligible. (a) Is the mechanical energy of the roller coaster conserved? (b) Add a coordinate system to the sketch in Figure P6.33. (c) If the roller coaster starts from rest at location A, what is its total mechanical energy at point A? (d) If VB is the speed at point B, what is the total mechanical energy at point B? (e) Find the speedofthe roller coaster when it reaches locationsBand C? (a) 516;, I“; #‘ri‘c flow 73 69/“:ch A . (b) (C) girth/‘7 700m “1/“ Mm”! [(64 ‘1 ¢ 14 . . m A ll»: 0 3:0 _> gram; Kg + F64: Mjlv. ; R‘i‘rm emote we weren‘ty‘fvcn M 50 628‘” lad/c M as an unknOWn, _ 3 ._ J. l 91'ng Kégfl 6:}; “AM“; + Malay; : Imvgafv [Li/7,” (A) (elfime érom: Cram: érm a «Mug Hwy: MW e ngy/NMW'WDI: I7- I ”—1 ' firs/WW “W“ .W W fing- 34. Consider again the roller coaster in Figure P6. 33, but now assume the roller coaster starts with a speed of 12 m/s at pomt A. Find the speed of the roller coaster when it reaches locationsBand C. 45cm?" Loft E‘TOTA : 6T0 1'13 : ETOTC swim I b ) r—owflfg gin/Hat V Zy/VZflIAyL‘A—Aykc‘iwm)A+9145/‘3J{_)Oml ¢— :Mls 47. Sketch how the potential energy, kinetic energy and total mechanical energy vary with time for an apple that drops from a tree. ,I ”MC 1“, L __ d) {>0 9 Wm 14th d7 {lamb a Var/lax, L‘ : O 49. A rock of mass 3.3 kg is tied to a string of length 1.2 m. The rock is held at rest as shown in Figure P6.49 so that the string is initially tight, and then it is released. (a) Find the speed of the rock when it reaches the lowest point of its trajectory. (b) What is the maximum tension in the string? , \ 1 _ ( £58005} ‘ The rock (S I , i'n2+fo~llj ovl’ gomc l L=I,LM \ (I ll ‘ASp . 1407le A oll)0v/C j H”! loLdéK‘l’ I907 nl', l O M T147; Potenfial €487 . . , _ 7 l 45 Convev’tul {'0 (<6 1):] “W624: poinf' l), I fl(L‘L(05Jt$0): Q(q*?fi)(l'lM'/'Qm(osolf€j:I (+81]: é) TL‘C +en'Sl0V’l £ofce OV’ti’thCS \S l: 5"an r‘ 'Clzj «HA . ( ‘ 0V6 ’t. a |t a ., (“Ml '5 Maxi/Mum ad’ 4ch Lel‘lom:\7 ’0 C (en “ID + {~Qrcci , . g ggjmwya FT-E33M6LC —> fiT: MF+Mj . " A . .9 CT: {£[email protected])%+(13K3l (149%) a PT: sank/Ml 50. A ball of mass 1.5 kg is tied to a string of length 6.0 m as shown in Figure P6.50. The ball is initially hanging vertically and is given an initial velocity of 5.0 m/s in the horizontal direction. The ball then follows a circular are as determined by the string. What is the speed of the ball when the string makes an angle of 30° with the vertical? WC fie Cal + AC Aeiylw‘l (IA H flecn «l’ke ffrlr’j lS a’l’ EOE: {’Lxen we apply [omerVallondC’meyj‘t l’\:L“ Lcasgoo‘; 6,0M'g,0M)c05 3700: 010%,”. ‘) K52: ”’l’Pég I KEL. 'f’PéA “7:0 -)’l‘ """\/~9‘+M .. l ' 9~ ' .1,er of—g Vi, arr/13% O a \/ a/ A - ‘ a v.- 43», =~ ($.og—‘jt..,mr—g2)(0£0+m) = 3 OT?“ 59. A block is dropped onto a spring with k = 30 N/m. The block has a speed of 3.3 m/s just before it strikes the spring. If the spring compresses an amount 0.12 m before bringing the blockto rest, what is the mass ofthe block? TAE block; in? ial Ké plus” ifs , fir‘avi‘lallonal Pé “V6. €7ual ’90 H": {inhl KE(J)Plu.£ HS “£3 nml ngtv‘n’cwfwnal PE (WHCL w’c (an Rf “f’o ma'xw—w ‘ lhl'l’lotl: final: imadl g 0¢)P|MI f’kf SP4“? I95: .9 KEJPE z~ thiéfl 443$ch lejm ' Vzl‘+mjy- .: i (/ 9\ t 02 \Xf ofl-> g 39 m(:.le*+jg;;)= :‘t m3 Mr~ _\,, /' i A i g a, ‘ 9\ 9m: _L__\ PW : tam): RM)... 5 “Vera 9% {18.3%} +(fi.£g.)(0,dm) 9 M$Q03&6Kq ‘9‘ 61. An archer’s bow can be treated as a spring with k = 3000 N/m. If the bow is pulled back a distance 0.12 m before releasing the arrow, what is the kinetic energy of the arrow when it leavesthebow? The P6 «from PUJUr/j back the, bow ES cam/04 +0 {’Lxc K5 whet/i «the, arrow {5 releotrecl Péz’: K516 -> ‘é‘KKlzKQ '9 K€_(= é(§000%)(01l9\m)2\; ll-éj 62. For the arrow in Problem 61, what is the work done on the bow as the bow string is pulled back into position? ASSLLMh/j no [05! Abra +0 friction, '4'th Work (low: mx «We. bow Y; equml "90 the, cLimm7e 9m PO'l'evaml enft’jy- The wot/K 91 fl?“ PON‘Hi/fi 1280mm ‘hlxfl Pull/raj {One and ‘l’Az. illrlolmmmrmr are ,‘n +L.C Same direc—tfon: . O H9 WSAPét-‘ikx.p$~% V a ’W: ALég'j H and». 68. A snowboarder of mass 80 kg travels down the slope of height 150 m shown in Figure P6.68. if she starts from rest at the top and has a velocity of 12 m/s when she reaches the bottom, what is the work done on her by friction? Note: Figure not drawn to scale. The work“ clone. b3 (fiction, W4, MW—l' Be added {’0 «the final Kg 1, Pé {’0 «(Lou/vi 40F 64” c9“ kL‘é initialeflerqy 3 o o Jég+Péz=K€4ePéi7+Wé 9 W4: Pézvkér a w; : Mgggrfmvj z (rakj)(q,gg)(isomi~g~(townie-59‘ 9W4: Lléxx 105;; ...
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