Chapter 2 solutions

Chapter 2 solutions - 2.5 Solutions 39 distance the...

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39 2.5 Solutions distance the rightmost point on the top block can hang out beyond the :x:<)~ table') How docs your answer bcha\e for S Solutions I, Hanging rope Let T(l'l bc the 1elbi(>ll ,b 2 timctiol1 of hc'lghL Con,ider a smail ple<.:e of the rope bcl\\eelll' nnd ,I' -r- til' (0 .I':'C L L Tile I')r<.:'" 00 this piec;: are n,1 ~ ,h) T(l'l d\moware!, and the pgdl' lhm11\\ aro, Since the rope IS at reSL I\e hDIC Tl.1' dll = T(l'i + fig £I" Expanding this to fir" order ill lit gill', = fig, The lClbion 'n the bottol11 of the rope i, lero, so intL'grating from\' = 0 up 10 position giYc;-; , It» TiyJ = I'gl', A:i n double-check, at tile lOp en,l Ill' hd\c TiL! = 11111<:11 h \'ll' Ileight nt',}l" entin: rope, as it ,b\llild be, ,'Iternatilcly, IOU can ,i:11I'II' IHIt" oOI\n the ;111 ,,\C 1', = fl.!!,L by not1l1g tltal the tensiOll at a Cll point III the r('pc i, II hdt 'UpPl1rL' the II eight nf all the l\)jK be' k1\\ i L ; BlOCh on iI plan~ 13~i,"ll1CJl1g tilL' forcl. .'" ",hl,}\\!i in F\g. 2,-1.1. p~irCl!kl ~md pl.·JT1 . . . ndil"ul~lr 1(.1 dll~ pbnc, \\,:: ;,('1. ..' that ,in fl ;jlld.\ = Ill,':. ! \.-'\):->';. I'hl' hnri/I,\;)i,\I I. .'\,)mpnr,:c:lt" llf 1;1,-'~(' ~jrc FCt,-. ./1 = mg:--mi!l't):--ri \:l\ lbl. .' rl:.:ht) .• mL'! \ :-.:11'"1 (":,,,u:--il1i! !liJ the 1. .,:flL rhl"l' :\rl' ,-"qll~l1. ~L" th:.,;~ IlHbi bl", bl',.:.!lhl' 111-': 11':( ht i ri7t"!H,:1 ['1.\]'(1. .' llll th . ., I"'it)l'!-. I" /":1\), fl.) Il:~l.\ i1ni/l' !!lC \ ~dth: llr m,r. !. "In i, l.\h tl, \\ (' l';Jn ('i11)l. . .'r t~ll-.I. .' th(' d •. .'rl\ Jll\;':. IJ1' \\;.,; 1.:;1)1 \\ r', 1 1.2 it ~I"-' UJ!( :::! fn)ll'i \\ hli.Jl ;! (k~l:' ll'.~ll ~hc mc\.\LllUm tl(\,.'";.l"" ~1l H :T. ...j. [hI. .' !j'':~I\inHjln \ ,du<. .' ~:., fJ/.'.!. .=:. "OIiolllr" chain L'. .'l thl' ",,-,un l' bl' d . .,. . l,;·ibl. .'d ;11\. ' rli!l\. .:ti~·;!l r j'\ 1. 1":1 it run t'l\);~l ;i !C' \ /; ll'lhidcr d :juk I1Il'l'l,: pi' thl.' l.'h~\jll hl';\\ \.' ;;I:d \ ~ \/\ ! "". > . .' l i~ :,-1: I, rhl' krlf: 1 \ll'!h~" pi . >,. ·l' \! l - (i, . ... \.11[-., I1L1"":"'! \ 1 . \\ 1I('1'I. .'} h I!h.' 111:\ . . " 1", -'1' Ulilt 1 k:l:;lh. [hl' l"~~I1~~"'\.\II\ . :1l1 \.\:'11:"",' ,t\ IUlil,l:l,I: ~11,. .'l",',,-"k' .11:,11'1 ;>11. ' l'll]'\ ",' ;" "m I' t:l \ I ~ ! idrl I; ). \\ ilh Ii()"<oi:i\ , .' . . ·t>lT"""'l'l\iidin= II.) 111('\ l!1~ ,li,ll'l!; t11I. .' clln c' trUl1l ~i In h. I hl' it)!:!: :'l!'I,. .'I. .; ~;k' \"'un l,' h thl. .'i'cl·\II\' I _ I I! / I ~l'(/ !,t! i ;/H} , 1-) !I Keeping a booh up (;'Ii filL" ll(jrm~ll !'Pl'l'l' fn)t11 til;.: \\;:JJ i." F L'l"'!!' :--1.: lhl~ fril'( tIll j'UJ'l',,' F, h,iding till' hl)i,)k 1-. ~ll m~bl flr \.-'~h/-j. Thl' lltl1 . . 'r \l'nlc,d (tlfl'l':- un tlil' :!I,IUh. <l!\. thl.? ~ il'jh (,ut lilat Illl; llll't:l{HJ ;.,If "i~)L'~:!lg -..11lI\\ II in Fig. ::.iO \\ itlt the I.--.j\.). .:,,:-. ",impl} ....:~k·h. ..:-d \11: :\'1' ~lL'h ();i1":T! du. .;~n '{ } :dd 1:11,. > (,ptimal t)\ S",'(' ! L III 2f)()," l fur;111 i!1tI,.;T. .;-. .rillg J:."<o(~h"i~)jlllr '\ r :n. . 'lhl.xt~. ilia ,~ - !Ii", ~ til El Fig, 2,41 I. " r /, " I'd\ ,/0 1 .\ . ,II Fig. 2,42
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40 Statics gralitallonal force. ,,'hleh is -JIg, and the \enical component of F. which is F sin H. If the book is to slay at rest. we must 11<1\<? F sin I) Ff·.t/g = O. Combining this with the condition F; ::: II F cos H gi\cs F(sinH+/lcoSH) .ltg. (218) Therefore. F must satbfy F > ~-~ .--'~~.--- (2.19) - sin H /1 cosH assliming that sin ti ~t-/i ,I is po,it]"':. Ifil is ncgatl\e. then there is no solution for (b) To minimize this lo\\er bound. we mllst m3"llnile the dCl1111l1l113tnr. Ta"ing the denlatl\': gi\es cos f-I I' Sill H O. so tall H 1/1. Plugging thl' \ alue PI' Ii back into Eg. e.llJ ) F (with Ian H = I !i I. (220) I I 4~ I" This is the smallest possible F that keep, the hook up. and the angk must he H tan-II I ./, ) for it to work \\·c slOe that if /' i.s \\oT) small. then to minimize your you should push es<,entialh \cmcally 1\ ith a force mg.
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Chapter 2 solutions - 2.5 Solutions 39 distance the...

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