111Samp1051190003 Case Digests Corporation Law51190003 Case Digests Corporation Law51190003 Case Digests Corporation Law51190003 Case Digests Corporation Law

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SAMPLE PROBLEMS: 111-SET #10 GENERAL EQUILIBRIUM PROBLEM: 10-1

1) When only the front wheels of n !to"o#$le re r!n onto %ltfor" s&le the s&le #ln&es t ' (Nwhen only the re wheels re r!n onto the s&le* $t #ln&es t + (N, Wht $s the we$ht of the !to"o#$len. how fr $s $ts &enter of r/$ty #eh$n. the front le 2he .$stn&e #etween the les $s 3,' ",

4ol!t$on: We h/e 5enerl5 e6!$l$#r$!" %ro#le" s$n&e ll

for&es $n the %ro#le" .o not &t thro!h s$nle %o$nt, 2h$s"ens tht the %ro#le" &nnot #e sol/e. !s$n only the 1st&on.$t$on of e6!$l$#r$!" 7Fnet8 0), We "!st lso e"%loy

the 3n. &on.$t$on: 7 net8 0),

In the 1st f$!re we .rw the &r w$th $ts front wheel on the#ln&e, 2he #ln&e re.s 59&r on #ln&e5 8 ' (N, en&e* thefor&e eerte. on the &r 7Nf) $s lso ' (N,

x

N f

W

Scale

N r2.8 m

In the 3n. f$!re* w$th the rer wheels on the #ln&e* we

f$n. tht 938 +(N, en&e* the 1st &on.$t$on of e6!$l$#r$!"$/es !s:

9hor: 0 8 0 9/er: Nf; Nr - W 8 0

2h!s the we$ht of the &r $s W 8 1< (N,

x

N f

WScale

N r2.8 m

2he .eter"$nt$on of the lo&t$on of the &enter of r/$ty 7%o$nt where W &ts) $n/ol/es .$stn&es =

hen&e tor6!es, We h/e $n.$&te. W &t$n t the >M 7.$stn&e 55 fro" rer le), 2he 3n. &on.$t$on ofe6!$l$#r$!" &n #e %%l$e. #o!t ny %o$nt, We sele&t %o$nt 5A5 s the rer le:

A 8 &(w - &&(w8 W 7) - Nf73,') 8 0

Insert$n the (now /l!es for W = 93* we h/e:

7' (N)73,' ") 8 71< (N) 8 1,+ "

7Note: yo! sho!l. o #&( now = %%ly the 3n. &on.$t$on #o!t the front le, ?o! sho!l. et the s"enswer,)

3) A +00 N #r$&(lyer $s 1,@ " fro" one en. of !n$for" s&ffol. " lon* we$h$n '00 N, A %$le of#r$&(s we$h$n @00 N $s " fro" the s"e en., If the s&ffol. $s s!%%orte. t the two en.s* &l&!lte thefor&e on e&h en.,

10-3


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4ol!t$on: We h/e enerl e6!$l$#r$!"%ro#le" s$n&e ll for&es .o not &t thro!h &o""on %o$nt, 4$n&e we "!st !se the 3n.&on.$t$on of e6!$l$#r$!" to sol/e th$s %ro#le"*We C!"% r$ht $n n. &l&!lte tor6!es,

Now there re 3 5!n(nown for&es5 T1 n. T3 ,A%%l$&t$on of the tor6!e &on.$t$on #o!t ny%o$nt $/es !s s$nle s&lr e6!t$on, 2h!s wenee. to &hoose %o$nts so tht one of the!n(nown for&es w$ll #e el$"$nte., If we&hoose %o$nt 5A5 s the left en. we w$ll el$"$nteT3, 2h!s:

Wm

T 1

T 2

Wb

1.5 m1.5 m

3.5 mW

s

7 m

A 8 &(w - &&(w 8 Ws7,@) ; W# 7


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Ml!"$n!"8 Al 8 Al7r1)3.1 8 73)

37,1ons$.er now the e6!t$on we !se. to &l&!lte 55, We note tht e&h 5we$ht5 ter"s $n/ol/es 5"ss5 , 4$n&e e/ery ter" $n the n!"ertor = .eno"$ntor &ont$ns 5we$ht5 then the 55 f&tor &n #e &n&elle.n. we h/e:

&" 8 "11 ; "33 8 " $$

"1; "3 " $

2h$s $s* of &o!rse* the 5for"!l5 for &l&!lt$n the %os$t$on of the >M,


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4ol!t$on: We f$rst .eter"$ne the nle of the l..er,

We h/e: &os 8 D3@ 8 73


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Now $s there %o$nt we &n &hoose wh$&h w$ll s$"!ltneo!sly el$"$nte #oth NC = fAs"2he nswer $s nos$n&e these 3 for&es re %rllel, 2h!s to &l&!lte NAwe &hoose ny %o$nt we wnt 7s$n&e we now (now#oth NC= fAs), Let !s &hoose %o$nt 5B5

B 8 &(w - &&(w 8 NA 7D3) - fAs73


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2he 6!est$on rer.$n how fr !% the l..er thewo"n &n &l$"# $n/ol/es .$stn&es* n. hen&e&n only #e nswere. #y &ons$.er$n tor6!es,Let 8 .$stn&e the wo"n $s !% the l..erfro" the #se, 2he for&e &on.$t$ons 7#o/e) renot ffe&te. #y th$s .$stn&e , We now $"%osethe 3n. &on.$t$on of e6!$l$#r$!"* tht the net

tor6!e #o!t ny %o$nt "!st #e Hero, Let !s&hoose %o$nt 5A5* the #se of the l..er,

A 8 &(w - &&(w 8 w 73+D3) &os

; W &os - N 73+) s$n 8 0

4$n&e #oth w = W re f$e. 7w 8 @3 l# W 8 1@+l#) n. the nle $s f$e.* then s 55 $n&reses we"!st h/e N $n&res$n, 2he "$n$"!" /l!e ofN o&&!rs #efore the wo"n ets on the l..er,9ro" the for&e e6!t$on N $s lwys 8 fr$&t$onl

for&e t the #se, en&e* when $n&reses* N$n&reses 7= hen&e 9$n&reses), 2h!s* $s "$"!" when the fr$&t$onl for&e $s

"$"!"* tht $s 8 +0 l#, Not$n tht &os 8

10D3+ we then h/e s$n 8 3M, If we &ons$.ere. tor6!es #o!t %o$nt 5A5* we wo!l. h/e n

!n#ln&e. tor6!e .!e to for&e P, 4$n&e th$s tor6!e $s &(w #o!t 5A5*then N"!st %ro.!&e &&(w tor6!e #o!t 5A5, 2h!s N"!st &t tthe #se of the #o to the r$ht of the >M,

C x

y

! x

"f

N

W

A

#

We %%ly the 1st &on.$t$on of e6!$l$#r$!":10-

9: P - f(8 0 n. 9y: N - W 8 0 ,


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We lso h/e the relt$on #etween f ( = N: f ( 8 (N ,

2h!s: N 8 W 8 '00 N n. f( 8 7,'0)7'00) 8 +


8/8

ere we &l&!lte the .$stn&e #etween the h$nes s: h - 3 . 8 3,@ - 73)7,) 8 1, " ,

Now %%ly the &on.$t$on #o!t %o$nt 5A5:

A 8 &(w - &&(w 8 W 7,+) - 9Bh 71,) 8 0 9Bh 8 + N,

2h$s rees w$th o!r &on&l!s$on #o/e tht the "n$t!.es of these for&es "!st #e the s"e, We now note

tht these for&es re .eter"$ne. $n.e%en.ent of the /ert$&l for&es, en&e* $f we h. not #een tol. thte&h h$ne s!%%orte. hlf the we$ht* we wo!l. st$ll rr$/e t the s"e nswers for the hor$Hontl for&es,2he 6!est$on then o&&!rs to !s: 54!%%ose we h. not #een tol. th$s f&t, >o!l. we &l&!lte 9 A/n. 9B/52he nswer to th$s $s noF 2he 1st &on.$t$on tells !s tht the$r s!" $s e6!l to W, We wo!l. h/e to $n/o(ethe 3n. &on.$t$on $n or.er to tte"%t to &l&!lte the$r $n.$/$.!l /l!es, owe/er* 9A/= 9B/re &oll$ner7tht $s* the &t lon the s"e l$ne), 2h!s sele&t$n ny %o$nt to el$"$nte 9A/lso el$"$ntes 9B/ sele&t$nny %o$nt to ret$n 9A/* lso ret$ns 9B/, 2h!s the$r $n.$/$.!l /l!es &nnot #e &l&!lte.,

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111Samp1051190003 Case Digests Corporation Law51190003 Case Digests Corporation Law51190003 Case Digests Corporation Law51190003 Case Digests Corporation Law