Assignment 3 My Solution

l, l

--- -r1__ !i Ir

(A) Reduction into a Force-Couple System at a point:Problem (1) t3.871: While tapping a hole, a mechinist applies thehorizontal forces shown to the handle of ihe tap wrench. Show that iheseforcd;d e{.uivalent to a single force, and specify, if possible, the point ofapplication of the single force on the handle.

(: (0, o7 u)*->r

F,t)oB Fr=

\*)Ft--

-L6,5t(,CIs2<i - z6,sr sinlEil.

"9r us?.5 i 4 2t * (ivrrs fi.

-; ttnnl fllL

on a=Ytrryud u( fr

&Lrr^{ q

H, ,'c, =

I

m;m.ct'.iap fUr.,.k,:n"{ f

L o't'arn+ QurnL Crnomr,fi

li -l lt

0 o CI,ot

-Z#wts o -1.r,51515

I9hJZ5

= -(:?,tZGo(?d

"'\I1

rt( =R=

bvtatti,r3 C- iltyu c,riginynomrr,t* ,'S I tb € orilq,

o o' - o,ol= - l7,o3 q t?6 ) J

o 29tntg

-'c h,t5hs ?5) j.AA'/'s Cot"l5't +2,E Srnlt r

hcrrt wt rf tuJ&J t]4A ( 1 rtr nn

oP {6ro- 1't, o.ttyt" finn d o rrvo.rrrla,i;l

u \ ?trir\ c-J->

* 't{ ,R = (t.scost(i + t.l 6w rl i ) . (* (.t{ro!r{'"

.'''' ' n:.r1 J-t.,R ':uJtL{/n

Rt **u trr-, r-ryu,:*lr^,,i, C.n\,hnr:1t",&rr& !y {{ trv. .!

\ a (rn3L

'?", cq e =-

I L, \enS?t t,l ,! S*^ zs r1.

u6

flo.R =.,(.,

\!

wt bn p.fuP axir e f

?olnto{ oqg16r,4*6 * r:* (avtt t5 uf\ e\trrl.hox

€-

WrRv.(y'^ in u^^^'(/^ ?R ='o.#

oC a Ct.SSin?s)

hr"l\ ( z(xF) -U

-+(o)(?,i,iol?6)

(t,r cos zE J )

- X ( l,tsiare ) )

' ?=o%

% Colls - X Sin ?l = -,\.6 G cos Zs

Xb,mt{ --1,6G

u----l .= - t.C( t xton^ .e g

-: Crf f,= o

-- \2

L

u(

oI

\

o*t{i 1J e*ra,^

}J\p'Yr) ,\rna

iz- = -\.G( j

bwo:Y- (o,o,-\,(6gd+t," Sr.orh o { Unoou dulsu, (tv6 ftr$r6 ' g

S vr^'("

?out o{

Problem (2) [3,1221: While a sagging porch is leveted andrepaired, a screw jack is used to suppoft the front tr trr. porch. As the jack isexpanded it exerts on the porch the force-couple system ,ho*n, whereR=300 N and M=37.5 N.m. Replace this forc"-couple system with anequivalent force-couple system at C.

od A=

$=C ?.G, rs , o'5)( t,\, t,47 o )

,AB

-.!.a'i l\=

- B-ft=

/50o { t

- o.tltl ,4j- o'5fi

:o'L| -t t,(] - c1f fr)

\i ot' { \.q? ;;'

r l8.q -f oot -J

( o,ti r,tri r0,5 []Lr o.t" + I ,{-rl-t rr,{?

' -l" t'j 'j';.

..,.u'' i

.,./-'/r'' .. .::1i-1 ' ', *" a' " t' 'ii

.."..*t.................................. i.i it:, _--_--__,_-?..k:-.. lj il. ,,,

--J

R -- 1- 4oi

K= 31,5 s

-)l^'1-t^n

5l-35r t\z'5( -.' ( = fo;o,,)

d-A.A-c = 2"6i+o'S?c

5; -?5r'l \?'i k - t4o\,1l.Q0j + lrg,'fii

{j51 + ?o5i r tho:5 tr i

- Qoi ,tt&i -looi.

eo1pr"rc"\*.'^{ 67;vq/g-!-,3 {\Bw. o* L

'-l

R is t!.r lon'vtr

t1c =

'[?s]

ft0,5

- ti:t'

11

' *

):l:Ilr

i Ht=

\R-i__

(B) Reduction into a Wrench:Problem (3) (3.131): The forces and couples shown are applied totwo screws as apiece of sheet metal is fastened to a block of wood. Riducethe forces and the couples to an equivalent wrench and determine (a) theresultant force R, (b) the pitch of the wrench, (c) the point where the axis ofthe wrench intersects the xz plane.

DOo 5, = -\\ ,f C o,s, -o,3r5)

(t = -\o,l (o10, o'5)

Hr= - 6 I

r1?- = - (S+;*'

f1o,= toro'5 I{o, -*llxo,il!

Ko - FlrtFtt

R : -2\ j

?-= 8_,H{l(tz

t\-tor *Y\ot : o'47sr,

MaXlla&e* = Zl

= _g*f?__5-3 = 4

44r 1

03= l?(] 8z:40'

tI

- \2:N 0 r'Qo

f1 s- e(=

frl xz p\on^q 9 :-0 X=oZ= \l?\= 6.0(t(i

-\zi

Ponn,{ f o, ', o'tr\tq )

Problem (4) 13.137]: Derermine wherher the force-and-couple systemshown can be reduced to a siqgle equivalent force R. If it can, determine Rand the point of where the line of action of R intersects the yz plane.If itcannot be so reduced, replace the given system with an equivalent wrenchand determine its resultant, its pitch, and the point where its axis intersects

06

the yz plane.

A= (or tlr 6)

G=C 16, o.,o)

ll = ("1n, 6/ _rt)

to i.

;i t' ^\:Fl' qtt6t-l2Vr

F. (t(r o, ()

= ( i+ 6.1 -l'l tt

t?o i

I

Fr=

Fr_ l( tt ( itC J -tt frl

/i,r 1 5z 1,1a T= c \1-)11/ o)

-' A[-- t6i -rtjTf = l{' -rljr6L

H --'. \10-_5

(

lo

ruio rzl

I\o o

Ko

R

lo+ Si-tl"Jt(nl *,6u,,\,, l l+ff r lfr (,[J

I

l.-r,'6o= t+ (\(i_r?3' *r5_gr.I f:" - tt?v\(r2r ttL

= -6c,rA I _ \l,e t1

'^lt

J

-tr\)

192i t36il.{.4

- l'1u, { lto, t t-'(njtHur,,

- (i {rj,tn2t9,81 i, +\('trr(i + tl{C. 62

"i l*(q5 , R 4s *:- ttt- ty {tr*^ oo,annel i: r (e, tl.^ c.o d t o ... Sivr 1\r {r:r 6-

-; brtli| co^" bg (tilukA t" a. rerrtn\\a.

?= R'It ,.--- = 'itlg.sL t 1\6,sG - ?9i,2rr ilKlt ---' \z+ 6? +LL

? = ,\ \,gE in

t( --' nna0ilg,tn6, qL U-lt{ tU

91

-: H, -- tR = 5q,52 1 + 9".1c i - ?:, =l 6 il(

*: 69,52 = ttr.6g - (g(+t - ZG) )

%Z,lZ = l{\,t( - tz(q) K (-tl ) -o (\:

-19,=19 = ttt6,(t -(xf6) -Ytq\) -''.

td\r^^{.., i\r*\t, <cc{. I yz ?\o,rtL" _

br *t*b t$ra-dlr^ A.3 -+ 7= - \t'o 3

L2 tr. s\vr5 eg^o*rua(! ---+, i = -{ (.o53

?oYnA t o, -{A-er1 , -\2,03)

socket joint at C and by two cables AD and BE. Determin" tlh. tension ineach cable and the reaction at C.

r , L,urr4oj mKin3 ( 0o origrfl ( u1u7,,) ,,,...*'1,' ; f-: B- (€ro,o) A,.\ o, ,^

'io"" A" -t::;i"

A = ((rorc,J -'' A0 = -g;+1+4{' I ,.,-'"n "'.; "^''"{),i'i-

E= ( o, ?, -3) Bc- -- -(i +t j+fi. , ,",'2 -:

oc1 nr*' ---r-r.

6- (o1 N 1(41 :.'3{.".-_ --'+;" , " i':*"_,

*_--c ,

*i !|1 y't' '--.

, Trie = \-'* --6 ir 2t -3u. { -c ' ' " r'-

u-er+rr[' ; t*(-i;r\'-l i) ""-^,"/" I

I ;;u; l: '

Go- To * -$"1-"r .t11 = rao ( -€ ; t aoi .,t i)tJ 9z 111qt

tfx = o

t ty =u

?{2 =o

. a-

= tri6

?,n

-f Go

$n,

\. I

(o.o9

i

f on I ^

A.,= [- l4 r r Y () Ino\ )- e

i

i

I

I

l+JKCIoQq *ttt

-\fn"+ Crr=o

+$Tno +h - [3t -= o

-4-Trie * t tAr: +(z=e.

Tnn t

I_%ts

K(,

ttlS

J

o

,fg I1g= o

+ $Tae =0

+ $ rne -\E?tr

'IaE j; = {+ t31* rLl+ t ) TrieTAn .: 639 ,\to

Tne = 642 \b

wefqh{:-t99i H^*..-+^f .,r,.. l.f

-o

oP Cx:9*6zr+gxqt[+e

^ rr IILK= \oot \t i

',..*-j(5 : \eg -?-*61L -! *(36a3lCl -= az ru{

, ...::::1

(a1 -tLz -- +*(1r _ I .* 48(-l 3)

\7-* t

\tz' 11 \b \. . -:

&, rcocJglov) C = [o.,tI -qgj+f r( l\

Problem (6) [4.116]: The 18-ft pote ABC is acred upon by a 2r0-1b force as shown. The pole is held by a bail-and-socker joint ai a ano uytwo cables BD and BE. For a=9 ft, determine the tension in each cable and

08

the reaction at A.

"S lqrtqKinS orig inat A A = (o,<rro)

oB R: ( 0, gro)

r=(-1,CI,6)c ' C o, lg, o1

E = (A,s,, ar 9)0 = ( \,5, ot _j)

BE -- h,5i-g,j +g(Ro = 4,bl-3i_tficF = -ei _r6i+6(

'; F= Tb+ (-ei_1gj+e ttl = _)oi_rrrl,+ffi

Tco+ ( q,li -3:- 1^)r<,5t tgr19r

?lR6 = lry- B

"l .,.11..';,-1."/-

"'{'i-'.d:i ;( "'llii t'l .,'" i

I

\, lt

T= A** A1i.t A.ti,

lqo = - Tao t li :-ti3 3'

-+3 +? f\)

-? al

og 1-(y =a

2('1 ="

7(r= o

yi -3jie()v'q..51+ri;;

Ax+fTnontTo.-56=o

Ae -? Tr" -bn, -lf o =t,

Az -$T?", * ?Tot *e"

gzi rt2 + 6t

= &e ('r, I

T t{r, = *r l'

t;

= Tne -:fr)

r ,l ^Ar= lno L-6r -Sv(l

\08 o +l6rorI

+ \(o

j,(3o-? L_l3

((i

Ho, = Tgn 1t(1o

o,-'lj -t l\

i

0

\lr5

t1u3 =

tD

ao

rJo rX

-90 -1$o

Ax=

A,( :

v(

CI

(,-

3o -\ * 3601

-Jo lb

tt-III

Ia

It

I

-; l{n^ = 6

\05 -,,

il{oz = o

6Trge -6tno t \oto = o

o =o

- jTn€ - jTrla -t tep = c

Tae =ttu \lc

Tnp :360 tt

-I3

A: : t8o t?+ 3gc-, *?=t(t(,c3?

41 = 54ult

Ar= *60 +?*r,"A.' (o lb

--: A: -ro1 + 5qo

lx rto

IJ -t (o {- rb

oB hf taKinl origra of Qt4

"J ( ho.,^,s

$vt t,t. ov, Sa fuibl+rFH = lrl

'; c=Ct,Iraa)F ' ( 3, o, -o,rg1

T = ( oz l,lz7 oJ

lJ = ( o, cs, -L,S)C= (oror 3,4)E -- (3, o, o,?-fJ

A= ( j,sroro)

-; F= -t(ol:IEc = -Gc *

Problem (7) [4.118]: Two sreer pipes ABCD and EBF are weldedtogether at B to form the boom shown. The boom is held by a ball_and_socket joint at D and by two cabres EG and ICFH; cable ICFH passesaround frictionless pulleys at c and F. for the loading shown, determinethe tension in each cable and the reaction at D.

{- g,i +?,lstl \

U 3l t ?,t(L

(-si -L?sa l

I= tEG t -1r.\ + z t

"1 ?9a)

TI Ftl -L lFt{ + fu (-\4'- 3Zs i)

uiti i-ia iT'r(T = T,-.\L ) = Tc, t- ustn\ + aqlsr i ) = Tr* [-(qse i +2t75, i)i- t,ti +l,si

V 1,{r lrttt

-. 1ft =o

Lr, :o

r)x - 4 Tec, -S* - (s/s? \H

D3 + * fro -56o -O

7f t =e +u_''}5

0z Tee -*li* =g

=o

1MltO, = lr"| 'E\>

i i 1l=t*i)rec0 o 3'(l-wq o -+,

I

Ko. = Tru

(03 = Tiu

Itoq = - 560

ii^a o -"t,5

-Vt o -r;;It3K

o l.\'l- o

- Tru (t zi)

= Trg (+4-L6a

*0

* i.5 ti = -teco ft-

l.-l' r(0Y,= O O-_o

(oj=6 -g TEc +zTrH=c

floz=o t:!3Tfu -t3(o=o

J{'lqo5j 5l

\ ox = \6\\'3 "t i

fJg = 5(s -g *'la6\,\q?

ri -

ot= 5t$.%s v'v) z--* jlg * Lo (l\,t - 1\lu^ { {-r ca..a(

: a = t4 6tr.g 1 - E? g,$ei -< e ,rt{ n{

-.- Tfu = tt56. = ?'61, I Mc

TFG = 'L6tels- -' t-T 6f ,ooe nY '

lJlTLT = ?o6r.rM ( C.e.Jh\o rctr$ -,t-o61,\N

D x = }1 * 1.16g + qh* ?o6t. t t 4tlr3 * ?c(1,\?e