A- Kinematics of particles (t,n & r,0)Problem #1

An outdoor track is

constant rate from 4

acceleration of the

o8 disla^q. Bc, rn

4 co\(ton'r{b

T\5vf= vo

utq =16

4r. =

eqhh,o'^t u P rnotuon

L + 2aras

t ? q!* 3u'

o,55 * /sec'

130 m in diameter. A runner increases her speed at ato'7 mls over a distance of 30 m. Determine the totar

runner ',2l'after she begins to increase her speed.

vo* t{*{secV$ - ? rnf s6c

E%

?

T Vo=

t=h ynlrec

ZTLC

Vg = vu4 AttUP , t( + or$[{ L'-*;" t

\vP ' 6,t m,/ set-i

.? t^[L = Dr \\ rt\4 \eL

-(6,t12 - oA nlsc*-\.._

-1A rou.l I =

rV ont 4 rgr t t/ o,fcz+ <.,,qt = 0, ( ?'l * / Sec'

b,tn-r - q.Sl. = Z6,oLo di-t-h \t.OrA

An= yLY 6si

7C-nt*-

-L

(nt

Problem #2

Coal is discharged from the tailga!" pr a dump truck with an initial velocityY n = 2 m/s at an angle of 500 with the horizontal. Determine the radius ofcurvature of the trajectory described by the coal (a) at point A, (b) at thepoint of the trajectory 1 m below point A.o8 4+ ?ovn4 A VA = ?-^ lsec .

3 Srn tLr:

1 ?t 4 Sr,,,r\ro"

orvr = uL

u,?Yut

arr*-,rr{tno

cru An:

*- Q.Q> lx (vnuto =

i| 't\"/ /' ^'r= o,6J\ rn

2t7

,VA

yxltt? r'o- u,o

)sY"

=hoL

?(,ol*uqv"o,p J." I vhzr is ?roj( Ct\L vrr.,tr_n

x -- -5a" V rt : Zrn / SCC. ^Aat gg =*1 Yn Trurd

oBuP --

-1, -V. gos

L=

! \b Sr"nq L-

2 en^-6o tL, tl,(32 to'?'Ll6 Sec_ ,

-ltablz-

-llz* q,t\ Lz

-t =a

VB ='3

4-

Vo Sun4 - Cb

2x sva -5t - 3,9\+ o,3?16

-ul, (94 ml set-3-

ob VP*,= .lq &rry : z cos-F".. _ \.zgs r,, lsec_

1gr

.fon - t

rf.8 LVPI = ,l u*rtvrr V( \r?(t

= ,n,i,Grr;;I6;, r, L ? ,

-c tt,G6 'nlftc t h'61? :- rl5

-gq + p- 15,33'I,t{S

h'\4= 3'( t* Srn .t6,3o e,(6 _r(11'.. ,

3 s* \j.3 "fivr : \zF

Problem #3

The oscillation of rod oA about o is defined by the relatio nV = uratri" r,where 0 and t arc exptessed in radial_r-s and seconds, respectively. coilDslides along the rod so that its distance from O ist-;= 16 fi; ; al .^lho.o v qnADrruED arulg rne roo so tnat lts dlstance from o isfi= 16/(t i 6)1 where r and tare expres sed in lqrn\and [s-econds'1 re specti vely. Wbggc,lj derermine (a)the velocity-.of th.e collar , (b1 thea'cceleration bf th"

"qll3f, (c),the

acceleration of the collar relative to the rod.

ry O=({l-.) (vrnrtL

A = L{ Costt L0- = - tt'Ct fyi^ -rtL

Al 1 tvrE tl-Sec

*\4o

to / cr +6)

\o 1l

-\" /,\q'b fzrts

Y& eo

+ toll * -{.,:- t'{,u I; u.r!

"1

..':(=

Y*

V eloQhr _ sAfLr-\o l,^g

{e-r4.g

Y=

Y=

l-

$=9=o-

-(Y' t\') {,

t--

= \ \r -:_"

-l /A-l w

l-\ 3qr

+

(_,

(",

t'

ac&Jrao\*r. .Zr nr€ Jt-r + Lrtg +zi'd ) {*

-'Lza. & + \,6:z

+ (u11 *o + Z+-lol,4"s*-q) &

-4-

= ; = 'hlZlZ ,r,r'/ SCc

0, O <3 vrnvtntls

Q"9

acklfia*bn "f c.dtorr rts\atw * {o vc d

Vg[,outr., {nAA rff-'- -'r ''-'J - y(*t' * [ry)' = 6'-7ta ^"' /sec

hm-l t4,/r-'-r-{ -+ .p = Z,oVSo

to/qg I

ACful-ua.fi"n r*qt = ,f-_J V '0,'lq2 I \,63t-2 : 22.8Vtt t* /(t

1a*-\ !,(rr- :5 X= \l,o3so.Zzns

Problem #4

To study the performance of a race car, a high-speed motion-picture camerais positioned at point A. The camera is mounted on a mechanism whichpermits it to record the motion of the car as the car travels on straightawayBC- Determine the speed of the car in terms of b, e. and o.

od) C.or" fywe I s 1i^\ I+ lrnro"o'iilc- b/us, = tlc"soft

%u !. = i tbl = *btc"sol-t g"

& q'-strotcos $)- J

V= :tsl s**" {-

(ps s) z

\ vt ..- -:-=I t"r g'ir^r V3s,

rf-o5 $J * 6So'

!, .- g' 9oCo\o,

b6 f ----€!i "to"ntd' I l,

COSO

= [ro'(,5 Ld

-5-

Problem #5

Determine the magnitude of theProb(4) in terms of b, e, o. and 6.

?r: b , r

coss Y -- be srr. g

tostg

acceleration of the race car of

{g*r i :ut*,*"'' ';

;l= | .t --DLg slnd

&s

+BtcosOl C,or ?O

L LCnsd ) Gsvrnu ) d

i,O t ed

t---bgtrnoc,os?g+bgto,=, -r -r\- nL^ nt tfJd Sr4n4

Lotto

Ar-= V _v-6L

hg

S-.* o Coslo + b d1 w(a (

C,o stgr ,,),Lv3g

t-o5CI

bp su,.o&s$ +

,,tbd I,n*cl

$"

+ + tr.,iro )

. ,1' r,.|

1,rsz+ bdl-(h^rd _h{

+ Tis t;u)a _L

-

tc_osc,

Cotc"

z bdsw,u(r\ ?-d .

/ffi. r rZ2 krQ Svnd

C,trlZs+ f hg SYvro coto,\

tqtu.f t d's# oJ'

n?)

Iffi

A \,\,^ -

B - Kinetics of particles.

(qt

A tractor-trailer is traveling at 90 km/h when the driver applies his brakes.Knowing that the braking forces of the tractor and the trailer are 16 kN and60 kN, respectively' determine (a) the distance traveled by the tractor-trailerbefore it comes to 4 stp-p, (b) the horizontal component of the force in thehitch between the tractor and the trailer while they are slowing down.o6 h&rO distqryr& *vo,.rcter)ftb ,^Jh"\e L45 ,u g 7ti{tt} t<{:

ly,,h{ dh'u hu,ig 6c oyrc .'].],lrt i'r

r*,,^;,i1,' J)", r#:;:ryffry-ffi': r r

P., idv-on r r r rcY (Q'c oF

ry ffiVo.furhrr^ /h s 25 urr lStC

t{vttv*-*-.1" l--? meo& tfr, -mA 6'nM# t I 'rrlq u(=.,

Problem #6

*Tg*ts3 N =.

A = -5.11

t^Jitq^^ -t tto

LUt "mt1

It{l ob* hm/st

'161ur,+ 19",-)-{ t,gl

t&i,rt"wr"qrhh (4tt&to\\og u&Io.otun co4 !hh",4 WC\

v(' * Vut + ?a asC -- GE) 2 -r t{ -s,l:l )

A E : ,lis pfu O,^ar\+

ibt z bo[r,us \la^p dottlt, n 4tn efri+

rul-.d 'l* itru ,i o\^{ huJ* ,-, g1uovr.

-*-+ fl\ A

F

V"drwt*, trc^"

w 0 S1"df P^r.{

Synes tu" ,a hils

a- *5,1?

b"Sf w,:\/ gi wt'-it^-7 -ntl!t"

(8q, r)

.% ho'n+ o.\st, mo{e(,^l,lt^ A= - E,la^/\r.

-- 7F1=o F_\6+1"3 = rnq

(= \(*ro1 - cgoo,rF S,\?

F= : l:t(6 N

bAa6rrl*vr{q d ln n6"r,to.{ L,rrn4"warrrf \9r s6 rJ,

Problem #7

2 9!^*r\ t '

Xc+Xrs = Cbrrtto**

Vc= -VglAc= -ARr-+ rD

la (n + jXe.- con $rr^{

YA= -iVe\ Aq= -jfie -*+(,,

II

Fi*rd fu'nt

\tu.,

t(q \c

til11ri*.ilritl

a;,:l

ii

aTc

,ll

Y,-\o.

',|.,"'

il.c

N

,::ni-'iiili-1:=illl.r\l:_:.?,iN

13.5 N ,

Dg

113, S

?* tool5

n -TR

gI: \.3a 46

tu loods ft

\'"t'( v - TR :- 6.r,tS$ o\ qvlurr dls c

i u' LV -Tc = o ,[,\ \?, aq-

tn\44

: 13,5 _ t,31 A s

: t{,S - o,t{S'b A4

= L4. ! - u'\At'Z' 6rt

f\O 'S [a + lc -+ 3| ---llR-a_,'

*\Jrr\et

U

tt'l-*-f ' 'l

Itjs

q,J M

-oo -flB

Tn

T..

fnrg = \,jac vtg.

fnp, .=- p,ut S?vt4

{\A a = o,tt \(? l(a

The system shown is initially at rest. Neglecting the masses of the pulleysand the effect of friction in the pulleys, determin e (a) the acceleration ofeach block, (b) the tension in each cable.

- Ldg hq^Je -) u*lives Ccatr"gls)

aln -at46

. ,TA,ltl::ll=i ,

t''

:ill:" : i '-

-+-'' l.l***

1

I

| ^r^J""-*-

:r$\i:,!

1.5 N

\,Yr, lnAM -zavo

ftol--/H

\4,S V

--+t*:

-8-

gub {\ r{nfu. UJ, in 'i

\3. S l.3J 4a -S(ur, S -o,tts10n)+,n.\ - o,uft qr

\N\! b , (b

r\,<- t,?10c, = -o,US% tt:or+_+ec )_ _\),US? [_Ou_1.g)

-Q,S [,3JAK-* t4,St0.G

-t-{.t =--r5.33 ftc

As--o!?Se *lseChc

.4n = a.2,,ZGun / seL ,

-fK

Tn

TC

(,u

Problem #8

A single wire ACB passes through a ring at c that is attached to a 5_kgsphere which revolves at a constant speed v in the horizontal circle shown.Knowing that 0, =500 and d = 0.8 m and that the tension in both portions ofthe wire is 34 N; determine (a) the angle 0r, (b) the speed u.

ivr brnoryno4 tllicctLv,E-oB 2 Fa :o

T q( gt t Tras$z _yy\3 : o

3q* Co S5r-, * 3ct* C1tgz : 5*?,6\

Co ENz _

''""

['-*k';.,

't*uf lTcoJdr:,&. r + Iuolcse!"

Tfyr,o,+Il*oi' l,-"' 'ir'"') '

, "l;1' j

. Ay,r

\,

;i** mJ

I

Norvna,t d ire c*vnn t"

Zfh - yyl Av1

( Etnpr * Snu r-) = 6*

+ [ su 6u + [vn3{,qi&)

?,?3: V2/B

\oz=0,-I9tq

36,g6"!

g,# 1 =..

! ig ?

*--fr#* pr

rtonnaz

(bl in

t- ttr' I

V2K

\J2

€

V=

v={

ttn"e"

9 , z?4( \,61_.oz d

t 3.4at '^"./ sec

tAl( ilr'n 4 hrra-ru C\ptaqr'-*4]Dr ,ht"ti tt. ,11n v^t(tt \o'|a{ldh

-taruor

r.- @,q -*o,\A3 jJ

r-,, =d

= \,620?m

-9 -

Problem #9nil

ovtru-d {" 1 {*'',1trtf eqrydirh

During a hammer thropzer's practice swings, the 3.6 N head A of the hammerrevolves at a qons1Qglbg:ec|J in a horizontul circle as shown .If p= 915 mmand 0=60", determine (a) the tension in wire BC, (b) the speed of thehammer's head.

'l0d ln brvtorrnol direql*,,YA 0\/n - 3. C = o,j61 w

t,qr\

€ {,o ="s wo rvlotion in rtI Srh Or _

T=mnSYn'cl

ouo in Mlvr,*o.l { rr g Chcn

{(6 * yy\Arr

Tcaso r. o,J 6? b+ V ?-_

P\- Co[o * tr r4.l s 6:r co: (o* = 'l,E "*/scc

"5 -w

5,(>

--S t'n(o

\ ,\s6t N ,Jfnrp,

fi o'S\S

o'1 6:1 D.j(4

-10-

rv\ h/ln -=. U- - V.trgut r4Ce,ql

A 40'5 N wrecking ball B is attached to a l2-m-long steel cable AB andswings in the vertical arc shown. Determine the tension in the cable (a) at thetop c of the swing, where 0 = 300, (b) at the bottom D of the swing wherethe speed of B is 561 cmls.

oB +h,t, is a ve{4ilal c^yu^l^a, wL-lhn

,"-.---*.--1't\2 - )^, - ?_ot C\_ coss)

T= mt L - ?4r rn3 * 3rng CoSO.

(41 oB

Problem #10

ffiffiffint end

CI=LlL

AL=

e

-AgvZ?v

It\ .?^r,*JslJ..t:

ttu, S S

( ' *-.-

t:

s li-i)-W

V-- o O = ?(j,

I t- v?7r1

t t- v?rrl

T_ ut,t?3{ * uq,6l * lt t \- Wzl ?q+ tto, S + 3*(a'u,I x V3L

= V 5,oa4.

\a

A/

(bl ftf b O=o V= 6,6i .n /sec'i

,564 -,'tz - -ZaxJ+-:-

tn1&LE$I -zK r,4.o,s

Lr-

utZ, ( sot ,V ,

l= *3x

- ll