statics problem dot product

# statics problem dot product - 2—83 Determine the...

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Unformatted text preview: 2—83. Determine the magnitude of the component of the position vector r along the 0:: axis. ,1' Hit-Euler 4* edition 2-3.3- Determioe the magnitude ofthe component ofthe position teeter ”lens the On Mir. We will ﬁrst write the 1.u'euator r in Cartesian vector ﬁrm. 1- nth-“+3131 Now let‘s ﬁnd a unit vector that points in the direction Eu. rm =[-2i+4j+4k]m 1'5." :11: +41 +d1m = 6m =ﬂ—3i+d]+dk} x New “emu use thedot podtettoﬁnd theeompenentoftheymiﬁmweualongtheﬂaaxis. m“ = rlu=[u—£_i}+#+m%]m =-2.ﬁTﬂt = 2.6Tm r-L'I .r “2—8-4. Determine the magnitude of that: component of the I'D-11:: F ill-ﬂing thc Aa axis- Hibbeler 4'“ Bdi‘t'iﬂlt 2-34 Determine the magnitude ul‘the mmpunent ctl‘lhe force F along the An axis. Notethatthe time Fpoittts along the: line ﬁrm: A toE. We will ﬁrst write lite ﬁrm F in Cartesian vector than. The ﬂame can be developed as a magnitudﬂ times a unit t-Bctﬂ-I' that points truth A t;- B. I r -mhr Jﬁm {-51 - 1th" - {- tttttztj-:tt.ttt}.ttIf Now let's ﬁnd a unit vector that points in the direction An. Now let's ﬁnd a unitvector that points in thttdirecticm M. r” = {-1i-tj+3k}m r“ =i21+61+33m =?m u=t{—2t—t]+3t} Now we can use the tint pmduct i;- ﬁnd the campunentut‘l?‘ along the Ar! axis. [titthhrh-t} + [-Etiﬂh'lﬂl T T =3t'tﬂt'tl' F‘.:F.“:[ 2-493. Detennitte the mtglee ti and «it made between the axes 0A at“ the ﬂag pole and each cable. AB and AC. Frill 2-H: Hihheier If“ edition 2-93 Determinetheengleeﬂandtbmedebemeenme I C .p, .1er DA ctfthe flag puknrtﬂ each Gable, AB and AC. Let's first write the three position vectors in Carteeinn form and determine their magnitudes. W ..-.,.Ii:lt._..-._..-._ rm = {ut-u-ekh; rm =5m r“={lji—t1j+3|t}ttt:r” =Wm r“={—2i—4j+ii}nt: Wm. x We can new ﬁnd the required angles by using ﬂiedet precinct. c053: rm 1r”| = WIMmHi-IIntH-Ilnti+{-3m}[3m) ={l_2t’tﬂ riUr-td {SHIHJETESHI} 5 = 14.41” ‘Z-IIIH. Detemine the angles a and dr bemoan the wire mgmﬁmﬁ. . 2 Fruit. I—‘Iﬂl Hibbdﬂﬁ‘ndlﬂm 2-1114 mum-mmamwmmm slug-lull. Lﬂsﬂmmhﬂpu-Ilhmm'mﬂmﬂn width-inﬁrm. r“ = {ﬁl-DJ]-D5k}n: r” = mn- I... = {unqu-ujuh; r" = ﬂy: I“ = {-ﬂjl-{Ilhﬂjﬂm r” = m. r”, = {mm-0| +ﬂk}ll: n, = u. Wuunmwﬁrﬂ timid-lulu bymlnglkuttpﬁm- rII -rl4. _ [ﬂHﬂjIH [-IILIII “ELIE“ [-ﬂjll- 95]] HEN - {ﬁnI-uﬁm] 9- “ﬂ" = H.215- HIE: m... = Iain. = F ”3 3* M. 1+ 1— M- th [tun m = 031': rural “ﬁll Elﬁn} i- 333?“ ...
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