Electrical Engineering 3BA3: Structure of Biological Materials. Solutions to Midterm Quiz #1 (2007)

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1 Elrial Enginring 3BA3: Sruur of Biologial Marials Pag 1 of 9 Soluions o Midrm Quiz #1 (007) 1. A snhi biomarial is a omposi of Marial #1 wih an lasi modulus of E 1 80 GPa and Marial # wih an lasi modulus of E 1.3 GPa. If h omposi s volum is 0% Marial #1 and 80% Marial #, hn h lasi modulus E of h omposi is: a. lss han 18 GPa, b. mor han 1.6 GPa,. dpndn on how h wo marials ar arrangd in h omposi, or d. all of h abov. (5 ps) Th answr is d. all of h abov. S nos from Tuorial #1 (or p. 359 or p. 381 of Brgr al.).. Th naural biomarial krain, found in human hair, is siffr han ollagn baus: a. i is a non-malli minral, b. i has mor ross-links,. i absorbs lss war, or d. non of h abov. (5 ps) Th answr is b. i has mor ross-links. S slid 13 from Lur #3 (or p. 344 of Brgr al.). 3. Th final sag of wound rpair is : a. inflammaion, b. rmodlling,. prolifraion, or d. oagulaion/hamosasis. (5 ps) Th answr is b. rmodlling. S slid 4 from Lur #5 (or p. 346 of Endrl al.). 4. During running, h runnr s vrial vloi is piall maximal: a. a h middl of h san phas, b. owards h nd of h san phas,. jus afr h bak foo lavs h ground, or d. whn h runnr s nr of mass is a is maximal high. (5 ps) Th answr is b. owards h nd of h san phas. S slid 9 from Lur #6 (or p. 393 of Brgr al.). Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

2 5. Th srss-lif diagram for a marial is normall rad b: Pag of 9 a. liall appling a fixd load unil h marial fraurs and rpaing his produr for a rang of loads wih a nw sampl of h marial ah im, b. appling a sadil inrasing load unil h marial fraurs,. liall appling a load, saring wih a high load and rduing h load whnvr frauring appars imminn, or d. appling a li load and masuring whn h marial wars hrough. (5 ps) Th answr is a. liall appling a fixd load unil h marial fraurs and rpaing his produr for a rang of loads wih a nw sampl of h marial ah im. S slids 17 0 from Lur #8 (or p. 67 or p. 375 of Brgr al.). 6. During running, h maximal join powr produion is grar in h ankl han in h kn baus: a. h ankl s maximal join momn during running is muh grar han h kn s, b. h im during whih h kn s join momn is posiiv is mor sprad ou,. h kn onl absorbs powr during running, or d. h ankl s roaional vloi is grar during h maximal join momn. (5 ps) Th answr is d. h ankl s roaional vloi is grar during h maximal join momn. Th maximal join momns ar of similar magniud (around 00 N m), h duraions of h posiiv join momns ar similar, and h kn produs powr as wll as absorbing i, so h answr mus b ha h ankl s roaional vloi is grar. S slid 11 from Lur #8 (or p. 400 of Brgr al.). 7. In funion lrial simulaion for drop foo, h iniial si of aion ponial gnraion is normall in: a. a moor nuron axon, b. h saroplasmi riulum,. a musl fibr, or d. h moor orx. (5 ps) Th answr is a. a moor nuron axon. S Sudn Prsnaion #3. Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

3 Pag 3 of 9 8. Th for ha a musl an gnra as a funion of is lngh is maximal whn h musl is a is naural lngh baus: a. mor fas-wih fibrs ar rruid a his lngh, b. of h fasr oxidaiv mabolism a his lngh,. a grar numbr of moor unis ar aivad a his lngh, or d. of h opimal ovrlap of ain and mosin filamns a his lngh. (5 ps) Th answr is d. of h opimal ovrlap of ain and mosin filamns a his lngh. S slid 14 from Lur #7 (or p. 407 of Brgr al.). 9. Disuss h biohial omplxiis of hoosing subjs for linial rials of biomdial hnologis o ra lif-hraning disass. (15 ps) Th main omplxiis aris from h possibl-omping goals of obaining h bs masurmn of bnfi and minimizing risk for h pains (non-malfin). If h hnolog has som subsanial risk of (i) no working suffiinl o kp h pain aliv or (ii) having harmful sidffs, hn h onl suiabl subjs migh b hos pains for whom all ohr ramn opions hav faild and ar likl o di soon. Howvr, if suh pains ar hosn as subjs, hn h ma b so sik ha (a) h full bnfi of h hnolog is no larl displad or (b) h di anwa, and i ma b diffiul o drmin whhr h biomdial hnolog onribud o h dah or no. Halhir subjs ma br displa h bnfi of h hnolog, bu h risks ma b oo gra, or hr ma b ohr viabl ramn opions sill availabl. 10. Explain wh plainum-iridium allos ar ofn h prfrrd marial for impland simulaing lrods. (15 ps) Plainum and iridium ar non-oxi and vr rsisan o orrosion and onsqunl qui bioompaibl. Furhrmor, h an dlivr fairl larg urrns o an lrol (suh as h bod s xrallular fluids) wihou lrod dissoluion, produion of gasss or inrasing h ph of h lrol. Iridium is auall vn lss suspibl o orrosion and produion of gasss han plainum, bu i is mor bril han plainum and onsqunl anno b asil mahind ino lrods. Thrfor, a plainum-iridium allo wih a grar prnag of plainum (piall 90:10) is prfrrd. (S slids 39 & 40 of Sudn Prsnaion #.) Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

4 Pag 4 of A sprinr is posiiond in hir saring bloks as illusrad blow. Assum h following: i. Th sid ross-sion of h saring bloks (as illusrad) is an quilaral riangl. ii. Th runnr is a rs for im < 0 and hn bgins o propl hmslvs forward a im 0. iii. On h runnr bgins proplling hmslvs forward, h lif hir hands immdial (i.., a im 0 ). iv. Th oal ground raion for a h saring bloks is normal o h fron surfa of h bloks and as hrough h nr of mass (COM) of h sprinr. v. Th oal ground raion for magniud a h saring bloks has a onsan valu of F g 5kN from im 0 o im 0.1s. vi. Th runnr has a mass of 90 kg, and h alraion du o gravi is g 9.8 m s. Wha is h inras in h oal mhanial nrg of h runnr s COM from im 0 o im 0.1s? (15 ps) Th inrnal angls bwn h sids of an quilaral riangl ar all 60, and hus, h fron surfas of h saring bloks ar inlind a an angl of 30 from vrial. Th ground raion for (GRF) F g, whih is normal o h fron surfa of h bloks, is onsqunl angld 30 from horizonal, as illusrad blow. Th horizonal and vrial omponns of h GRF ar hus: and: F F os kn, for s, g g F F sin 30.5 kn, for s, gz g rspivl. Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

5 Pag 5 of 9 Th horizonal alraion g a, dpndn onl on a F m F g, is givn b: m s, for 0 0.1s. Consqunl, h horizonal vloi v 1 () 0 0 varis as a funion of im aording o: v v 0 + a ds ds m s, for s, suh ha a im 0.1s, v m s. Th vrial alraion z gz az, dpndn on F gz and h for du o gravi, is givn b: a F m g Consqunl, h vrial vloi v m s, for 0 0.1s. 1 () z z z 0 0 z varis as a funion of im aording o: v v 0 + a ds ds m s, for s, suh ha a im 0.1s, Th vrial displamn im aording o: v z dz m s. () () z z z 0 0, rlaiv o h iniial high of h COM, varis as a funion of d d 0 + v ds s ds 8.99 m, for 0 0.1s, suh ha a im 0.1s, d m. z Th iniial horizonal and vrial vloiis ar zro, and hn h iniial kini nrg is zro. Th inras in kini nrg a im 0.1s is hus: 1 1 Eki n vz kj, ( 0.1s) m ( 0.1s) + mv ( 0.1s) ( ) and h inras in graviaional ponial nrg a im 0.1s is: Egrav ( 0.1 s) mgdz ( 0.1 s) J, giving a oal inras in mhanial nrg a im 0.1s of E o 1.7 kj. Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

6 Pag 6 of 9 Th alulaion of h GRF angl is illusrad blow for a singl blok. No howvr ha h GRF magniud for h wo bloks ombind was givn in h qusion, and h ombind GRF was assumd o a dirl hrough h sprinr s COM. 60 F g 30 F gz F g Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

7 Pag 7 of 9 1. A nw mal allo bing dvlopd for orhopadi implans has a nsil srss-srain rlaionship givn b: τ 1 GPa, for 0, 1+ whr τ is h nsil srss (in unis of GPa), is h nsil srain, and is h srain a failur. a. If h ulima nsil srngh is 950 MPa, wha is h srain a failur? b. Wha is h lasi modulus E for h linar porion of h srss-srain urv?. Find h ild srss, if i is dfind as h srss a whih h slop of h srss-srain urv is onl 40% of h slop of h linar porion. (15 ps) a. Aording o h givn quaion, h srss a failur, rfrrd o as h ulima nsil srngh (UTS), is: GPa. 1+ Solving for givs: log 0.05 ( 1.95 ) 0.05 log b. Th srss-srain urv is linar for small and boms non-linar a highr srains. Thrfor, h lasi modulus E for h linar porion of h srss-srain urv is h slop of h urv a 0. Th driva of h givn quaion is: ( + ) dτ d GPa, for 0. ( 1+ ) Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

8 Pag 8 of 9 Evaluaing h driva a 0 givs: dτ E 50 GPa. d ( 1+ ) ( + ) Alrnaivl, h lasi modulus an b simad from h raio of τ o for xrml small valus of : τ E 1, for ( 1+ ) 5 Evaluaing his xprssion for 1 10 givs: GPa E Th slop a h ild srngh (YS) is 40% of 50 GPa, i.., 100 GPa. Th ild srain, h srain a whih h slop is 100 GPa, an b found aording o: GPa ( 1+ ) ( 1 ) 10 ( ) This is a quadrai quaion wih h soluions: ± 1 1 8± or Solving for givs: 500 log7.873 or log0.170 log7.873 log0.170 or log7.873 log0.170 or ± Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007

9 Sin Pag 9 of 9 is a nsil srain, i mus b h posiiv valu. Solving for h srss a givs a ild srngh of: τ GPa MPa Th rsuls ar shown graphiall in h figur blow. UTS1 τ (GPa) YS 0.5 Srss srain urv x 10 Slop of srss srain urv E dτ/d (GPa) x 10 Dr. I. Bru EE3BA3 Midrm Quiz #1 Soluions 06/11/007