Biomechanics Sample Problems PDF

Preview

Summary

Download Biomechanics Sample Problems PDF

Description

BiomechanicsSampleProblems  Forces 1)A90‐kgicehockeyplayercollideshead‐onwithan80‐kgicehockeyplayer.Ifthefirst personexertsaforceof450Nonthesecondplayer,howmuchforcedoesthesecond playerexertonthefirst?450N  2)Howmuchforcemustbeappliedbyakickertogiveastationary2.5‐kgballan accelerationof40m/s/s?100N  3)A65‐kgrunnerhadamaximalverticalgroundreactionforceof1700Nwhilerunningat moderatepace.Whatwastherunner'sweightinNewtons?637NWhatisthemaximal verticalgroundreactionforcewhenexpressedinmultiplesofbodyweight(1bodyweight istheweightoftherunner).2.67timesgreaterthanbodyweight  4)Ahighjumperwithabodyweightof712Nexertsaforceof3000Nagainsttheground duringtakeoff.Howmuchforcedoesthegroundonthehighjumperexert?3000Ninthe oppositedirection  5)Atrackathleterunningatfastpacehadaninstantaneousresultantforceof2800N actingthroughtheheelduringheelstrike.Iftheangleoftheresultantforcewas120 degreeswithrespecttothehorizontal,whatwerethehorizontalandverticalforcesacting ontheheel?Estimatehisbodymassifyouknowthatingeneralverticalgroundreaction forcefoundinrunningareabout4.3timesthevalueofbodyweight.1400Nhorizontal; 2425Nvertical;57.5kg  6)Thecoefficientoffrictionbetweenabasketballshoeandacourtis0.56,andthenormal reactionforceactingontheshoeis350N.Howmuchhorizontalforceisrequiredtomake theshoeslide?>196N  7)A70‐kgskierisinatuckpositionandmovingdowna20‐degreehill.Airresistance appliesaresultantforceof15Nagainstthemovementoftheskier.Thecoefficientof frictionbetweentheskisandthesnowis0.09.Whatistheresultantdownhillforceacting ontheskier?161Ndownhill  8)(Useg=‐10)Ifa70kgpersonwassittingonaswing(centeredevenlyinthemiddle betweenthetworopes),whatwastheforcebeingsupportedbyeachverticalrope(in Newtons)?350NeachIfthesamepersonwassittinginthemiddleofahammock,andeach ropehadanangleof30degreeswithrespecttothehorizontal,howmuchforcewaseach ropesupporting?(Note:Forceintheropeisnotthesameinthetwosituations.)700Neach  9)An85kgcyclist(person+bike)wastravelingataconstantspeedlevelroad.Upon startingupahillwitha15‐degreeinclination,thecycliststoppedpedalingandcoasted. Whatwasthetotaldownhillforceactingonthecyclistconsideringthecoefficientoffriction betweenthetiresandtheroadis0.1?136Ndownhill

 10)Thecoefficientofstaticfrictionbetweenasledandthesnowis0.19,withacoefficient ofdynamicfrictionof0.16.A25‐kggirlsitsonhersledfacingdowna10‐degreehill.What istheminimumpushherfriendneedstoexerttostartmovingdownthehill?Aftergetting apush,doesshecontinuetoslidedownthehill?Explain.>4Npushdownhilltostart moving;yes,shecontinuestoslideafterapush;Fdownhill=43N;Fstaticfrictionuphill=47N; Fdynamicfrictionuphill=39N  11)Twopeopleareplayingtug‐of‐war.Duetotheirchoiceoffootwear,theircoefficientof staticfrictionisdifferent.Participant1hasamassof60kg,acoefficientofstaticfrictionof 2.0,andcanpullwithamaximumforceof1000N.Participant2hasamassof80kganda coefficientofstaticfrictionof1.2,andcanpullwithamaximumforceof1200N.Whowins? participant1wins  12)Afootballplayerpusheda60kgblockingsledwithaconstanthorizontalforceof400 N.Thecoefficientofkineticfrictionbetweenthesledandgroundis0.5.Howmuch horizontalforceopposestheforwardmotionofthesled?294NWhatisthesled’s horizontalacceleration?(assumethattheplayingsurfaceislevel).1.77m/s2  LinearKinematics 1)A75kgjumperlandsstiff‐leggedonthefloorandchangeshisvelocityfrom–4.5m/sto zeroin0.15seconds.Computetheaverageresultantforceworkingonthejumper.2250N Ifheincreasedtheimpacttimeto0.2s,whathappenstotheresultantforceworkingonthe jumper?1688N  2)Ifanathletejumped2feethighandleftthegroundatanangleof20degreeswith respecttothehorizontal,howfastwastheathletegoingintheforward(positive horizontal)andupward(positivevertical)directionsimmediatelyaftertakeoff?Vertical velocity=3.46m/sHorizontalvelocity=9.51Iftheheightoftakeoffwasthesameasthe heightoflanding,howfastwastheathletegoinginthehorizontalandverticaldirections rightbeforelanding?Verticalvelocity=‐3.46m/sHorizontalvelocity=9.51  3)AnOlympicdiverdropsfromthe10meterplatformwithaninitialverticalvelocityof0.0 m/s.Whatwastheverticalvelocityofthediverimmediatelybeforehe/shehitsthewater? 14m/sHowlongdidittakethedivertoreachthewater?1.43s  4)Alongjumperleavesthegroundatanangleof25degreeswithrespecttothehorizontal witharesultantvelocityof30ft/s.Whatwasthehorizontalvelocityofthejumperat takeoffinm/s?Horizontalvelocity=8.29Whatwastheverticalvelocityattakeoffinm/s? Verticalvelocity=3.86m/sHowhighdidtheCMriseabovethepointoftakeoff?0.76m  5)Twoballswerethrownupwardandwerecaughtatthesameheightfromwhichthey werereleased.BallAwasthrownupwardwithaverticalvelocityof10m/s.BallBwas thrownupwardwithaverticalvelocitywhichwastwicethatofballA.Howfardideachball riseabovethepointofrelease?BallA:5.1mBallB:20.4m Howlongdideachballstayintheair(totaltime)?BallA:2.0sBallB:4.1s

 6)Ifashotisputanangleof41degreesrelativetothehorizontalwithavelocityof36ft/s inthedirectionoftheput,whatwillbetheupward(vertical)velocityattheinstantof release?7.2m/sWhatwillbetheforward(horizontal)velocity?8.3m/sHowhigh (abovethepointofrelease)willtheshotgo?2.64mWhatisthetimeittakestheshotto reachitsmaximumheight?0.73s  7)Iftheshotinproblem6isreleasedfromaheightof6ftandlaterlandsontheground (height=0.0ft),whatwasthetotaltimeofflight?1.69sHowfardidtheshottravel horizontally?14.0m  8)Whatistheaveragespeedofabreastrokeswimmerwhocompletes100minatimeof 1:15?1.3m/s  9)Whatistheaveragevelocityofabreastrokeswimmerwhocompletes100minatimeof 1:15?0m/ssincetheystartandfinishinthesamelocation 10)Aballisthrownverticallyupwardwithavelocityof15ms‐1.Iftheaccelerationdueto gravityis9.8m/s2,whatisthevelocityoftheball2secondsafterbeingthrown?‐4.6m/s Istheballstillgoinguporisitcomingdown?Down  10)Anorienteerrunsnorthat5m/sfor120seconds,andthenwestat4m/sfor 180seconds.Whatistheresultantdisplacementwithrespecttothestartingposition? Provideananglewithrespecttothenorthdirection.937mat50deg  11)Askierwasglidingdownhillat15m/s.Howlongdidittakehertoskithe630mtothe baseofthehill?10.5sAlessproficientskieraveraged12m/sdowntheslope.Ifthey startedtogether,howfarbehindthefirstskierwashebythetimeshegottothebottomof thehill?126m  12)Theworldrecordforthe24‐hourrunisabout160miles.Whatisthisdistancein meters?257,488mWhatis24hoursinseconds?86,400sWhatwouldbearunner's averagespeedingoing160milesinadayinm/sandmin/mi?2.98m/sor9:00/mi  13)Bobsledsacceleratefromresttohighspeedsinafewseconds.Ifonesled'sspeed increasedfrom0to32m/sin8seconds,whatwasitsaverageaccelerationduringthat timeperiod?4m/s2Howfardidthesledtraveldownthetrackinthe8seconds?128m  ProjectileMotion  1)Asoccerballiskickedwithaninitialhorizontalspeedof5m/sandaninitialvertical speedof3m/s.Assumingprojectionandlandingheightsarethesame,identifythe followingquantities(ignoringairresistance): a.Theball’shorizontalspeed0.5secondsintoitsflight:5m/s b.Theballshorizontalspeedmidwaythroughitsflight:5m/s c.Theballshorizontalspeedimmediatelybeforecontactwiththeground:5m/s d.Theball’sverticalspeedattheapexofflight:0m/s

e.Theball’sverticalspeedmidwaythroughitsflight:0m/s f.Theball’sverticalspeedimmediatelybeforecontactwiththeground:‐3m/s g.Theball’svelocitythroughoutthefilght:‐9.8m/s2  2)Arugbyplayerattemptsakickafterscoringatry.Theballwaskickedatanangleof60 degreeswithaninitialresultantvelocityof40miles/hour(ignoringairresistance). a.Whatwastheinitialresultantvelocityinmeters/second?17.9m/s b.Whatwastheinitialhorizontalvelocityinm/s?9.0m/s c.Whatwastheinitialverticalvelocityinm/s?15.5m/s d.Iftheplayerwas40metersawayfromthegoal,andtheheightofthehorizontal barwas3meters,didtheplayerscore?Assumethatthetrajectoryoftheballwas ontarget!No  3)Asoccerballiskickedfromtheplayingfieldata45°angle.Iftheballisintheairfor3 seconds,whatisthemaximumheightachieved(ignoringairresistance)?11.0m  4)Amountainbikerencountersadeepgorge.Hehas“heard”thatifhejumpsoffthelog ontheedgeofhissideofthegorgehecanexpect50°forhistrajectory.Hehasalso“heard” thattheothersideofthegorgeis1metershigherthatthesideheison.Heknowsthathe canridetoamaximumspeedof20mi/hronthetrailapproachingthegorgeandoffoflog. Assumingwhattherider“heard”isaccurate,howwidecanthegorgebeforhimtonotdrop downthegorge?7.1m  Momentum 1)Twoiceskatersstartoutmotionlessinthecenteroftheicerink.Theythenpusheach otherapart.Theman(mass=80kg)movestotherightwithaspeedof2.5m/s.The womanmovestotheleftatsomeunknownspeed. a)Ifhermassis58kg,calculatethatspeed.(assumefrictionlessice)3.45m/s b)Whathashappenedtothetotalmomentumofthesystem(woman+man)during thepush‐off?Itwasmaintainedsincetheresultantexternalforcewaszerowhen consideringbothpeople.  2)LinemanAhasamassof100kgandistravelingwithavelocityof4m/swhenhe collideshead‐onwithLinemanB,whohasamassof90kgandistravelingat4.5m/s. Ifbothplayersremainontheirfeet,whatwillhappen?(Answer:BwillpushAbackward withavelocityof0.03m/s)  AngularKinematics 1)Agolferacceleratestheclubfromthetopofthebackswinguntilimpactwiththeball withanaverageangularaccelerationof30rad/s2foraperiodof0.5s.Theradiusof rotationis1.1m.Computetheangularvelocityoftheclubatimpact,thelinearvelocityof theclubheadatimpact,andtheradialaccelerationoftheclubheadatimpact.16.5m/s  2)Achampionhammerthrowerrotatesatarateof3.2rev/sjustpriortoreleasingthe hammer.

a)Ifthehammerislocated1.6mawayfromtheaxisofrotation,whatisthe centripetalaccelerationexperiencedbytheathlete?646m/s2 b)Howmuchtension(i.e.force)isneededtoproducethisradialaccelerationifthe massofthehammeris7.26kg?4696N   3)Aspeedskaterincreaseshisspeedfrom10m/sto12.5m/soveraperiodof3seconds whilecomingoutofacurveof20mradius.Whatarethemagnitudesofhistangential, centripetal,andresultantaccelerationsasheleavesthecurve?(Answer:at=0.83m/s2;ac =7.81m/s2;a=7.85m/s2)  4)Akicker’sextendedlegisswungfor0.4secondsinacounter‐clockwisedirectionwhile acceleratingat200deg/s2.Whatistheangularvelocityofthelegattheinstantofcontact withtheball?(Answer:80deg/sor1.4rad/s)  5)A1.2mgolfclubisswunginaplanarmotionbyaright‐handedgolferwithanarm lengthof0.76m.Iftheinitialvelocityofthegolfballis35m/s,whatwastheangular velocityoftheleftshoulderatballcontact?Assumethattheleftarmandgolfclubforma straightlineandthattheinitialballvelocityisthesameasthelinearvelocityoftheclub headatimpact.(Answer:17.86rad/s)  AngularKinetics 1)A65kggymnastbeginstoprepareforhisdismountfromthehighbarbyincreasinghis angularvelocitybyafactorof3.Bywhatfactordoesthecentripetalforcechange?(you mayassumethatrdoesnotchange)Itincreasesbyafactorof9  2)Apitchedballwithamassof1kgreachesacatcher'sglovetravelingatavelocityof28 m/s. a.Howmuchmomentumdoestheballhave? b.Howmuchimpulseisrequiredtostoptheball? c.Iftheballisincontactwiththecatcher'sglovefor0.5secondsduringthecatch, howmuchaverageforceisappliedbytheglove? (Answer:a.28kgm/s;b.28Ns;c.56N)  3)A108‐cm,0.73kggolfclubisswungfor0.5secondswithaconstantaccelerationof10 rad/s2.Whatisthelinearmomentumoftheclubheadwhenitimpactstheball?(Answer: 3.9kgm/s)  4)Avolleyballplayer's3.7‐kgarmmovesatanaverageangularvelocityof15rad/sduring theexecutionofaspike.Iftheaveragemomentofinertiaoftheextendingarmis0.45kg m2,whatistheaverageradiusofgyrationforthearmduringthespike?(Answer:0.35m)  5)Thepatellartendonattachestothetibiaata20degangle,3‐cmfromtheaxisofrotation attheknee.Ifthetensioninthetendonis400N,whatistheresultingangularacceleration ofthe4.2kglowerlegandfootgivenaradiusofgyrationof30cmforthelowerleg/foot withrespecttotheaxisofrotationattheknee?(Answer:15.6rad/s2)

 6)A60kgdiverispositionedsothathisradiusofgyrationis0.5masheleavestheboard inalayoutpositionwithanangularvelocityof4rad/s.Whatisthediver’sangularvelocity whenheassumesatuckposition,alteringhisradiusofgyrationto0.25m?(Answer:ω=16 rad/s)  8.Thekneeextensorsinsertonthetibiaatanangleof30degrees(fromthelongitudinal axisofthetibia),atadistanceof3cmfromtheaxisofrotationattheknee.Howmuchforce mustthekneeextensorsexerttoproduceanangularaccelerationatthekneeof1rad/s2, givenamassofthelowerlegandfootof4.5kg,andaradiusofgyrationof23cm?(Answer: F=15.9N)

 TorqueProblems 1)Whatisthetorqueonaboltifyouarepullingwithaforceof200Ndirected perpendiculartoawrenchoflength25cm?Howdoesthetorquechangeforawrenchof twicethelength?50Nm100Nm  2.Incycling,thetorquegeneratedaboutthecrankaxisdependsonthemagnitudeof theforceappliedtothepedalandalsotheanglebetweenthecrankarmandthe forcevector.Inthediagrambelow,an800Nverticalforceappliedtothepedal willcreateacounter‐clockwisetorqueof140Nmwhenthecrankisat90degrees (wheregreatesttorqueisgenerated). Howmuchtorquewillthesameforcegeneratewhenthecrankisat75degrees andat105degrees?Whattorquewillthatsameverticalforcegeneratewhenthe crankisat180degrees? (Answers:at75and105degrees,torque=135.2Nm,at180degrees,torque=0) 3.Whatisthetorqueabouttheshoulderifthearmisheldinanabductedpositionat 60degreesfromthebodyinthefrontalplanewhileholdinga10kgdumbbell? Assumethatthemassofthearmis6kg,itscenterofmassislocated38cmfrom theshoulderjointcenter,andthearm'stotallengthis80cm. (Answers:torqueofdumbbell=‐69.3Nm;torqueofarmweight=‐19.7Nm; Torqueattheshoulder=89Nm) 4.ShortEssayReponse:Thetorqueyoucanapplytotherearwheelofyour mountainbikedependsonwhichgearyouareusing.Explainhowandwhythe gearingofthebackwheelaffectstorque. 5.A35Nhandandforearmareheldata45°angletotheverticallyoriented humerus.Thecenterofgravityoftheforearmandhandislocatedatadistanceof 15!cmfromthejointcenterattheelbow,andtheelbowflexormusclesattachata distanceof3cmfromthejointcenter(assumethatthemusclesattachatanangle of45°totheaxisoftheforearm). a.Howmuchforcemustbeexertedbytheforearmmusclestomaintain thisposition?(answer:175N) b.Howmuchforcemusttheforearmflexorsexertifa50Nweightis heldinthehandatadistancealongthearmof25cm?(Answer:591.7 N) 6.Ahandexertsaforceof90Nonascaleat32cmfromthejointcenteratthe elbow.Thetricepsattachtotheulnaata90°angle,andatadistanceof3cm fromthejointcenter.Theweightoftheforearmandthehandis40Nwiththe forearm/handcenterofgravitylocated17cmfromtheelbowjointcenter. Consideringtheseconditions,howmuchforceisbeingexertedbythetriceps? Rememberthatyouareinterestedintheforcesactingontheforearmsystem. (answer:733.3N) 7.Atherapistappliesalateralforceof80Ntotheforearmatadistanceof25cm fromtheelbowjointcenter.Thebicepsattachestotheradiusata90°angleand atadistanceof3cmfromtheelbow. a.Howmuchforceisrequiredofthebicepstostabilizethearmin position?(answer:666.7N)

b.Whatisthemagnitudeofthereactionforceexertedbythehumeruson   1.Afigureskaterisrotatingwithcounterclockwiseangularvelocityinanoverheadview. Ifherangularaccelerationisclockwiseatthattime,thisimpliesthat: (a)sheisnotchangingthespeedofherrotation. (b)herrotationisspeedingup. (c)herrotationisslowingdown. 2.Whichofthefollowingistrue? (a)Iflocationisconstant,velocityhastobezero. (b)Ifvelocityisconstant,accelerationhastochangeataconstantrate. (c)Ifaccelerationisconstant,velocityalsohastobeconstant. 3.Abusismovingforwardat12.5m/s.Youareinsidethebus,movinglaterallyrelativeto theseatsinthebus(i.e.,sidewaysfromaseatontherightsideofthebustoaseatonthe leftsideofthebus)at4.6m/s.Whatisthevalueofyourresultantvelocityvectorrelative tothestreet? (a)between0.00m/sand5.00m/s (b)between5.01m/sand9.00m/s (c)between9.01m/sand13.00m/s (d)between13.01m/sand16.00m/s (e)morethan16.01m/s 4.Twobobsleddingcompetitorspushtheirsledfor3.2swithacombinedhorizontalforce of110N.Themassofthesledis65Kg.Assumethattherearenofrictionforces betweenthesledandthesnow.Calculatethehorizontalaccelerationofthesled. (a)between0.0m/s2and2.0m/s2 (b)between2.1m/s2and4.0m/s2 (c)between4.1m/s2and7.0m/s2 (d)between7.1m/s2and8.5m/s2 (e)morethan8.6m/s2 5.A200meterswimmingracetakesplaceina50meterpool.Assumethatthepositive directionisthedirectionofswimminginthefirststretch(first50meters).Howwillthe accelerationoftheswimmerbewhentheswimmerisslowingdowntomakehissecond turn,thatis,asheapproachesthe100meterpointoftherace? (a)positive (b)negative (c)zero 6.Ifweignoretheeffectsofairresistance,thesumofthehorizontalforcesexertedona gymnastwhilesheisintheair: (a)iszero. (b)dependsonthemassofthegymnast. (c)isequaltotheweightofthegymnast. (d)dependsonthecurrenthorizontalvelocityofthegymnast. 7.Whichofthefree‐bodydiagramsbelowiscorrect?Thesystemisthesoccerplayerwho iskickingtheball;theballisNOTapartofthesystem. (a)(b)(c)(d) 8.Acyclistisridinginthepositivehorizonaldirectionat12.3m/sonahorizontallevel

surface.Sheencountersanairresistanceforceof27N.Theactionsonthepedalsbythe cyclistcauseabackwardforceof153Ntobeexertedbytherearwheelontheground. Themassofthecyclist‐plus‐bikesystemis61Kg.Calculatethehorizontalacceleration ofthecenterofmassofthesystem.(HINT:firstmakeafree‐bodydiagramofthe system.) ...