Download Turns Math Worksheet (Support for Online Questions)

Transportation1
TurnsMathWorksheet(SupportforOnlineQuestions)
Name______________________________
Frictionisaforcecreatedwhentwosurfacescomeintocontactwitheachother.InPredictionschapter2,youlearned
thatfrictiondependson(a)theroughnessorstickinessofthetwosurfaces,and(b)theforcepushingthetwosurfaces
together.Therougherorstickierthesurfacesare,thegreatertheamountoffrictionbetweenthem.Themoreforce
pushingthetwosurfacestogether,thegreatertheamountoffriction.
Anumbercalledcoefficientoffrictionrepresentstheroughnessorstickinessofthetwosurfaces.Thebiggerthe
coefficientoffriction,themorefrictiontherewillbe.Thecoefficientoffrictioncanvaryfrom0.05orless(forsmooth
surfacessuchasasledonice)to2.0orhigher(forstickysurfaces,suchasracingtiresonasphalt).Notethatthe
coefficientoffrictionisdeterminedbythepropertiesofbothsurfaces.
Inmathlanguage:forceoffriction=coefficientoffrictionxforcepushingthesurfacestogether
Forceoffrictionisoftenwrittenas
.ThecoefficientoffrictionisabbreviatedbytheGreekletter“mu”whichlookslike
this: Foracaronaflatroad,theforcepushingthesurfacestogetherisproducedbygravityactingonthecar(
)in
combinationwiththe“up”pushfromtheroad,theforcethatbalancesgravity.Recallalsothattheweightofanobject
equalsitsmassinkilogramsmultipliedbytheaccelerationduetogravity( =9.8m/s2).Soforacaronaflatroad,
CheckforUnderstanding
Theforceoffrictiondependsononlytwofactors:___________________________________and__________________
_______________________.Iftwosurfacesweresandedsmooth,wewouldexpecttheforceoffrictionbetweenthe
surfacestobe____________thanbefore.Afterward,ifthesetwosurfaceswerepushedtogetherwithmoreforcethan
before,theforceoffrictionbetweenthemwould____________.The_________________________________________
indicatestheroughnessorstickinessoftwosurfaces.Foracaronaflatroad,thisvalue,alongwiththe______________
ofthecar,aretheonlyquantitiesneededtodeterminetheforceoffrictionbetweenthetiresandtheroad.Theweight
ofthecaristhesameastheforcepushingthetiresandtheroadtogether,becauseweightofthecar(pullingdown)is
balancedbythe__________(pushingup).
Trytheseproblems.Showallworkinyourcompositionbook:
1. Acarwithamassof2700kghastiresthathave
acoefficientoffrictionwiththeroadequalto
0.56.Whatistheforceoffriction?
2. Acertainturnintheroadrequiresa34000N
forceoffrictionforacarweighing6500kgto
“maketheturn”(ifthedriverisobeyingthe
speedlimit).Whatcoefficientoffrictionis
neededforthecartomakeit?
3. (a)Whatforceisneededbya1250-kgdragster
thatacceleratesat24m/s/s?(Hint:Use
.)
(b)Whatcoefficientoffrictionisrequiredto
obtainthisforce?
Centripetalaccelerationoccurswhenanobjectchangesdirection.Thedirectionofcentripetalaccelerationisinward,
towardthecenterofthecirclearoundwhichtheobjectismoving.Theabbreviationforcentripetalaccelerationis .
Wecannotuseouroldformulaforacceleration
tofindcentripetalacceleration,becausethisequationonly
appliestochangesinspeed.Wemustdevelopanewequationbasedonthefactthatonlydirectionischanging.
Physicistshavedeterminedthatcentripetalaccelerationcanbefoundfromtheequation
.,where isthe
speedoftheobjectand istheradiusofitsmotioninacircle.SinceNewton’ssecondlawsaysthattheunbalanced
forceonanobjectcanbefoundbymultiplyingitsmassbyitsacceleration,anunbalancedforcethatcreatescentripetal
accelerationobeystheformula
where
equalscentripetalforce.Notethat
•
Increasingthemassincreasestheneedforcentripetalforce,becausetheobject’sinertia(itstendencytomove
inastraightline)isgreaterforlargermasses.
• Increasingthespeedincreasestheneedforcentripetalforce.Infact,doublethespeedincreasesthecentripetal
forcetofourtimesitsoriginalvalue.
• Decreasingtheradiusofaturnincreasescentripetalforce.Itismoredifficultto“maketheturn”iftheradiusis
small.
Inanunbankedturn,allofthecentripetalforceneededto“maketheturn”comesfromfrictionbetweenthetiresand
theroad.Inabankedturn,theroadprovidessomeorallofthecentripetalforce.
CheckforUnderstanding
Theoldaccelerationformulawillnotworkforcentripetalaccelerationbecause____________isnotchanging,only
_____________ischanging.Newton’s___________lawallowsustowriteaformulaforcentripetalforcefromthe
centripetalaccelerationformula.
Increasing_________or__________increasesthecentripetalforcerequiredtomoveinacircleormakeaturn,while
increasingtheradius________________therequiredcentripetalforce.Alloftheforceacarneedstomakeaturnmust
comefrom______________between___________andtheroadunlesstheturnis___________.
Trytheseproblems.Showallworkinyourcompositionbook:
4. Whatisthecentripetalforceona1790-kgcar
movingat26m/sthroughaturnofradius100
m?
5. Findthecentripetalforceforan18-wheelerwith
amassof36,000kgthatismovingthrougha
turnofradius130mat29m/s.
6. Whatisthespeedofa405-kgmotorcycleina
turnof29-mradiusifthecentripetalforceis
3400N?
Bringingitalltogether…
7. (a)Whatistheforceoffrictionfora1500-kgcar
onaroadwithacoefficientoffrictionof0.82?
(b)Willthiscarbeabletomakea62-mradius
turnataspeedof36m/s?
8. Onanicyday,thecoefficientoffrictionisonly
0.21fora1320-kgcar.
(a)Whatistheforceoffrictionforthiscar?
(b)Whatisthemaximumspeedatwhichthiscar
couldmakeaturnofradius30m?