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Theplan
• Today:FinishChapter5
• Wed-Mon:Chapter6
• Readingassignment:
• Wednesday: 6.1-6.2
• Friday:6.3-6.4
• Monday:6.5-6.6
• HomeworkdueThursdayonChapter5
• Labreport#2dueFriday!
• Myofficehours:
• Noofficehourstoday
• Futureweeks: OfficehourswillbeMonday(3:45-5:45)and
Thursday(1:00-2:00pm)
Today’stopics
• Conceptreview:
• Objectsincontact
• Stringtension
• Friction
• Newconcepts:
• Coefficientoffriction
• Airresistance/dragforce
Objectsincontact:
Keypoints:
1. Considereachobjectseparately.
• Eachitemgetsitsownfreebody diagram
• EachitemgetsitsownequationsforNewton’s2nd law.
2. Identifyforcesthatareaction/reactionpairs.
• Equatemagnitudes, butnotnecessarily directions.
3. Ifobjectsareincontactthentheiraccelerationisthe
same.(IFtheystayincontact.)Becarefulaboutthe
signs,becausethedirectionsmightnotbethesame.
• Hint:theforcesinaction/reactionpairsinNewton’s3rd
lawshouldneverbeonthesame freebodydiagram!
ClickerQ
• Considertheforcesactingoneachobject
independently.
(a) Tension inRope2>tensioninRope1
(b) Tension inRope2<tensioninRope1
(c) Tension inRope2=tensioninRope1
Clicker Question -- Friction
The coefficient of static friction is
A. smaller than the coefficient of kinetic friction.
B. equal to the coefficient of kinetic friction.
C. larger than the coefficient of kinetic friction.
D. not discussed in this chapter.
Slide 5-4
AreviewofFriction
• Allfrictionforcesactparalleltothesurface.
• Kineticfrictioniftheobjectslides.
𝐹"
• Staticfrictioniftheobjectdoesnotmove.
𝐹#
• Rollingfrictioniftheobjectrolls.
𝐹$
• Frictionalforceopposes motion.
• Frictionalforceopposesattemptat motion.
• Frictionalforceopposesmotion.
Staticfriction:thestrongest frictiontype!
• Opposesattempteddirectionofsliding.
• Adjustsitselftobalanceopposingforce,untilthe
opposingforcebecomessogreatthatstaticfriction
isovercome.
à Staticfrictionhasavaryingvaluebuthasamaximum.
Mathematically,
𝐹#,&'( = 𝜇# 𝑁
Frictionalforceisrelatedtothenormalforce.Butnote
thatthedirectionsaredifferent!
• 𝝁𝒔 isthecoefficientofstaticfriction,determined
bythematerial.
Kineticfriction
• Thewimpylittlebrotherofstaticfriction.
• It’sweakerbecausethesurfacesdon’tsettleintoeach
other.
𝐹" = 𝜇" 𝑁
• 𝝁𝒌 isthecoefficientofkineticfriction,determined
bythematerial.
Rollingfriction
• Frictionalrollingforceà howdifficultitistorollan
object.
• NOTthesameaskineticfriction.
• Theactualinteractionisstaticfriction(plusafewother
things)
• Asusual,
𝐹$ = 𝜇$ 𝑁
• 𝝁𝒌 isthecoefficientofrollingfriction,determined
bythematerial.
Staticequilibriumwithfriction
Ablockrestsonanincline.Thecoefficientofstatic
frictionis0.18.Whatisthesteepestangleatwhichthe
blockwillstayatrest?
Clicker Question – Air resistance
Which of the following is not important for the drag
force?
A. Air density
B. Area of the projectile
C. Velocity of the projectile
D. Mass of the projectile
Slide 5-4
Airresistance(“drag”force)
• Dragforce:
• Oppositedirectiontovelocity
• Dependsonvelocity,area,andairdensity
Area(crosssection)
1
𝐷 = 𝜌𝐴𝑣 6
4
Dragforce
Velocity
Airdensity(1.2kg/m3 atsealevel)
*Note:thisformulaonlyworksforobjectsofsizefew
mmtofewmeters,neartheEarth’ssurface,andfor
speedsbelowafewhundredm/s.
Terminalspeed
• Dragforce(airresistance)increaseswithvelocity.
• Oncevelocityishighenough,dragforceequals
weight.
• Balancedforcesà nomoreacceleration!
• Wecallthisterminalspeed.
Ex.5.14:Askydiverandhispetmousejumpfroma
plane.Estimatetheirterminalspeeds.
Usemassesof75kgand20g.
Useareasof1.8mx0.4mand7cmx3cm.
Airdensityis1.2kg/m3