Final Exam Review

Prof.BinChenDepartmentofPhysics

Physics111

Exam Information

•  Time:Dec18,2018(Tuesday),11:30AM-2:00PM•  Location:MechanicalEngineeringCenterBuilding(ME;nexttotheGITC)Room221•  Sameformatasbefore,butmorequestions(27intotal)•  Youhaveabout5.6minutes,onaverage,toworkoneachquestion

Exam Information: Topics

AllmaterialsinWeeks1-14•  RoughlyhalfofthequestionscomefromthoseafterCommonExam#3,i.e.,topicsinWeeks11-14:RotationalDynamics,StaticTorque,FluidMechanics,Gravitation.

•  AnotherhalfofthequestionscomefromthosealreadycoveredinCommonExams#1-3,i.e.,topicsinWeeks1-10.

Final Exam Information: Review Sessions

•  Thursday(Dec13,ReadingDay)11:30am–1:30pmTiernanLectureHall1withProf.GordonThomas

•  Saturday(Dec15)11:00am–1:00pmTiernanLectureHall1withSocietyofPhysicsStudents

FORMULAS – Final Exam Conversion Factors: 1 inch = 2.54 cm; 1 mi =1609.3 m; 1 cm=10-2m; 1 mm= 10-3 m; 1 gram=10-3 kg; Physical constants: 9.8g = m/s2 ; 116.674 10G −= × N m2/kg2 ; 245.97 10EarthM = × kg ; 66.37 10EarthR = × m Math: 360° = 2π radians = 1 revolution. Arc length s rθ= ; 34 / 3sphereV Rπ= ; 24sphereA Rπ= ; 2

circleA Rπ=

quadratic formula to solve 2 0ax bx c+ + = : 2 4

2b b acx

a− ± −=

Vectors: ˆ ˆx yA A i A j= +

r ; cos( )xA A θ=

r ; sin( )yA A θ=

r ; 2 2

x yA A A= +r

; tan y

x

AA

θ =

C A B= +r r r

implies x x xC A B= + ; y y yC A B= +

𝐴 ∙ 𝐵%⃗ = '𝐴''𝐵%⃗ ' cos 𝜃 = 𝐴𝑥 𝐵𝑥 + 𝐴𝑦 𝐵𝑦 + 𝐴𝑧 𝐵𝑧 ; 𝑖̂ ∙ 𝑖̂ = 𝑗̂ ∙ 𝑗̂ = 𝑘5 ∙ 𝑘5 = 1 ; 𝑖̂ ∙ 𝑗̂ = 𝑖̂ ∙ 𝑘5 = 𝑗̂ ∙ 𝑘5 = 0 sinA B A B θ× =

r rr r ; ˆˆ ˆ( ) ( ) ( )y z z y z x x z x y y xA B i A B A B j A B A B k A B A B× = − + − + −r r

ˆ ˆˆ ˆ ˆ ˆ 0i i j j k k× = × = × = ; ˆˆ ˆi j k× = ; ˆˆ ˆj k i× = ; ˆ ˆ ˆk i j× =

1D and 2D motion:

avgxvt

Δ=Δ

; avgvat

Δ=Δ

; dxvdt

= ; 2

2

dv d xadt dt

= =

avgrvt

Δ=Δ

rr ; avgvat

Δ=Δ

rr ; dxvdt

=rr ;

2

2

dv d radt dt

= =r rr

212i ix x v t at= + + ; iv v at= + ; 2 2 2 ( )i iv v a x x= + − ; 21

2i ir r v t at= + +r r r r ; iv v at= +r r r

Circular motion: 2 /T R vπ= ; 2 /T π ω= ; 2 /ca v R= Newtons Laws: F ma=∑

r r ; 12 21F F= −r r

Friction: 𝑓𝑠 ≤ 𝜇𝑠𝑁 ; 𝑓𝑘 = 𝜇𝑘 𝑁

Energies: 𝐾 = 12

𝑚𝑣2 ; 𝑈𝑔 = 𝑚𝑔𝑦 ; 𝑈𝑠 = 12

𝑘𝑥2 ; 𝑊 = ∫ �⃗� ∙ 𝑑𝑟 = �⃗� ∙ ∆𝑟

total g SE K U U= + + ; mech g s sE K U U f dΔ = Δ +Δ +Δ = ; /P dW dt F v= =r rg ; K WΔ =

Momentum and Impulse: p mv=r r ; I Fdt p= = Δ∫r r r

Center of mass: /cm i i ii i

r m r m=∑ ∑r r ; /cm i i ii i

v m v m=∑ ∑r r

Collisions: pr = const and E≠ const (inelastic) or pr = const and E= const (elastic) Rotational motion: 2 / Tω π= ; /d dtω θ= ; /d dtα ω= ; tv rω= ; ta rα= 2 2/c r ta a v r rω= = =

2 2 2tot r ta a a= + ; cmv rω= (rolling, no slipping) ; cma rα=

o tω ω α= + ; 2 / 2f i ot tθ θ ω α= + + ; 2 2 2 ( )f i f iω ω α θ θ= + − 2

pointI MR= ; 2hoopI MR= ; 2 / 2diskI MR= ; 22 / 5sphereI MR= ; 22 / 3shellI MR= ; 2

( ) /12rod centerI ML= 2

( ) / 3rod endI ML= ; 2i i

iI m r=∑ ; 2

cmI I Mh= + ; r Fτ = ×rr r ; Iτ α=∑ ; L r p= ×

r r r ; L Iω=r r

Energy: 2 / 2rotK Iω= ; rot cmK K K= + ; 0K UΔ + Δ = ; W τ θ= Δ ; instP τω=

Fluid: 𝜌 = 𝑀𝑉

; 𝑃 = 𝑃𝑜 + 𝜌𝑔ℎ ; 𝐴1𝑣1 = 𝐴2𝑣2; 𝑃1 + 𝜌𝑔𝑦1 + 12

𝜌𝑣12 = 𝑃2 + 𝜌𝑔𝑦2 + 12

𝜌𝑣22 ; 𝐵 = 𝜌𝑓𝑙𝑢𝑖𝑑 𝑉𝑜𝑏𝑗𝑒𝑐𝑡 𝑔

Gravitation: 1 2122ˆg

Gm mF rr

= −r

; 2( ) /g r GM r= ; 1 2 /U Gm m r= − ; 2

2 34T aGMπ=

Fluid

Cubic water balloon

26. Aliquidhasadensityof150kg/m3.Itfillsacubictankthatmeasures0.1mineachside.Howmuchdoesitweigh,inN?

a.0.15b.1.5c.15d.150e.  1500

Density=m/VW=mgW=density*V*g=1.5

Drowning a Balloon

27.Ascientisthasaballoonthatweighs0.001kg.Sheimmersesitinwaterbypushingdownwith15N.Thedensityofwateris1000kgm-3.Howbigistheballoon,in(1/1000)m3?a.1.5b.0.65c.6.5d.0.15e.Can’ttell.

Water Pressure in the Home •  Waterentersahousethroughapipewithaninside

diameterof2.0cmatanpressureof4×105Pa.A2.0-cm-diameterpipeleadstothe2ndfloorbathroom5mabove.Whentheflowspeedattheinletpipeis1.5m/s,Findthepressureonthesecondfloorin105pa.

A)3B)1C)4.5D)4E)3.5

p2 = p1 −

12ρ(v2

2 − v12)− ρg( y2 − y1)=3.5×105Pa

v2 =

A1A2v1 =1.5m/s

2222

2111 2

121 vgypvgyp ρρρρ ++=++

Gravity

Gravitation field

Aplanethasagravitationalfieldof15.7N/kgonitssurface.While

descendingontotheplanet,anastronautmeasuresagravitational

fieldof0.63N/kg.Whatisthedistanceoftheastronautabovethe

planet’ssurface,intermsoftheplanet’sradius?a.  2b.  25c.  16d.  4e.  5 g=GM/R2

Elevator on another planet

25.Anemptyelevator,M=100kg,hasacounterweightm=90kgconnectedbyacableoverapulleywithcoefficientoffriction0.05.Theelevatorfalls20mandlandswithavelocityof1m/s.Theaccidenthappensnotonearthbutonadifferentplanet.WhatisginN/kg?•  a.48•  b.24•  c.9.5•  d.4.3•  e.2.1

F.d=(M+m)vv/2=95F=(M-m)g–mu(M+m)gg=F/[M-m-mu(M+m)]=F/[0.5]g=(95/20)/.5=9.5

Astronaut in Orbit

•  Iweigh600Nonthesurfaceoftheearth.IfItravelonaspaceshuttleorbitingatadistanceof3timestheEarth’sradiusaboveground.Whatismymassinkgatthespaceshuttle?

a.3.83b.6.80c.15.3d.3.83e.61.2

Massisanintrinsicmeasureoftheobject,anddoesnotchangewithdistance!

MorePracticeProblems

Testing a weapon

14.A0.007kgbulletisfiredintoastationaryblockwithmass3.5kg,onafrictionless,horizontalsurface.Afterthecollision,thebulletgetsstuckintheblockandtheymovetogetherat1m/s.Findtheinitialspeedofthebulletinm/s.a.500b.200c.150d.125e.10

mV=(M+m)vV=v(M/m)approx.V=500

Rock climber hangs on

18.Arockclimberonaledgepushesablockofmassm=2.1kgupagainstaverticalwallatanangleof40degrees.Thecoefficientofstaticfrictionbetweentheblockandthewallis0.5.Whatistheminimumforce,inN,neededtokeeptheblockfromslidingdown?a. 15b. 41c. 25d. 19e. 0

Fup=FdownFup=Fcos40+m*Fsin40Fdown=mgF=mg/(cos40+m*sin40)=19

Walking in a Wind storm

22.AstrongwindisblowingSouthwithaforceof15N.Awomanmoves4meastandthen3mNorth.Howmuchworkisdonebythewindduringherwalk?a. +45Jb. -45Jc. +60Jd. -75Je. +15J

W=F.dF=-15d=3oppositeW=-45

Rotating disk

• Astudentdropsaringonarotatingdiskwithanangularspeedof10radians/s.Thediskhasmomentofinertiaof4.0kgm2.Afterthedrop,thediskandringarerotatingtogetherwithanangularspeedof5kgm2radians/s.Whatisthemomentumofinertiaofthering?• A.4• B.2• C.1• D.5•  E.16

Inthefigure,pointPisatrestwhenitisonthex-axis.ThelinearspeedofpointPwhenitreachesthey-axisisclosestto

• A)0.18m/s.• B)0.24m/s.• C)0.35m/s.• D)0.49m/s.•  E)0.71m/s.