APPhysics C- MechanicsName

Due: September 2, 2016

Time Allotted: 8- 10 hours

BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS

SUMMER ASSIGNMENT

2016-2017

Teacher: Mrs. Kent

Textbook: Physics for Scientists and Engineers, 9th Edition, Serway; Jewett, Chapters 1-14

Welcome to APPhysicsC: Mechanics, I look forward to working with you in September.

This course is unusual in that we will only be studying the first semester of a college physics course: Kinematics and Dynamics. It is also unusual in that it will be taught on the honors college level as a calculus based course.

This assignment is designed to refresh the concepts and skills in which you acquiredproficiency and understanding during high school physics

IF you get stuck on a fewproblems, simply do the bestyoucan,butshow some work/effortinordertoreceive credit.

Please refer to the following sections in your textbook to work on this packet:

Chapter 1 Physics and Measurement

Chapter 2Motion in One Dimension

Chapter 3Vectors

APPENDIX B: Mathematics Review pp. A-4 to A-21.

***MITx’s EdX

PLEASE ENROLL FREE ONLINE “MECHANICS ReView”:

AP PHYSICS C: MECHANICS COURSE (15 weeks at your pace)

SUBMIT your MIT Certificate of Completion for a grade when you complete the course.

  • Watch the Kinematics Video Lessons under AP Physics C
  • University of Illinois:
  • Watch “Lectures” 1, 2, & 3 under “Linear Dynamics”

Sections:

 / Review Topic / Problems / Pages / Resources
  1. Algebra
/ a-c / 3-5 / Chapter 1, Appendix B
  1. Measurements
/ a-m / 5 / “
  1. Geometry
/ a-j / 6-8 / “
  1. Trigonometry
/ a-f / 8 / “
  1. Vector Review
/ (read) / 9-10 / Chapt.3; MIT Online Lecture “Vectors”
  1. Resultants
/ a-e / 11 / “
  1. Vector Addition
/ a-f / 12 / “
  1. Components
/ a-d / 13 / “
  1. Trig and Vector Combo
/ a-e / 14-15 / “
  1. More Practice with Resultants
/ a-f / 16 / “
  1. Vector Applications
/ a-i / 17-18 / “
  1. Calculus (for students who took this course only)
/ a-h / 19-20 / Appendix B
  1. Algebra

a.SIMPLIFICATION.Placetheanswerinscientificnotationwhenappropriateandsimplifytheunits(Scientificnotationisusedwhenittakeslesstimetowritethantheordinarynumberdoes. Asanexample200iseasiertowritethan2.00E2,but2.00E8iseasierto writethan200,000,000).Doyourbesttocancelunits,andattempttoshowthesimplifiedunitsinthefinalanswer.

b.OftenproblemsontheAPexamaredonewithvariablesonly.Solveforthevariableindicated.

c.Usingyourcalculatortosolveequations:Sometimesitiseasiertouseyourcalculatortosolveanequationratherthanalgebra.Todothis,grapheachsideofthe=signasadifferentfunction.Thenuseyourcalculatortofindthepoint(s)wherethegraphsintersect.

a.sincos22

b.sincossin1

  1. “Agreement of units” of Measurement. Scientists use the mks system (SI system) of units. mks stands for meter-kilogram-second. Master how to make the following conversions:

kilometers(km) ↔ meters(m) gram(g)↔kilogram(kg)centimeters(cm) ↔ meters(m) Celsius(oC)↔Kelvin(K)

millimeters(mm) ↔ meters(m) atmospheres(atm)↔Pascals(Pa)

nanometers(nm) ↔ meters(m) liters(L)↔cubicmeters(m3)

micrometers(m) ↔ meters(m)

Otherconversionswillbetaughtastheybecomenecessary.

a.
b. / 4008g
1.2km / =kg
=m / h.
i. / 25.0μm
2.65mm / =m
=m
c. / 823nm / =m / j. / 8.23m / =km
d. / 298K / =oC / k. / 5.4L / =m3
e. / 0.77m / =cm / l. / 40.0cm / =m
f. / 8.8x10-8m / =mm / m. / 6.23x10-7m / =nm

g. 1.2 atm =______Pa

  1. Geometry Review

g.Howlarge is,δ,γ,β,andα?J.Howlargeisa,b,andc?

h.Theradiusofacircleis5.5cm,

i.Whatisthecircumferenceinmeters? ______m

ii.Whatisitsareainsquaremeters? _____ m2

4

i.Whatistheareaunderthecurveto theright? ______m2

4. Usingthegenerictriangletotheright,RightTriangleTrigonometryandPythagoreanTheoremsolvethefollowing.Yourcalculatormustbeindegreemode.

1220

4.Vectors

Magnitude:Sizeorextent.Thenumericalvalue.

Direction:Alignmentororientationofanypositionwithrespecttoanyotherposition.

Scalars:Aphysicalquantitydescribedbyasinglenumberandunits.Aquantitydescribedbymagnitudeonly.

Examples:time,mass,andtemperature

Vector:Aphysicalquantitywithbothamagnitudeandadirection.Adirectionalquantity.

Examples:velocity,acceleration,force

Notation: AorALengthofthearrowisproportionaltothevectorsmagnitude.

Directionthearrowpointsisthedirectionofthevector.

8.Component Vectors

.

Aresultantvectorisavectorresultingfromthesumoftwoormoreothervectors.Mathematicallytheresultanthasthesamemagnitudeanddirectionasthetotalofthevectorsthatcomposetheresultant.Couldavector bedescribedbytwoormoreothervectors?Wouldtheyhavethesametotalresult?

Thisisthereverseoffindingtheresultant.Youaregiventheresultantandmustfindthecomponentvectorsonthecoordinateaxisthatdescribetheresultant.

R

+Ry

R

+Rxor

R

+Ry

+Rx

Anyvectorcanbedescribedbyanxaxisvectorandayaxisvectorwhichsummedtogethermeantheexactsamething.Theadvantageisyoucanthenuseplusandminussignsfordirectioninsteadoftheangle.

Forthefollowingvectorsdrawthecomponentvectorsalongthexandyaxis.

  1. c.
  1. d.

Obviouslythequadrantthatavectorisindeterminesthesignofthexandycomponentvectors.

9.Trigonometryand Vectors

Thesumofvectors xandydescribethevectorexactly.Again,anymathdonewiththecomponentvectorswillbeasvalidas withtheoriginalvector. Theadvantageisthatmathonthexand/oryaxisisgreatlysimplifiedsincedirectioncanbespecifiedwithplusandminussignsinsteadofdegrees.But,howdoyoumathematicallyfindthelengthofthecomponentvectors?Usetrigonometry.

cosadj

hyp

sinopp

hyp

1010

adjhypcosopphypsin

yxhypcosyhypsin

40o

40o

x

x10cos40o

x7.66

y10sin40o

y6.43

Solvethefollowingproblems.Youwillbeconvertingfromapolarvector,wheredirectionisspecifiedindegreesmeasuredcounterclockwisefromeast,tocomponentvectorsalongthexandyaxis.Remembertheplusandminussignsonyouanswers.Theycorrespondwiththequadranttheoriginalvectorisin.

Hint:Drawthevectorfirsttohelpyouseethequadrant.Anticipatethesignonthexandyvectors.Donotbothertochangetheangletolessthan90o.Usingthenumbergivenwillresultinthecorrect+and–signs.

Thefirstnumberwillbethemagnitude(lengthofthevector)andthesecondthedegreesfromeast.

Yourcalculatormustbeindegreemode.

Example:250at235o

235o

250

  1. 89at150o
  1. 6.50at345o

b.0.00556at60o

xhypcos

x250cos235o

x143

yhypsin

y250sin235o

y205

  1. 7.5x104at 180o

e.12at265o

f.990at320o

g.8653at225o

10.Giventwocomponentvectorssolvefortheresultantvector. UsePythagoreanTheoremtofindthehypotenuse,thenuseinverse(arc)tangenttosolvefortheangle.

Example:x=20,y=-15R2 x2 y2

tanopp

adj

opp

Rx2y2

tan1

adj

y

20R

202152

tan1

-15

R25

x

360o36.9o 323.1o

  1. x=600,y=400

b.x=-0.75,y=-1.25

c.x=-32,y=16

d.x=0.0065,y=-0.0090

  1. x=20,000,y=14,000
  1. x=325,y=998

11. Vector Applications

Speed

Speedisascalar.Itonlyhasmagnitude(numericalvalue).

Vs=10m/smeansthatanobjectisgoing10meterseverysecond.But,wedonotknowwhereitisgoing.

Velocity

Velocityisavector.Itiscomposedofbothmagnitudeanddirection.Speedisapart(numericalvalue)ofvelocity.

V=10m/snorth,orv=10m/sinthe+xdirection,etc.Therearethreetypesofspeedandthreetypesofvelocity

Instantaneousspeed/velocity:Thespeedorvelocityatan instant intime.Youlook downat yourspeedometeranditsays20m/s.Youaretravelingat20m/satthatinstant.Yourspeedorvelocitycouldbechanging,butatthatmomentitis20 m/s.

Averagespeed/velocity:Ifyoutakeatripyoumightgoslowpartofthewayandfastatothertimes.Ifyoutakethetotaldistancetraveleddividedbythetimetraveledyougettheaveragespeedoverthewholetrip.Ifyoulookedatyourspeedometerfromtimetotimeyouwouldhaverecordedavarietyof instantaneousspeeds.Youcouldgo0m/sinagasstation,oratalight.Youcouldgo30m/sonthehighway,andonlygo10m/sonsurfacestreets. But,whiletherearemanyinstantaneousspeedsthereisonlyoneaveragespeedforthewholetrip.

Constantspeed/velocity:If youhavecruisecontrolyoumighttravelthewholetimeatoneconstantspeed.Ifthisisthecasethenyouaveragespeedwillequalthisconstantspeed.

Constantvelocitymusthavebothconstantmagnitudeandconstantdirection.

Rate

Speedandvelocityarerates.Arateisawaytoquantifyanythingthattakesplaceduringatimeinterval.Ratesareeasilyrecognized.Theyalwayshavetimeinthedenominator.

10m/s10meters/second

The veryfirst Physics Equation

VelocityandSpeedbothsharethesameequation.Rememberspeedisthenumerical(magnitude)partofvelocity.Velocityonlydiffersfromspeedinthatitspecifiesadirection.

v= x

t

vstandsforvelocityxstandsfordisplacementtstandsfortime

Displacementisavectorfordistancetraveledinastraightline.Itgoeswithvelocity.Distanceisascalarandgoeswithspeed.Displacementismeasuredfromtheorigin.Itisavalueofhowfarawayfromtheoriginyouareattheendoftheproblem.Thedirectionofadisplacementistheshorteststraightlinefromthelocationatthebeginningoftheproblemtothelocationattheendoftheproblem.

SOLVE thefollowingproblems:

Always use thekmssystem:Units must be inkilograms,meters,seconds. On the alltests,including theAP examyou must:

1.List the originalequation used.

2.Show correct substitution.

3.Arrive at the correct answerwith correct units. Distanceanddisplacementaremeasuredin (m)Speedandvelocityaremeasured in (m/s)Time ismeasured in (s)

Example:Acartravels1000metersin10seconds.Whatisits velocity?

vx

t

v1000m

10s

v100ms

a.Acartravels35kmwestand75kmeast.Whatdistancedidittravel?

b.Acartravels35kmwestand75kmeast.Whatisitsdisplacement?

c.Acartravels35kmwest,90kmnorth.Whatdistancedidittravel?

d.Acartravels35kmwest,90kmnorth.Whatisitsdisplacement?

e.Abicyclistpedalsat10m/sin20s.Whatdistancewastraveled?

f.Anairplaneflies250.0kmat300m/s.Howlongdoesthistake?

g.Askydiverfalls3kmin15 s.Howfastaretheygoing?

h.Acartravels35kmwest,90kmnorthintwohours.Whatisitsaveragespeed?

i.Acartravels35kmwest,90kmnorthintwohours.Whatisitsaveragevelocity?

12.