Student Worksheet for Uniform Circular Motion

Advanced Physics Uniform Circular Motion

Student Worksheet for Uniform Circular Motion

After you’ve worked through the sample problems in the videos, you can work out the problems below to practice doing this yourself. Answers are given on the last page.

Friction:

Fk = μkN

Fs = μsN

Centripetal Force:

a F = m = Rmv2

Law of Gravitation:

F = r2Gm m1 2

Free-fall acceleration:

go = r2GM

Gravitational Potential Energy:

)U = − ( r122

Gm m1 2 + r132

Gm m1 3 + r232

Gm m2 3 + …

Escape Speed:

v = √ R2GM

Law of Periods:

) r3T2

= (4π2

GM

Energy in Planetary Motion: E = K + U

and K U = − rGMm = 2r

GMm

© 2014 Supercharged Science www.ScienceLearningSpace.com


Practice Problems:

1. A car travels around a corner on an unbanked track. The radius of the track is 12 meters and the car is traveling at a velocity of 5 meters per second. Find the angle that a strap hanging from the inside of the car will make as the car travels around the corner.

2. A student stands on a merry-go-round of radius 4.3 m. The merry-go-round revolves once every 30 seconds. Find the speed of the child on the outer rim of the merry-go-round. What must be the coefficient of static friction between the boys shoes and the merry-go-round for him to stay on the merry-go-round?

3. A bicyclist rides in a circle with a radius of 20 m at a speed of 5 m/s. If the combined mass of the bike and the rider is 90 kg, what is the force of friction exerted on the bike by the road? What is the total force exerted by the road on the bike?



4. A child of mass 73 kg is on a Ferris wheel. At the top of the Ferris wheel the child has an apparent weight of 637N. What is the child’s apparent weight at the lowest point? Find the apparent weight of the student at the highest point if the speed of the Ferris wheel was tripled.

5. A car driver takes a turn of radius 10 m at a speed of 25 m/s. How many g’s of acceleration will the the driver experience?

6. An 11kN car rounds an unbanked curve with a radius of 70 m at a speed of 15 m/s. Find the force of friction of the road on the tires to keep the car on its path. If the coefficient of friction between the tires and the road is 0.33, will the car slip out of its turn?



7. Which takes more energy: Putting a satellite up to 1500 km or putting a satellite in orbit that is already at 1500 km? What about at 3000 km and 4500 km instead of 1500km? The Earth’s radius is 6000 km.

8. An asteroid with mass 1.2x10-4 times the mass of the Earth revolves in a circular orbit around the sun. The asteroid’s orbit is 1.5 times that of Earth’s. Find the period the asteroid’s revolution in Earth years. What is the ratio between the kinetic energy of the asteroid and Earth?

9. Assuming the Earth travels in a circular orbit, how far does the Earth travel in 70 seconds?



10. Phobos orbits the planet Mars at a radius of 9.3x106 m with a period of 8 hours. Find the mass of Mars.

11. If a satellite is placed into orbit, around the Earth, at a radius of three quarters of the Moon’s orbit radius, what is the satellite’s period of revolution in lunar months?

12. A spaceship is 77,850 light years from the center of a galaxy. The mass of the galaxy 1.4x1011 times the mass of our sun. Assume the galaxy acts as a spherical distribution so you can use of the law of gravitation. What minimum speed must the spaceship have to escape the galaxy?



13. What is the escape velocity of a planet of radius 700 km with gravitational acceleration one half of Earth’s gravitational acceleration? How high will a particle go if it is launched up with an initial speed of 998 m/s on this planet? What speed will the object reach if it is dropped from a height of 2000 km (2300 km from the center of the planet?)

14. In a double star system, two stars orbit about their shared center of mass. Both stars share the same mass of 3.0x1030 kg and are a distance of 2.0x1011 m from each other. What is their angular speed? If a meteorite travels through the center of mass between the two planets what must its speed be to escape the gravitational field of the two stars?

15. Find the gravity on the surface of the moon. What is the period of a pendulum on the moon, if the pendulum normally has a period of three seconds on Earth?



16. A person weighs 600 N at sea level on Earth. If you ride an elevator up to 500 meters, what will be your new apparent weight?

17. If you draw a line from the center of Earth to the center of the Sun. Where must a particle be on that line in order for the gravitational field of the Earth and the Sun the cancel eachother out?

18. What is the ratio between Earth’s acceleration towards the sun when the moon is between the Earth and the sun compared to when the Earth is between the moon and the sun?


AdvancedPhysics UniformCircularMotion

©2014SuperchargedScience www.ScienceLearningSpace.com Page1

StudentWorksheetforUniformCircularMotionAfteryou’veworkedthroughthesampleproblemsinthevideos,youcanworkouttheproblemsbelowtopracticedoingthisyourself.Answersaregivenonthelastpage.

Friction:

Fk = μkN

Fs = μsN

Centripetal Force:

F = ma = mRv2

Law of Gravitation:

F = Gmr12m2

Free-fall acceleration:

go = GrM2

Gravitational Potential Energy:

U = − (Gmr112m2 2 + Gmr113m2 3 + Gmr223m2 3 + …)

Escape Speed:

v = √2GRM

LawofPeriods:

Tr32 = (G4πM2)

EnergyinPlanetaryMotion:E=K+U

U = − GMr m and K = G2Mrm

Adva

©20

Prac

1

2

ancedPhysic

014Superch

cticeProblem

1. Acartravistraveliofthecar

2. Astudenseconds.coefficienmerry‐go

cs

hargedScien

ms:

velsaroundngatavelocrwillmakea

ntstandsonFindthespentofstaticfro‐round?

Unif

nce www.Sc

acorneroncityof5metasthecartr

amerry‐go‐eedofthechrictionbetw

formCircula

cienceLearni

nanunbanketerspersecoavelsaroun

‐roundofradhildontheoweentheboy

arMotion

ngSpace.com

edtrack.Theond.Findthedthecorner

dius4.3m.Touterrimoftysshoesand

m

eradiusofteanglethatr.

Themerry‐gthemerry‐gdthemerry‐g

thetrackis1astraphang

go‐roundrevgo‐round.Whgo‐roundfor

12metersangingfromth

volvesoncehatmustberhimtostay

Page2

ndthecarheinside

every30theyonthe

2

Adva

©20

3

4

ancedPhysic

014Superch

3. Abicyclisbikeandtotalforc

4. Achildoweightothestude

cs

hargedScien

stridesinatheriderisceexertedby

fmass73kgf637N.Whaentatthehig

Unif

nce www.Sc

circlewitha90kg,whatytheroado

gisonaFerratisthechildghestpointi

formCircula

cienceLearni

aradiusof2tistheforcenthebike?

riswheel.Atd’sapparentifthespeed

arMotion

ngSpace.com

20mataspeoffrictione

tthetopofttweightattoftheFerris

m

eedof5m/sexertedonth

theFerriswthelowestpswheelwas

s.Ifthecombhebikebyth

wheelthechiloint?Findthstripled.

binedmassoheroad?Wh

ldhasanapheapparent

Page3

ofthehatisthe

parenttweightof

3

Adva

©20

5

6

7

ancedPhysic

014Superch

5. Acardrivthedrive

6. An11kNfrictionotiresand

7. Whichtaalreadya

cs

hargedScien

vertakesaterexperienc

carroundsoftheroadodtheroadis

akesmoreenat1500km?

Unif

nce www.Sc

turnofradiue?

anunbankeonthetirest0.33,willth

nergy:PuttinTheEarth’s

formCircula

cienceLearni

us10mata

edcurvewithtokeepthechecarslipou

ngasatellitesradiusis60

arMotion

ngSpace.com

speedof25

haradiusofcaronitspatutofitsturn

eupto1500000km.

m

m/s.Howm

f70matasth.Ifthecoe?

0kmorputti

manyg’sofa

peedof15mefficientoffr

ingasatellit

acceleration

m/s.Findthrictionbetw

teinorbitth

Page4

willthe

eforceofeenthe

hatis

4

Adva

©20

8

9

1

ancedPhysic

014Superch

8. Anastero

sun.TheEarthyea

9. Assumin

10. PhobosoMars.

cs

hargedScien

oidwithmaasteroid’soars.

gtheEartht

orbitsthepla

Unif

nce www.Sc

ss1.2x10‐4torbitis1.5ti

travelsinac

anetMarsat

formCircula

cienceLearni

timesthemamesthatof

circularorbi

taradiusof

arMotion

ngSpace.com

assoftheEaEarth’s.Find

it,howfard

9.3x106mw

m

arthrevolvesdtheperiod

doestheEart

withaperiod

sinacirculadtheasteroid

thtravelin7

dof8hours

arorbitaroud’srevolutio

70seconds?

.Findthem

Page5

undtheonin

massof

5

Adva

©20

1

1

ancedPhysic

014Superch

11. Ifasatellradius,w

12. Aspacesthemassgravitati

cs

hargedScien

liteisplacedwhatisthesa

hipis77,85sofoursun.on.Whatmi

Unif

nce www.Sc

dintoorbit,aatellite’sper

0lightyearsAssumetheinimumspee

formCircula

cienceLearni

aroundtheEriodofrevol

sfromtheceegalaxyactsedmustthe

arMotion

ngSpace.com

Earth,atarautioninluna

enterofagaasasphericspaceshiph

m

adiusofthrearmonths?

alaxy.Themcaldistributihavetoescap

eequarterso

assofthegaionsoyoucpethegalaxy

oftheMoon

alaxy1.4x10canuseofthy?

Page6

n’sorbit

011timeselawof

6

Adva

©20

1

ancedPhysic

014Superch

13. WhatistEarth’sgspeedof2000km

cs

hargedScien

theescapevgravitational998m/son

m(2300kmf

Unif

nce www.Sc

elocityofaplaccelerationthisplanet?fromthecen

formCircula

cienceLearni

planetofradn?Howhigh?Whatspeenterofthepl

arMotion

ngSpace.com

dius700kmhwillapartidwilltheoblanet?)

m

mwithgraviticlegoifitisbjectreachi

tationalacceslaunchedufitisdroppe

elerationoneupwithaninedfromahe

Page7

ehalfofnitialeightof

7

Adva

©20

1

1

1

ancedPhysic

014Superch

14. Inadoubmassof3ameteorescapeth

15. Findthependulum

16. Apersonyournew

cs

hargedScien

blestarsyste3.0x1030kgaritetravelsthhegravitatio

gravityontmnormally

nweighs600wapparentw

Unif

nce www.Sc

em,twostarandareadishroughtheconalfieldoft

hesurfaceohasaperiod

0Natsealevweight?

formCircula

cienceLearni

rsorbitaboustanceof2.0centerofmathetwostar

ofthemoon.dofthreese

velonEarth

arMotion

ngSpace.com

uttheirshar0x1011mfroassbetweenrs?

WhatisthecondsonEa

.Ifyouride

m

redcenterofmeachothenthetwopla

periodofaarth?

anelevator

fmass.Bother.Whatisthanetswhatm

pendulumo

upto500m

hstarsshareheirangularmustitsspee

onthemoon

meters,what

Page8

ethesamerspeed?Ifedbeto

n,ifthe

twillbe

8

Adva

©20

1

1

ancedPhysic

014Superch

17. Ifyoudralineinor

18. Whatistandthes

cs

hargedScien

awalinefrorderfortheg

theratiobetsuncompare

Unif

nce www.Sc

omthecentegravitationa

tweenEarth’edtowhent

formCircula

cienceLearni

erofEarthtoalfieldofthe

’sacceleratitheEarthisb

arMotion

ngSpace.com

othecentereEarthandt

ontowardsbetweenthe

m

oftheSun.WtheSunthec

thesunwheemoonandt

Wheremustcanceleach

enthemoonthesun?

taparticlebotherout?

nisbetween

Page9

beonthat

ntheEarth

9

Student Worksheet for Uniform Circular Motion

Documents

Transcript of Student Worksheet for Uniform Circular Motion