Physics Lab 4.pdf - Course PHYS202 Section FEB 2017 Name...

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Unformatted text preview: Course:​ ​PHYS202 Section:​​ ​FEB​ ​2017 Name: Instructor​ ​Name:​ ​Dr.​ ​Pam​ ​Khurana __________________________________________________________________________ Title​:​ ​Pendulum​ ​Motion __________________________________________________________________________ Abstract:​ ​The​ ​Earth’s​ ​gravity​ ​and​ ​the​ ​gravity​ ​of​ ​other​ ​planets​ ​can​ ​be​ ​calculated​ ​using​ ​the foundation​ ​of​ ​knowledge​ ​of​ ​pendulum​ ​motion.​ ​A​ ​pendulum​ ​is​ ​set​ ​in​ ​motion​ ​on​ ​a​ ​simulator,​ ​and from​ ​the​ ​parameters​ ​of​ ​the​ ​pendulum​ ​the​ ​gravity​ ​is​ ​calculated​ ​using​ ​the​ ​relationship​ ​between​ ​the period​ ​of​ ​the​ ​pendulum​ ​and​ ​the​ ​length​ ​of​ ​the​ ​string​ ​the​ ​weight​ ​swings​ ​on.​ ​Earth’s​ ​gravity​ ​is​ ​first calculated​ ​to​ ​prove​ ​whether​ ​or​ ​not​ ​the​ ​calculation​ ​derived​ ​is​ ​correct.​ ​Once​ ​this​ ​is​ ​done,​ ​the gravity​ ​of​ ​Planet​ ​X​ ​can​ ​be​ ​calculated​ ​and​ ​compared​ ​to​ ​Earth.​ ​The​ ​results​ ​showed​ ​that​ ​Planet​ ​X had​ ​a​ ​higher​ ​gravity​ ​and​ ​that​ ​the​ ​calculations​ ​used​ ​were​ ​indeed​ ​correct.​ ​These​ ​types​ ​of​ ​problems are​ ​based​ ​on​ ​Newton’s​ ​laws​ ​of​ ​gravity​ ​and​ ​provide​ ​potential​ ​for​ ​more​ ​complex​ ​calculations. __________________________________________________________________________ Introduction:​​ ​Pendulum​ ​motion​ ​occurs​ ​when​ ​“a​ ​weight​ ​[is]​ ​hung​ ​from​ ​a​ ​stationary​ ​point​ ​in​ ​a way​ ​that​ ​allows​ ​it​ ​to​ ​swing​ ​freely​ ​back​ ​and​ ​forth”​ ​(Wood,​ ​n.d.).​ ​This​ ​is​ ​the​ ​basis​ ​for​ ​the experiment​ ​at​ ​hand​ ​and​ ​the​ ​conditions​ ​that​ ​change​ ​pendulum​ ​motion.​ ​Pendulum​ ​motion​ ​was​ ​first notably​ ​ascertained​ ​by​ ​Galileo​ ​Galilei​ ​when​ ​he​ ​commented​ ​on​ ​the​ ​motion​ ​of​ ​a​ ​swinging​ ​lamp​ ​in a​ ​cathedral​ ​(Fowler,​ ​n.d.).​ ​Pendulum​ ​motion​ ​later​ ​became​ ​the​ ​basis​ ​for​ ​a​ ​new​ ​type​ ​of​ ​clock​ ​that was​ ​far​ ​more​ ​accurate​ ​than​ ​its​ ​predecessors​ ​(Fowler,​ ​n.d.).​ ​With​ ​the​ ​equations​ ​for​ ​pendulum motion,​ ​the​ ​following​ ​experiment​ ​was​ ​performed. For​ ​the​ ​experiment,​ ​the​ ​angles​ ​used​ ​will​ ​only​ ​be​ ​small​ ​angles.​ ​The​ ​equation​ ​for​ ​small pendulum​ ​motion​ ​is​ ​accurate​ ​to​ ​1%​ ​only​ ​for​ ​angles​ ​less​ ​than​ ​about​ ​20​ ​degrees.​ ​Also,​ ​for​ ​the experiment​ ​friction​ ​will​ ​not​ ​be​ ​taken​ ​into​ ​account.​ ​The​ ​reason​ ​for​ ​this​ ​is​ ​to​ ​better​ ​calculate​ ​the force​ ​of​ ​gravity​ ​without​ ​additional​ ​variables.​ ​With​ ​these​ ​considerations,​ ​the​ ​length​ ​of​ ​the​ ​period of​ ​pendulum​ ​motion​ ​depends​ ​on​ ​the​ ​gravity​ ​and​ ​length​ ​of​ ​the​ ​massless​ ​string.​ ​For​ ​these calculations,​ ​the​ ​following​ ​equation​ ​will​ ​be​ ​used: T = 2π √ L g For​ ​this​ ​experiment​ ​the​ ​gravity ​of​ ​an​ ​unknown​ ​planet,​ ​referred​ ​to​ ​as​ ​Planet​ ​X,​ ​will​ ​be​ ​calculated. With​ ​the​ ​equation​ ​above​ ​rearranged,​ ​the​ ​amount​ ​of​ ​gravity​ ​can​ ​be​ ​calculated​ ​if​ ​the​ ​period​ ​and length​ ​of​ ​the​ ​massless​ ​string​ ​in​ ​the​ ​pendulum​ ​are​ ​known.​ ​From​ ​these​ ​calculations,​ ​I​ ​believe​ ​that the​ ​gravity​ ​on​ ​Earth​ ​as​ ​well​ ​as​ ​Planet​ ​X​ ​can​ ​be​ ​calculated. __________________________________________________________________________ Methods:​ ​The​ ​first​ ​step​ ​of​ ​the​ ​experiment​ ​is​ ​to​ ​verify​ ​the​ ​initial​ ​conditions.​ ​To​ ​do​ ​this,​ ​start​ ​by using​ ​the​ ​Earth’s​ ​gravity​ ​and​ ​verifying​ ​that​ ​it​ ​is​ ​correct.​ ​For​ ​this,​ ​use​ ​3​ ​different​ ​small​ ​angles​ ​and use​ ​the​ ​period​ ​and​ ​length​ ​of​ ​the​ ​massless​ ​string​ ​of​ ​the​ ​pendulum​ ​to​ ​calculate​ ​the​ ​gravity.​ ​The source​ ​of​ ​this​ ​equation​ ​comes​ ​from​ ​the​ ​formula​ ​for​ ​calculating​ ​the​ ​period​ ​of​ ​a​ ​pendulum rearranged. T = 2π √ L g ⇒ T 2π = √ L g T 2 ⇒ ( 2π ) = L g T 2 ⇒ g ( 2π ) =L⇒g= L T 2 ( 2π ) Once​ ​Earth’s​ ​gravity​ ​has​ ​been​ ​verified,​ ​the​ ​experiment​ ​can​ ​begin.​ ​For​ ​consistency,​ ​the​ ​same angle​ ​of​ ​5​ ​degrees​ ​will​ ​be​ ​used​ ​for​ ​every​ ​experiment.​ ​Using​ ​this​ ​angle​ ​set​ ​the​ ​conditions​ ​as follows: ● Length:​ ​2.5​ ​m ● Mass:​ ​1​ ​kg ● Friction:​ ​None ● Gravity:​ ​Planet​ ​X ● Check​ ​photogate​ ​timer With​ ​these​ ​conditions,​ ​bring​ ​the​ ​pendulum​ ​to​ ​5​ ​degrees​ ​and​ ​release.​ ​Press​ ​“Start”​ ​on​ ​the photogate​ ​timer​ ​and​ ​record​ ​the​ ​results.​ ​Once​ ​the​ ​results​ ​are​ ​recorded​ ​press​ ​“Reset”​ ​and​ ​change the​ ​length​ ​to​ ​2.3​ ​m.​ ​Repeat​ ​the​ ​process​ ​for​ ​this​ ​length​ ​as​ ​well​ ​as​ ​2​ ​m,​ ​1.3​ ​m,​ ​and​ ​1​ ​m. __________________________________________________________________________ Results:​​ ​The​ ​results​ ​of​ ​the​ ​experiment​ ​showed​ ​that​ ​the​ ​gravity​ ​of​ ​Planet​ ​X​ ​was​ ​greater​ ​than​ ​that of​ ​Earth.​ ​The​ ​gravity​ ​of​ ​Earth​ ​in​ ​the​ ​simulation​ ​was​ ​shown​ ​to​ ​be​ ​correct​ ​at​ ​9.8​ ​ m/s2 ​ ​with​ ​the following​ ​results​ ​received​ ​when​ ​performed​ ​at​ ​5​ ​degrees: Length​ ​(m) Period​ ​(s) Gravity​ ​( m/s2 )* 2.5 3.1732 9.80 2.3 3.0436 9.80 2.0 2.8382 9.80 1.3 2.2881 9.80 1 2.0067 9.80 *Rounded​ ​to​ ​2​ ​decimal​ ​places Next,​ ​the​ ​same​ ​tests​ ​show​ ​that​ ​the​ ​gravity​ ​was​ ​in​ ​fact​ ​higher​ ​than​ ​that​ ​of​ ​Earth.​ ​The​ ​tests​ ​were performed​ ​at​ ​5​ ​degrees​ ​just​ ​like​ ​the​ ​one​ ​for​ ​Earth’s​ ​gravity.​ ​The​ ​results​ ​were​ ​as​ ​follows: Length​ ​(m) Period​ ​(s) Gravity​ ​( m/s2 )* 2.5 2.6374 14.19 2.3 2.5297 14.19 2.0 2.3589 14.19 1.3 1.9018 14.19 1 1.6679 14.19 *Rounded​ ​to​ ​2​ ​decimal​ ​places ​ ​From​ ​this,​ ​the​ ​gravity​ ​of​ ​Planet​ ​X​ ​was​ ​calculated​ ​to​ ​be​ ​14.19​ ​ m/s2 . __________________________________________________________________________ Discussion:​ ​The​ ​results​ ​from​ ​the​ ​experiment​ ​showed​ ​consistency​ ​throughout​ ​the​ ​experiment. The​ ​known​ ​gravity​ ​of​ ​Earth​ ​was​ ​shown​ ​to​ ​be​ ​correct;​ ​from​ ​this,​ ​it​ ​can​ ​be​ ​reasonably​ ​said​ ​that​ ​the gravity​ ​of​ ​Planet​ ​X​ ​is​ ​approximately​ ​14.19​ ​ m/s2 .​ ​The​ ​information​ ​provided​ ​in​ ​these​ ​tests​ ​also demonstrated​ ​a​ ​valid​ ​way​ ​to​ ​find​ ​the​ ​gravity​ ​of​ ​a​ ​planet,​ ​given​ ​the​ ​conditions​ ​are​ ​the​ ​same​ ​as​ ​in the​ ​test.​ ​From​ ​this,​ ​further​ ​tests​ ​can​ ​be​ ​done​ ​to​ ​add​ ​in​ ​other​ ​variables​ ​and​ ​use​ ​these​ ​tests​ ​for​ ​more real-life​ ​scenarios. __________________________________________________________________________ Conclusion:​​ ​ ​Pendulum​ ​motion​ ​is​ ​yet​ ​another​ ​process​ ​that​ ​is​ ​an​ ​example​ ​of​ ​Newton’s​ ​first​ ​law​ ​of motion.​ ​This​ ​experiment​ ​showed​ ​a​ ​way​ ​that​ ​gravity​ ​can​ ​be​ ​calculated​ ​using​ ​pendulum​ ​motion without​ ​friction​ ​present.​ ​This​ ​is​ ​a​ ​basic​ ​equation​ ​that​ ​can​ ​possibly​ ​lead​ ​to​ ​more​ ​advanced calculations​ ​and​ ​hypotheses.​ ​When​ ​learning​ ​and​ ​experimenting​ ​with​ ​these​ ​principles,​ ​it​ ​is important​ ​to​ ​remember​ ​the​ ​significance​ ​of​ ​the​ ​origin​ ​of​ ​these​ ​equations.​ ​With​ ​Newton’s​ ​laws​ ​and equations​ ​such​ ​as​ ​the​ ​ones​ ​in​ ​this​ ​experiment,​ ​it​ ​is​ ​possible​ ​to​ ​build​ ​up​ ​to​ ​more​ ​advanced calculations,​ ​which​ ​in​ ​turn​ ​lead​ ​to​ ​more​ ​complex​ ​problems.​ ​This​ ​way​ ​of​ ​thinking​ ​is​ ​what advances​ ​our​ ​knowledge​ ​of​ ​physics​ ​and​ ​propels​ ​us​ ​technologically​ ​as​ ​a​ ​society. __________________________________________________________________________ References: Fowler,​ ​M.​ ​(n.d.).​ ​The​ ​Pendulum.​ ​Retrieved​ ​March​ ​23,​ ​2017,​ ​from . Wood,​ ​D.​ ​(n.d.).​ ​Pendulums​ ​in​ ​Physics:​ ​Definition​ ​&​ ​Equations.​ ​Retrieved​ ​March​ ​24,​ ​2017,​ ​from . ...
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