L151_Kunkler_Kuil_Newland_Merril07.pdf

L151_Kunkler_Kuil_Newland_Merril07.pdf - Kristina Kuil...

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Unformatted text preview: Kristina​ ​Kuil Andrea​ ​Newland Rebecca​ ​Merrill Liz​ ​Kunkler PHY​ ​151L​ ​/​ ​Report​ ​No.​ ​07 10/26/2017​ ​Thurs. Air​ ​Resistance Objectives: ➢ Observe​ ​the​ ​effect​ ​of​ ​air​ ​resistance​ ​on​ ​falling​ ​coffee​ ​filters,​ ​forming​ ​data​ ​plots​ ​for​ ​both​ ​position and​ ​velocity​ ​versus​ ​time​ ​for​ ​a​ ​filter​ ​released​ ​from​ ​rest​ ​in​ ​air. ➢ Determine​ ​how​ ​air​ ​resistance​ ​and​ ​mass​ ​affect​ ​the​ ​terminal​ ​velocity​ ​of​ ​a​ ​falling​ ​object. ➢ Choose​ ​between​ ​two​ ​competing​ ​force​ ​models​ ​for​ ​the​ ​air​ ​resistance​ ​on​ ​falling​ ​coffee​ ​filters. ➢ Form​ ​free-body​ ​diagrams​ ​for​ ​each​ ​phase​ ​of​ ​motion​ ​experienced​ ​by​ ​the​ ​coffee​ ​filter​ ​from​ ​its release,​ ​to​ ​the​ ​point​ ​where​ ​it​ ​reaches​ ​terminal​ ​velocity,​ ​to​ ​its​ ​impact​ ​with​ ​the​ ​ground. Materials: ● ● ● ● Vernier​ ​computer​ ​interface Logger​ ​Pro​ ​and​ ​Microsoft​ ​Excel Vernier​ ​Motion​ ​Detector 5​ ​basket-style​ ​coffee​ ​filters Diagram​ ​of​ ​Setup​: Preliminary​ ​Questions: 1. Hold​ ​a​ ​single​ ​coffee​ ​filter​ ​in​ ​your​ ​hand.​ ​Release​ ​it​ ​and​ ​watch​ ​it​ ​fall​ ​to​ ​the​ ​ground.​ ​Next,​ ​nest two​ ​filters​ ​and​ ​release​ ​them.​ ​Did​ ​two​ ​filters​ ​fall​ ​faster,​ ​slower,​ ​or​ ​at​ ​the​ ​same​ ​rate​ ​as​ ​one filter?​ ​What​ ​kind​ ​of​ ​mathematical​ ​relationship​ ​do​ ​you​ ​predict​ ​will​ ​exist​ ​between​ ​the velocity​ ​of​ ​fall​ ​and​ ​the​ ​number​ ​of​ ​filters? ➢ Two​ ​filters​ ​fell​ ​faster​ ​than​ ​one​ ​filter​ ​when​ ​released​ ​from​ ​your​ ​hand.​ ​The​ ​mathematical relationship​ ​that​ ​exists​ ​is,​ ​the​ ​more​ ​filters​ ​that​ ​are​ ​dropped,​ ​the​ ​faster​ ​the​ ​velocity​ ​will be. 2. ​ ​Sketch​ ​your​ ​prediction​ ​of​ ​a​ ​graph​ ​of​ ​the​ ​velocity​ ​vs.​ ​time​ ​for​ ​one​ ​falling​ ​coffee​ ​filter. 3. If​ ​a​ ​filter​ ​is​ ​moving​ ​at​ ​a​ ​constant​ ​velocity,​ ​what​ ​do​ ​you​ ​know​ ​about​ ​the​ ​forces​ ​on​ ​the​ ​filter? Be​ ​specific,​ ​and​ ​describe​ ​what​ ​logic​ ​leads​ ​you​ ​to​ ​form​ ​your​ ​conclusion. ➢ If​ ​a​ ​filter​ ​is​ ​moving​ ​at​ ​a​ ​constant​ ​velocity,​ ​the​ ​net​ ​force​ ​acting​ ​on​ ​it​ ​is​ ​zero.​ ​This​ ​is because​ ​the,​ ​if​ ​velocity​ ​is​ ​constant,​ ​that​ ​means​ ​that​ ​acceleration​ ​is​ ​equal​ ​to​ ​zero.​ ​In​ ​the equation​ ​ F = ma ,​ ​if​ ​acceleration​ ​is​ ​equal​ ​to​ ​zero,​ ​then​ ​the​ ​net​ ​force​ ​is​ ​also​ ​equal​ ​to​ ​zero. Data​ ​&​ ​Observations: Data/Tables: Number​ ​of​ ​Filters Terminal​ ​Velocity VT​ ​(m/s) 1 -0.9974 0.9948 2 -1.409 1.985 3 -1.513 2.289 4 -1.781 3.172 5 -2.579 6.551 Noteworthy​ ​Observations: (Terminal​ ​Velocity) VT 2 ​ ​(m 2 /s 2 ) 2 ➢ The​ ​terminal​ ​velocity​ ​of​ ​the​ ​coffee​ ​filter​ ​increases​ ​as​ ​the​ ​number​ ​of​ ​filters​ ​(mass) increase. Results​ ​of​ ​Analysis: Questions: 1. Use​ ​a​ ​drawing​ ​program​ ​to​ ​draw​ ​a​ ​free​ ​body​ ​diagram​ ​of​ ​a​ ​single​ ​falling​ ​coffee​ ​filter​ ​during each​ ​of​ ​the​ ​following​ ​phases:​ ​Before​ ​release,​ ​immediately​ ​after​ ​release,​ ​a​ ​“short”​ ​time​ ​after release,​ ​a​ ​“long”​ ​time​ ​after​ ​release,​ ​just​ ​as​ ​it​ ​makes​ ​impact​ ​with​ ​the​ ​ground,​ ​and​ ​after​ ​it makes​ ​impact​ ​with​ ​the​ ​ground. No​ ​exact​ ​values​ ​are​ ​needed,​ ​but​ ​it​ ​is​ ​important​ ​to​ ​clearly​ ​label​ ​the​ ​forces​ ​acting​ ​on​ ​your coffee​ ​filter​ ​and​ ​represent​ ​the​ ​air​ ​drag​ ​force​ ​with​ ​respect​ ​to​ ​the​ ​weight​ ​vector​ ​of​ ​your​ ​filter. Additionally,​ ​note​ ​the​ ​value​ ​for​ ​the​ ​net​ ​acceleration​ ​of​ ​the​ ​filter​ ​at​ ​each​ ​phase​ ​relative​ ​to the​ ​acceleration​ ​due​ ​to​ ​gravity.​ ​ ​(i.e.​ ​a​ ​=​ ​g,​ ​a​ ​<​ ​g,​ ​a=​ ​0,​ ​etc.) ➢ 2. Provide​ ​a​ ​general​ ​expression​ ​for​ ​the​ ​acceleration​ ​a​ ​of​ ​an​ ​object​ ​experiencing​ ​air​ ​drag​ ​in terms​ ​of​ ​mass​ ​m,​ ​acceleration​ ​due​ ​to​ ​gravity​ ​g,​ ​and​ ​air​ ​drag​ ​F​g​. ➢ a= mg−F m g 3. What​ ​specific​ ​characteristics​ ​from​ ​both​ ​your​ ​position​ ​vs.​ ​time​ ​and​ ​velocity​ ​vs.​ ​time​ ​plots allowed​ ​you​ ​to​ ​conclude​ ​the​ ​filter​ ​had​ ​reached​ ​terminal​ ​velocity?​ ​Support​ ​your​ ​response with​ ​clear​ ​reasoning. ➢ We​ ​determined​ ​that​ ​the​ ​filter​ ​reached​ ​terminal​ ​velocity​ ​when​ ​the​ ​position​ ​vs.​ ​time​ ​slope had​ ​a​ ​constant​ ​slope,​ ​and​ ​velocity​ ​vs.​ ​time​ ​had​ ​a​ ​slope​ ​of​ ​zero.​ ​In​ ​the​ ​position​ ​vs.​ ​time plot,​ ​the​ ​velocity​ ​was​ ​terminal​ ​at​ ​a​ ​constant​ ​slope,​ ​this​ ​constant​ ​slope​ ​represents constant​ ​velocity.​ ​When​ ​an​ ​object​ ​has​ ​constant​ ​velocity,​ ​the​ ​acceleration​ ​is​ ​equal​ ​to​ ​zero. For​ ​the​ ​velocity​ ​vs.​ ​time​ ​plot,​ ​the​ ​slope​ ​was​ ​zero.​ ​Because​ ​the​ ​slope​ ​of​ ​this​ ​plot represents​ ​the​ ​acceleration,​ ​this​ ​shows​ ​that​ ​the​ ​acceleration​ ​of​ ​the​ ​filter​ ​was​ ​zero, meaning​ ​that​ ​it​ ​was​ ​at​ ​terminal​ ​velocity. 4. Depending​ ​on​ ​the​ ​object,​ ​the​ ​drag​ ​force​ ​is​ ​either​ ​proportional​ ​to​ ​the​ ​speed​ ​of​ ​the​ ​object,​ ​or the​ ​square​ ​of​ ​the​ ​speed​ ​of​ ​the​ ​object.​ ​From​ ​the​ ​experiment,​ ​and​ ​your​ ​Excel​ ​analysis, considering​ ​the​ ​number​ ​of​ ​filters​ ​dropped​ ​serves​ ​as​ ​an​ ​indication​ ​for​ ​what​ ​the​ ​drag​ ​force​ ​is (i.e.​ ​more​ ​filters,​ ​more​ ​mass;​ ​more​ ​mass,​ ​more​ ​force​ ​due​ ​to​ ​gravity;​ ​more​ ​force​ ​due​ ​to gravity,​ ​the​ ​higher​ ​the​ ​upward​ ​drag​ ​force​ ​is​ ​when​ ​the​ ​object​ ​reaches​ ​equilibrium,​ ​as acceleration​ ​is​ ​now​ ​zero)​ ​would​ ​you​ ​say​ ​that​ ​the​ ​drag​ ​force​ ​of​ ​an​ ​object​ ​is​ ​linearly proportional​ ​to​ ​the​ ​terminal​ ​speed​ ​of​ ​an​ ​object​ ​in​ ​free-fall​ ​(–bv)​,​ ​or​ ​the​ ​terminal​ ​speed squared​ ​(​–cv2​ ​)​?​ ​Support​ ​your​ ​response​ ​with​ ​reasoning. ➢ The​ ​drag​ ​force​ ​of​ ​an​ ​object​ ​is​ ​linearly​ ​proportional​ ​to​ ​the​ ​terminal​ ​speed​ ​squared​ ​( − cv 2 ).​ ​If​ ​a​ ​graph​ ​is​ ​proportional​ ​its​ ​best​ ​fit​ ​line​ ​goes​ ​through​ ​the​ ​origin.​ ​If​ ​you​ ​look​ ​at​ ​our graphs​ ​above,​ ​the​ ​best​ ​fit​ ​line​ ​of​ ​the​ ​terminal​ ​speed​ ​is​ ​linear​ ​but​ ​does​ ​not​ ​go​ ​through​ ​the origin​ ​therefore​ ​it​ ​is​ ​not​ ​proportional. 5. Let's​ ​say​ ​you​ ​increase​ ​the​ ​mass​ ​of​ ​an​ ​object​ ​to​ ​twice​ ​its​ ​original​ ​value​ ​(which​ ​again, doubles​ ​the​ ​weight,​ ​which​ ​doubles​ ​the​ ​drag​ ​force​ ​when​ ​equilibrium​ ​is​ ​reached);​ ​would​ ​you say​ ​the​ ​terminal​ ​speed​ ​of​ ​the​ ​object​ ​(the​ ​speed​ ​at​ ​which​ ​it​ ​is​ ​no​ ​longer​ ​accelerating)​ ​also doubles?​ ​In​ ​other​ ​words,​ ​if​ ​you​ ​drop​ ​an​ ​object​ ​that​ ​weighs​ ​100​ ​N​ ​and​ ​it​ ​reaches​ ​terminal speed​ ​at​ ​40​ ​m/s,​ ​would​ ​a​ ​200​ ​N​ ​object​ ​of​ ​the​ ​same​ ​shape​ ​and​ ​size​ ​reach​ ​terminal​ ​speed​ ​at 80​ ​m/s?​ ​Explain​ ​your​ ​reasoning​ ​by​ ​stating​ ​why​ ​you​ ​agree​ ​with​ ​that​ ​statement​ ​or​ ​not. ➢ If​ ​you​ ​were​ ​to​ ​double​ ​the​ ​weight,​ ​the​ ​terminal​ ​velocity​ ​would​ ​not​ ​double.​ ​If​ ​you​ ​look​ ​at our​ ​graphs,​ ​the​ ​plotted​ ​points​ ​for​ ​the​ ​terminal​ ​velocity​ ​vs​ ​the​ ​number​ ​of​ ​coffee​ ​filters increases​ ​but​ ​does​ ​not​ ​double.​ ​ ​Something​ ​with​ ​a​ ​larger​ ​mass​ ​does​ ​fall​ ​more​ ​quickly​ ​with air​ ​resistance​ ​than​ ​something​ ​with​ ​less​ ​mass.​ ​This​ ​was​ ​shown​ ​in​ ​the​ ​bowling​ ​ball​ ​and feathers​ ​video.​ ​It​ ​was​ ​also​ ​shown​ ​in​ ​our​ ​graphs​ ​that​ ​the​ ​more​ ​when​ ​the​ ​number​ ​of​ ​coffee filters​ ​was​ ​doubled,​ ​the​ ​terminal​ ​velocity​ ​increased​ ​but​ ​did​ ​not​ ​double.​ ​Kristina​ ​and Andrea​ ​also​ ​tried​ ​this​ ​on​ ​our​ ​own​ ​but​ ​dropping​ ​one​ ​plastic​ ​cup​ ​and​ ​four​ ​plastics​ ​cups, and​ ​the​ ​four​ ​plastic​ ​cups​ ​fell​ ​more​ ​quickly,​ ​but​ ​not​ ​twice​ ​as​ ​fast. 6. Consider​ ​the​ ​relationship​ ​you​ ​determined​ ​between​ ​the​ ​number​ ​of​ ​coffee​ ​filters​ ​dropped​ ​and the​ ​terminal​ ​speed​ ​of​ ​those​ ​filters;​ ​by​ ​now,​ ​you’ve​ ​either​ ​concluded​ ​that​ ​the​ ​number​ ​of filters​ ​dropped​ ​relates​ ​linearly​ ​to​ ​the​ ​terminal​ ​speed​ ​of​ ​the​ ​filters,​ ​or​ ​the​ ​terminal​ ​speed squared.​ ​Using​ ​your​ ​conclusion​ ​as​ ​a​ ​guide,​ ​how​ ​does​ ​the​ ​time​ ​of​ ​fall​ ​relate​ ​to​ ​the​ ​weight​ ​of the​ ​coffee​ ​filters​?​ ​If​ ​one​ ​filter​ ​falls​ ​in​ ​time​ ​“t​ ​”,​ ​how​ ​long​ ​(in​ ​terms​ ​of​ ​“t”)​ ​would​ ​it​ ​take​ ​four filters​ ​to​ ​fall,​ ​assuming​ ​they​ ​reached​ ​terminal​ ​speed​ ​very​ ​quickly? ➢ The​ ​number​ ​of​ ​coffee​ ​filters​ ​related​ ​linearly​ ​to​ ​the​ ​terminal​ ​speed.​ ​As​ ​the​ ​weight​ ​of​ ​the coffee​ ​filters​ ​increases,​ ​the​ ​time​ ​it​ ​takes​ ​for​ ​them​ ​to​ ​fall​ ​decreases.​ ​If​ ​one​ ​filter​ ​falls​ ​in time​ ​“t,”​ ​then​ ​it​ ​would​ ​take​ ​four​ ​filters​ ​to​ ​fall​ ​in​ ​about​ ​“⅓​ ​t”​ ​because​ ​even​ ​though​ ​the​ ​it relates​ ​linearly​ ​it​ ​does​ ​not​ ​relate​ ​proportionally.​ ​The​ ​more​ ​mass​ ​added​ ​the​ ​shorter​ ​the time​ ​it​ ​takes​ ​to​ ​fall,​ ​however​ ​each​ ​coffee​ ​filter​ ​added​ ​does​ ​not​ ​cut​ ​the​ ​time​ ​in​ ​half​ ​when added. 7. Suppose​ ​you​ ​were​ ​to​ ​analyze​ ​the​ ​motion​ ​of​ ​a​ ​college​ ​physics​ ​textbook​ ​dropped​ ​in​ ​a​ ​similar manner​ ​to​ ​that​ ​which​ ​you​ ​released​ ​your​ ​coffee​ ​filters;​ ​how​ ​would​ ​you​ ​expect​ ​the​ ​position​ ​vs. time​ ​and​ ​velocity​ ​vs.​ ​time​ ​plots​ ​for​ ​this​ ​object​ ​to​ ​compare​ ​to​ ​those​ ​for​ ​your​ ​coffee​ ​filters?​ ​Be sure​ ​to​ ​clearly​ ​state​ ​any​ ​expected​ ​similarities​ ​and​ ​differences. ➢ The​ ​slope​ ​of​ ​the​ ​dropped​ ​book​ ​is​ ​steeper​ ​than​ ​that​ ​of​ ​our​ ​coffee​ ​filters.​ ​A​ ​difference​ ​in the​ ​plots​ ​ ​is​ ​that​ ​the​ ​velocity​ ​does​ ​not​ ​become​ ​constant​ ​at​ ​any​ ​point​ ​for​ ​the​ ​book dropping​ ​as​ ​it​ ​did​ ​for​ ​the​ ​coffee​ ​filters.​ ​This​ ​is​ ​because​ ​the​ ​book​ ​is​ ​so​ ​heavy​ ​that​ ​air resistance​ ​never​ ​equals​ ​the​ ​gravitational​ ​force​ ​on​ ​the​ ​book​ ​in​ ​the​ ​short​ ​distance​ ​it​ ​is dropped.​ ​A​ ​similarity​ ​is​ ​that,​ ​as​ ​we​ ​increase​ ​the​ ​number​ ​of​ ​coffee​ ​filters,​ ​the​ ​slopes​ ​get steeper​ ​due​ ​to​ ​the​ ​increasing​ ​weight​ ​of​ ​the​ ​coffee​ ​filters.​ ​This​ ​is​ ​similar​ ​to​ ​the​ ​book because​ ​the​ ​book​ ​is​ ​heavy​ ​and​ ​its​ ​slope​ ​is​ ​steep​ ​due​ ​to​ ​this. ...
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  • Spring '14
  • AndrewB.Reeves
  • Physics, Resistance, Velocity, represents​ ​the​ ​acceleration

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