The Roller Coaster of Resonance

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The Roller Coaster of Resonance

• Ashley Cho, Hope Gong, Allison Grossman, Julia
  Gudish, Stephanie Kuo, Lindsay Tom, and Noëlle
  Yasso

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Lab Diagram
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Explanation

• What are we doing?
• Finding the initial velocity of a car
• Finding the velocity of a metal ball upon
  collision
• Determining the horizontal displacement of a
  projectile metal ball
• Finding the wavelength of a resonating sound wave
• Determining the location and magnification of the
  image of a tuning fork produced by a lens

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What will we collect and how?

• Mass of ball on pendulum scale
• Mass of metal ball scale
• Mass of toy car scale
• Original height of pendulum ruler
• Pendulum height after collision ruler
• Initial car height (stool) ruler
• Final car height (table) ruler
• Frequency of tuning fork - given

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Finding the initial velocity of a car

• Computing Initial Velocity of PendulumPEi
  KEfmgy ½ mv2v _____
• Computing Final Velocity of PendulumPEi
  KEfmgy ½ mv2v _____
• Initial Velocity of Toy CarPi Pfm1v m1v
  m2vv _____

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Finding the velocity of a metal ball upon
collision

• Finding the initial velocity of the carPEi KEi
  KEfmgy ½ mv2 ½ mv2v _____
• Finding the final velocity of the car? y vit
  ½ gt2t _____? x v/ t v _____
• Finding the velocity of the ball after collision.
  Pi Pf
• M1v1i M1 v1f M2 v2i
• v _____

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Determining the horizontal displacement of a
projectile metal ball

• Finding the time
• ?y Vit ½ gt2
• t ______
• Finding the displacement
• V ?x / t
• ?x ____

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Finding the wavelength of a resonating sound wave

• V ?
• ? _____

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Finding the magnification of the image

• Determining magnification
• M -s
• s
• M _____

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Presentation!
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Data Collected

• Mass of ball on pendulum 0.094kg
• Mass of metal ball 0.0275kg
• Mass of toy car 0.036kg
• Original height of pendulum 0.01m
• Pendulum height after collision 0.004m
• Initial car height (stool) 0.58m
• Final car height (table) 0.743m
• Horizontal displacement of car 0.53m
• Frequency of tuning fork 341.3Hz
• Object distance .2m
• Image distance .18m

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Equations with Substitutions

• ? Finding initial velocity of the toy car
• Computing Initial Velocity of PendulumPEi
  KEfmgy ½ mv2 (.094kg)(9.8m/s2)(.01m) ½
  (.094kg)v2 v 0.44 m/s
• Computing Final Velocity of PendulumPEi
  KEfmgy ½ mv2 (.094kg)(9.8m/s2)(.004m) ½
  (.094kg)v2 v 0.28 m/s
• Initial Velocity of Toy CarPi Pfm1v m1v
  m2v (.094kg)(.44m/s) (.094kg)(.28m/s)
  (.036kg)v v .418 m/s

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Finding the velocity of a metal ball upon
collision

• Finding the initial velocity of the carPEi KEi
  KEfmgy ½ mv2 ½ mv2
• gy ½ v2 ½ v2 (9.8m/s2)(.58m) ½ (.418m/s)2
  ½ v2
• v 3.4 m/s
• Finding the final velocity of the car? y vit
  ½ gt2 .743m ½(9.8m/s2)(t2) t .389s
• v ?x / t v 0.53m / .389s v 1.36m/s
• Finding the velocity of the ball after collision.
  
• Pi Pf
• M1v1i M1 v1f M2 v2i
• (.036kg)(3.4m/s) (.0275kg) v
  (.036kg)(1.36m/s)
• v 2.67m/s

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Determining the horizontal displacement of a
projectile metal ball

• Finding the time
• ?y Vit ½ gt2 .743m 0 ½ (9.8m/s2)t2
• t .389s
• Finding the displacement
• V ?x / t 2.67m/s ?x / .389s
• ?x 1.03m

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Finding the wavelength of a resonating sound wave

• V ?
• 345m/s (341.5Hz)?
• ? 1.01m

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Finding the magnification of the image

• Determining magnification
• M -s M -.18m/.2m
• s
• M -0.9

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Results

• Initial Velocity of pendulum .44m/s
• Final velocity of pendulum .28m/s
• Velocity of car at top of track (after colliding
  with pendulum) .418m/s
• Velocity of car at bottom of track (right before
  collision with metal ball) 3.4m/s
• Velocity of car after collision 1.36m/s
• Horizontal velocity of metal ball 2.67m/s
• Horizontal displacement of ball 1.03m
• Wavelength of the resonant vibration 1.01m
• Magnification of image -0.9

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Sources of Error

• Human error in measurement
• If the pendulum were pushed and not just released
• Friction on the track
• Collisions were not truly elastic (sound is heard
  when pendulum hits car and when car hits ball)
• If metal ball is not actually at the edge of the
  table. Any displacement before it becomes
  projectile will cause error in initial velocity.
• If ball is unsuccessful in hitting the tuning
  fork

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Want more? Heres some BLING!!!!!!!

• Collisions
• http//blue.utb.edu/pdukes/PhysApplets/collisions
  /Collisions.html
• Projectile motion
• http//www.walter-fendt.de/ph11e/projectile.htm