Physics 399 Presentation(2)

Physics 399 Physics 399 Research PresentationResearch Presentation

Impulse-Momentum Impulse-Momentum TheoremTheorem

Gavan KaizawaGavan Kaizawa

Sam CampbellSam Campbell

HCPS III Physics standardsHCPS III Physics standards

Standard 1: Scientific InvestigationStandard 1: Scientific Investigation – – Discover, invent, and investigate using the skills Discover, invent, and investigate using the skills necessary to engage in the scientific process.necessary to engage in the scientific process.

Standard 2: Nature of ScienceStandard 2: Nature of Science – Understand – Understand that science, technology, and society are that science, technology, and society are related.related.

Standard 3: Matter and Energy conservationStandard 3: Matter and Energy conservation

Standard 4: Force and motionStandard 4: Force and motion

Presentation Format follows the Presentation Format follows the Scientific Method used for Scientific Method used for

Lab ReportsLab Reports

Physical ObservationPhysical ObservationResearch / Literature ReviewResearch / Literature ReviewHypothesisHypothesisExperiment (safety, materials, procedures)Experiment (safety, materials, procedures)Analysis (Data Table, Graphs, Sample Analysis (Data Table, Graphs, Sample Calculations, Error Analysis, Percent Error)Calculations, Error Analysis, Percent Error)ConclusionsConclusionsPeer ReviewPeer Review

Physical ObservationsPhysical Observations

Students observe that various colliding Students observe that various colliding objects will have a different time interval objects will have a different time interval due to the impactdue to the impactStudents observe that inelastic collisions Students observe that inelastic collisions stick together causing the time interval to stick together causing the time interval to be infinitebe infiniteStudents observe that elastic collisions do Students observe that elastic collisions do not stick together but time interval do vary not stick together but time interval do vary over a range of elasticityover a range of elasticity

Research & Literature SearchResearch & Literature Search

Impulse is the integral of force over time Impulse is the integral of force over time measured in SI units of Nmeasured in SI units of N..ss

Applying Newton’s 3Applying Newton’s 3rdrd law, every impulse has an law, every impulse has an equal and opposite impulseequal and opposite impulse

Deriving Impulse (J) from Newton’s 2Deriving Impulse (J) from Newton’s 2ndnd Law Law

FFnetnet = m = m..aa

= (m= (m..v)/v)/tt

FFnetnet t = (mt = (m..v)v)

Impulse (J) = change of momentum (p)Impulse (J) = change of momentum (p)

Research & Literature Search Research & Literature Search (cont’d)(cont’d)

Unbalanced forces always accelerates an Unbalanced forces always accelerates an objectobject

In a collision, an object will experience a In a collision, an object will experience a force resulting in a change of momentumforce resulting in a change of momentum

The object will either speed up, slow down The object will either speed up, slow down or change directionsor change directions

Impulse, as well as force and change in Impulse, as well as force and change in velocity, is a vector quantityvelocity, is a vector quantity

Research & Literature SearchResearch & Literature Search(cont’d)(cont’d)

When calculating a quantity is a result When calculating a quantity is a result from multiplying units measured by the y-from multiplying units measured by the y-axis and x-axis, you calculate the area axis and x-axis, you calculate the area under the graph for the relevant integral under the graph for the relevant integral

Research & Literature Search Research & Literature Search SourcesSources

Baker, Martin John (2009), Baker, Martin John (2009), Physics – ImpulsePhysics – Impulse: On-line @ : On-line @ http://www.euclideanspace.com/physics/dynamics/collision/impulse.ihttp://www.euclideanspace.com/physics/dynamics/collision/impulse.index.htmndex.htmFranklin, Bill (2005), Franklin, Bill (2005), Impulse and Momentum: An AAPT / PTRA Impulse and Momentum: An AAPT / PTRA ManualManual, AAPT: College Park, MD., AAPT: College Park, MD.Science Joy Wagon (2009), Science Joy Wagon (2009), Impulse -When Push Comes to ShoveImpulse -When Push Comes to Shove: : On-line @ On-line @ http://regentsprep.org/Regents/physics/phys01/impulse/default.htmhttp://regentsprep.org/Regents/physics/phys01/impulse/default.htmSpark Notes from Barnes & Nobles (2009), Spark Notes from Barnes & Nobles (2009), SAT Physics – ImpulseSAT Physics – Impulse: : Online @ Online @ http://www.sparknotes.com/testprep/books/sat2/physics/chapter9sehttp://www.sparknotes.com/testprep/books/sat2/physics/chapter9section2.rhtmlction2.rhtmlThe Physics Classroom-comPADRE (2009), The Physics Classroom-comPADRE (2009), The Impulse-The Impulse-Momentum Change TheoremMomentum Change Theorem: On-line @ : On-line @ http://www.physicsclassroom.com/class/momentum/U4/1b.cfmhttp://www.physicsclassroom.com/class/momentum/U4/1b.cfm

HypothesesHypotheses

IfIf the mass of an object is increased the mass of an object is increased thenthen the impulse created by the object will the impulse created by the object will increase increase becausebecause of the greater force of the greater force exerted by the object.exerted by the object.

IfIf the elasticity of an object is increased the elasticity of an object is increased thenthen the impulse created by the object will the impulse created by the object will increase increase becausebecause of the greater change in of the greater change in momentum of the object.momentum of the object.

Impulse-momentum free fall Impulse-momentum free fall lablab

In a nutshell:In a nutshell:How mass affects impulseHow mass affects impulse. Drop a solid . Drop a solid wooden ball, racquetball, and tennis ball wooden ball, racquetball, and tennis ball onto a force plate and record the impulse onto a force plate and record the impulse created by each. created by each. How elasticity affects impulseHow elasticity affects impulse. Drop a . Drop a frozen (“inelastic”) racquetball and frozen frozen (“inelastic”) racquetball and frozen (“inelastic”) tennis ball on a force plate and (“inelastic”) tennis ball on a force plate and compare to racquetballs and tennis balls at compare to racquetballs and tennis balls at room temperature.room temperature.

Safety precautionsSafety precautions

No horseplay! (Sam!)No horseplay! (Sam!)

Clear area of trip hazardsClear area of trip hazards

Potential electrical hazards when Potential electrical hazards when recharging Vernier LabQuest and laptop recharging Vernier LabQuest and laptop computerscomputers

Clean up lab work area when finishedClean up lab work area when finished

MaterialsMaterials

Vernier LabQuest data collectorVernier LabQuest data collector

Vernier Logger Pro software Vernier Logger Pro software

laptop computerlaptop computer

Vernier force plate Vernier force plate

Wooden ball, tennis ball, racquetballWooden ball, tennis ball, racquetball

Meter stick and hollow tube Meter stick and hollow tube

FreezerFreezer

Equipment set upEquipment set up

ProceduresProcedures

Set up free fall apparatus as shown in Set up free fall apparatus as shown in previous diagram.previous diagram.

Collect various balls to test the effects of Collect various balls to test the effects of masses and degree of (in)elasticity.masses and degree of (in)elasticity.

Connect the force plate to the LabQuest Connect the force plate to the LabQuest unit and set data collection parameters: 2 unit and set data collection parameters: 2 sec record time, 120 samples/s.sec record time, 120 samples/s.

Zero force plate. Zero force plate.

Procedures (cont’d)Procedures (cont’d)

Take individual runs for each ball on the Take individual runs for each ball on the force plate while recording force and time force plate while recording force and time data through the LabQuest unit.data through the LabQuest unit.

Download data into a laptop computer and Download data into a laptop computer and analyze with Logger-Pro.analyze with Logger-Pro.

Analyze and present data as force, time Analyze and present data as force, time interval of impact, and impulse in a data interval of impact, and impulse in a data table and in graph form. table and in graph form.

Sample Vernier graph:Sample Vernier graph:2 bounces of a racquetball2 bounces of a racquetball

Sample Vernier graph (cont’d)Sample Vernier graph (cont’d)First racquetball bounce, zoomedFirst racquetball bounce, zoomed

Sample Vernier graph (cont’d)Sample Vernier graph (cont’d)Impact of first racquetball bounce, zoomedImpact of first racquetball bounce, zoomed

Demonstrates Demonstrates IntegrateIntegrate function to function to calculate impulse.calculate impulse.

Analysis: Sample CalculationsAnalysis: Sample Calculations

Impulse = FImpulse = FΔΔttWe can’t just multiply the peak force (highest We can’t just multiply the peak force (highest force recorded) by the time interval (force recorded) by the time interval (ΔΔt) because t) because throughout the impact the force varies through throughout the impact the force varies through time.time.Realize that Realize that the area under the curve is the the area under the curve is the impulseimpulse on the force plate by the ball. on the force plate by the ball. Vernier units contain a function called Vernier units contain a function called IntegrateIntegrate that calculates the area under the that calculates the area under the curve for you.curve for you.

Use Use IntegrateIntegrate to calculate the ball’s impulse. to calculate the ball’s impulse.

Analysis: Data tableAnalysis: Data table

Ball TypeBall Type ∆∆t (sec)t (sec) Force peak (N)Force peak (N) Impulse (N*s)Impulse (N*s)

wood ballwood ball 0.02160.0216 165.5165.5 2.0432.043

tennis balltennis ball 0.02160.0216 73.573.5 0.94140.9414

"inelastic" tennis ball"inelastic" tennis ball 0.02420.0242 65.365.3 0.92310.9231

racquetballracquetball 0.0220.022 65.165.1 0.66130.6613

"inelastic" racquetball"inelastic" racquetball 0.02470.0247 59.359.3 0.64810.6481

Analysis: Data graphsAnalysis: Data graphsBall type vs. Impulse

0

0.5

1

1.5

2

2.5

wood ball tennis ball "inelastic"tennis ball

racquetball "inelastic"racquetball

type

impulse (N*s)

Inelastic vs. elastic impulse differences (zoomed in)

0.62

0.67

0.72

0.77

0.82

0.87

0.92

tennis ball "inelastic" tennis ball racquetball "inelastic" racquetball

type

impulse (N*s)

c

Error AnalysisError Analysis

The free fall apparatus helped to maintain The free fall apparatus helped to maintain a consistent height for each dropa consistent height for each drop

The experimenter dropping the balls may The experimenter dropping the balls may had a parallax error when aligning each had a parallax error when aligning each ball to dropball to drop

The free fall apparatus was resting on the The free fall apparatus was resting on the force plate and could have attributed to a force plate and could have attributed to a dampening affect on the datadampening affect on the data

Error Analysis Error Analysis (con’t)(con’t)

The balls had to be perfectly aligned in the The balls had to be perfectly aligned in the center of the free fall apparatus. If they center of the free fall apparatus. If they touched the apparatus during the fall, touched the apparatus during the fall, friction could have affected the resultsfriction could have affected the results

The assumption that freezing the tennis The assumption that freezing the tennis ball and racquet ball over a period of time ball and racquet ball over a period of time will cause the balls to become inelastic; or will cause the balls to become inelastic; or rather, become more inelasticrather, become more inelastic

Percent ErrorPercent Error-the affect of mass on Impulse--the affect of mass on Impulse-

Since there was no standard impulse Since there was no standard impulse available for comparison (no control in the available for comparison (no control in the first experiment), the data presented first experiment), the data presented shows a correlation of impulse to mass for shows a correlation of impulse to mass for ball dropped (see bar graphs!!!)ball dropped (see bar graphs!!!)

Percent DifferencePercent Difference-comparing the affects of elasticity--comparing the affects of elasticity-

The percent difference comparing the The percent difference comparing the affects of elasticity to inelasticity for:affects of elasticity to inelasticity for: Tennis ballTennis ball% difference = [(0.9914 - 0.9231) / 0.9914] 100% difference = [(0.9914 - 0.9231) / 0.9914] 100

= 1.943 % difference= 1.943 % difference

Racquet ballRacquet ball% difference = [(0.6613 - 0.6481) / 0.6613] 100% difference = [(0.6613 - 0.6481) / 0.6613] 100

= 1.996 % difference= 1.996 % difference

ConclusionsConclusions

IfIf a ball’s mass is increased a ball’s mass is increased thenthen it will it will have a greater impulse on the object it have a greater impulse on the object it strikes. strikes.

IfIf the elasticity of an object is increased the elasticity of an object is increased thenthen the impulse created by the object will the impulse created by the object will increase.increase.

Focusing activity: clocking your Focusing activity: clocking your fastballfastball

How can you figure out an object’s speed How can you figure out an object’s speed just by measuring how hard it hits another just by measuring how hard it hits another object?object?

Students throw a racquetball with all their Students throw a racquetball with all their might against an immoveable force plate, might against an immoveable force plate, as a LabQuest unit records force and time as a LabQuest unit records force and time data.data.

Clocking your fastball calculations Clocking your fastball calculations Impulse = FImpulse = FΔΔt = t = ΔΔ mv. mv. We want to solve for v into the plate, not We want to solve for v into the plate, not ΔΔv, so v, so we need to use a highly elastic ball so that vwe need to use a highly elastic ball so that v finalfinal ~ ~ vvinitialinitial..

ΔΔv = vv = vfinalfinal – v – vinitialinitial. Therefore if the ball is perfectly . Therefore if the ball is perfectly elastic, elastic, ΔΔv = 2v. “Bouncing.”v = 2v. “Bouncing.”We can get force and We can get force and ΔΔt readings from the force t readings from the force plate, and can measure the mass of the ball.plate, and can measure the mass of the ball.v = (v = (FFΔΔt)/(2m)t)/(2m)Students convert m/s to mph; compare to Roger Students convert m/s to mph; compare to Roger Clemens’ fastball. Clemens’ fastball.

Other student extensionsOther student extensions

Using a GoMotion sensor, students can Using a GoMotion sensor, students can record data on a ball’s position as it falls. record data on a ball’s position as it falls.

Along with force plate data, students can Along with force plate data, students can verify the velocity of the ball at impact verify the velocity of the ball at impact using:using:

1)1) Kinematic equations: v = vKinematic equations: v = voo + gt + gt

2)2) Impulse-momentum: v = (FImpulse-momentum: v = (FΔΔt)/(2m)t)/(2m)

3)3) Conservation of energy: v = sqrt(2gh)Conservation of energy: v = sqrt(2gh)

Mahalo!Mahalo!

Questions?Questions?

“ “Damn it, Jim! The GoMotion detector is less than functional!”Damn it, Jim! The GoMotion detector is less than functional!”