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Conservation of Momentum LAB 8

Herrick Ong

Jordan Henry

Ravi Gogna

Sunny Kalra

April 21, 2009

Las Positas College – Livermore, CA

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Abstract

Verify Conservation of Momentum Laws Use Kinematic Equations with

Conservation laws to predict Where ball will land.

Run experiment 10 times Found Conservation laws to be correct

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Introduction

Momentum is defined as velocity times the mass of an object.

Momentum laws allow is to solve certain class of problems, Collisions.

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Theory

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Finding Initial Velocity Using Conservation of Energy

2211 KEPEKEPE

mghPE 2

21 mvKE

Potential Energy

Kinetic Energy

222

211 2

12

1 mvmghmvmgh

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Finding Initial Velocity Using Conservation of Energy

Ball Rotating2

21 I

Angular Velocity r

v

Moment of Inertia 2

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2mrI eSolidSpher

2222

211 2

12

12

1 Imvmghmvmgh

2

2222

22211 5

2

2

12

12

1r

vmrmvmghmvmgh

22

221 5

12

1 mvmvmgh

12 10

7ghv

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Conservation of MomentumInitial Momentum = Final Momentum

fi PP

Vector Decomposition

21 mmi PPPFinal Momentum Has Two Masses

jvmivmjvmivmP fyfxfyfxiˆˆˆˆ

2211

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Experiment Apparatus

Height of ramp

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Experiment

Set ramp Measure height Make sure the collision takes place at

approximately 45 degrees Run trial. Place paper on floor, take measurements Redo with tape.

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Final Velocity of Steel Ball and Marble

0.0

10.0

20.0

30.0

40.0

50.0

-30.0 -20.0 -10.0 0.0 10.0 20.0

x (cm)

y (c

m) Steel Ball

Marble

Origin

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ResultsResults

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Measured QuantitiesMeasured QuantitiesName Units Quantity Estimated error

(ILE)

Steel Marble grams 8.34 0.01

Glass Marble grams 3.79 0.01

Glass Marble w/ Tape

grams 3.82 0.01

Height of Ramp

cm 12.3 0.1

Height from Floor to Bottom of

Ramp

cm 83.2 0.1

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Measured QuantitiesMeasured QuantitiesSteel on Glass

name X(cm) Std dev ‘x’ Y(cm) Std dev ‘y’

Steel 11.9 0.49 22.3 0.40

Glass -25.6 0.80 40.7 1.18

Steel on Glass w/ Tape

Steel 7.7 0.73 27.3 0.65

Glass -13.6 1.24 26.3 2.80

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Analysis - ElasticAnalysis - ElasticMomentum in x (meter-

gram/s)

Error x Momentum in y (meter-

gram/s)

Error y

Steel 2.4 9.4 4.5 8.1

Glass -2.4 7.4 3.7 10.1

Total 0 8.2

Initial Momentum:

0 in x 10.9

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Analysis - InelasticAnalysis - InelasticMomentum in x (meter-

gram/s)

Error x Momentum in y (meter-

gram/s)

Error y

Steel 1.6 14.7 5.5 13.1

Glass -1.3 11.5 2.4 26.0

Total 0.3 7.9

Initial Momentum:

0 in x 10.9

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AnalysisAnalysis Note: Error bounds too large (larger than expected values),

possible low accuracy of experiment. Error larger in inelastic collision.

Momentum in ‘x’ conserved in both cases

Momentum in ‘y’ 27% less than expected

However, only 4% difference between observed total ‘y’ momentum in both experiments: consistent results.

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DiscussionDiscussion Momentum was conserved in the elastic Momentum was conserved in the elastic

and inelastic collisions within error and inelastic collisions within error bounds.bounds.

Experiment should be reevaluated to Experiment should be reevaluated to decrease size of error boundsdecrease size of error bounds

Expected momentum in ‘Expected momentum in ‘yy’ should be ’ should be obtained experimentally.obtained experimentally.

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Conclusion

For both the elastic and inelastic collisions:

Momentum conserved in x and y direction.

Since our error is so high a better result can be obtained by reworking the experiment and/or reworking the calculations.