Impulse Momentum The impulse-momentum theorem Conservation of momentum Inelastic collisions
Conservation of Momentum LAB 8
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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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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
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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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.