The Problem with Acceleration

The Problem with Acceleration James Vesenka ([email protected]) Department of Chemistry and Physics University of New England Physics Biddeford, ME 04...
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The Problem with Acceleration James Vesenka ([email protected]) Department of Chemistry and Physics University of New England Physics

Biddeford, ME 04005

NQLB – Orono 6/23-24/11

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Motivation

 UNE: Modeling Instruction  Student centered, guided inquiry  Studio physics: observe & analyze 1st  Emphasis on Multiple Representations

 A continuing challenge: The Ratio

 Velocity, acceleration, etc. (units)  Slope of graph (units)  Trigonometry & Scaling (comparison)  Assessment: TUG&K NQLB – Orono 6/23-24/11

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Naïve Physics Student gravity

torque F=ma

Disconnected Factons kinematics

impulse

energy

projectiles

centripetal force

vectors

momentum rotation

units NQLB – Orono 6/23-24/11

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Experienced Physicist

“Expert” Thinker http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

NQLB – Orono 6/23-24/11

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Model Approach: Mechanics Conservation of Energy ΔE = W + Q + R Constant Force Particle v≠constant ΣF=ma Restoring Force Particle: F=-kΔx

Free Particle

Impulsive Force v=constant ΣF=0 Particle: ΣFΔt=Δp Central Force Particle: F=mv2/r (in)

NQLB – Orono 6/23-24/11

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E.g. Tumble Buggy

 Reality Perception Mental Model

Verbal Physical Phenomena

Diagrammatic Graphical

Mental Picture

Mathematical NQLB – Orono 6/23-24/11

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  1.  2.  3.    1.  2.  3.   

Tumble Buggy Motion

What do you observe? Moves at constant speed Moves (mostly) in a line Lights blink, wheels turn, noisy… What can you measure (units too)? Position (“X” in meters) Time (“t” in seconds) Buggy color, blink frequency, etc… What are the constants? (speed) NQLB – Orono 6/23-24/11

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How does __ depend on __?   So we have “variables” X and t.   Which variable is independent (you

control). Which variable is dependent upon the variable you control?   Depends on how you collect data…   We will use a metronome as our timer: http://www.metronomeonline.com/

NQLB – Orono 6/23-24/11

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Whiteboard Discourse

Diagrammatic 3

+X(m) 2

Graphical

y = mx + b

X=(+0.4m/s)t+0.5m

2 1 t=0

Δx

1 =

Δx Δt

→a =

Δv Δt

→ Δx =

NQLB – Orono 6/23-24/11

1

2

aΔt

2

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Faster and Faster Particle 4

+x

16 x(m)

3

How do we linearize this data? Workshop 9 tomorrow

2

4

1 t=0

1 0

1

NQLB – Orono 6/23-24/11

2

3

4

t(s) Page 22

“Kinematics Stack”

Bonus:

a≡ =

=

= =

Δv

4

+x x(m) 16

Δt vf − vi

9

tf − ti −

3

4 1 8 v(m/s)

t(s)

0

t(s)

3s − 2s + 3s − 2s

2 1 a v t=0

a(m/s/s)

2 0

NQLB – Orono 6/23-24/11

t(s)

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Motion Map the Following +x x(m) 80 60 40 20 0 v(m/s)

t(s)

0

t(s) a(m/s/s)

0

1

NQLB – Orono 6/23-24/11

2

3

4

t(s) Page 24

t=0 a v

a≡ =

=

= =

Δt vf − vi

Motion Map Result

1

x(m) 80

2

60

Bonus:

Δv

+x

tf − ti

40 3



20 t(s) t(s)

0 0

3s − 2s + 3s − 2s

4

-40 v(m/s) 0 -10

1 a(m/s/s)

NQLB – Orono 6/23-24/11

2

3

4 t(s) Page 25

“Kinematics Stack”

Bonus:

a≡ =

=

= =

Δv

Δt vf − vi

tf − ti − 3s − 2s

4 3 2

1

+ 3s − 2s t=0 a v

+x x(m) 16 9

4 1 8 v(m/s)

0 -2

a(m/s/s)

NQLB – Orono 6/23-24/11

t(s)

t(s) t(s)

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TUG&K Results (R Beichner)  Test for Understanding Graphs in Kinematics:  less (technology)  is more (understanding). 9;):)6*." 9-6*:)6*." 748)"2345+."

5-"?2@$'A" BCD)E*=;)"?2@F!A"

/)001-"20-66."

:;4>5,-+40"?2@&GA" /)001-"2345+." ()*)+,-+." !"

#!"

$!"

%!"

NQLB – Orono 6/23-24/11

&!"

'!!"

'#!" Page 27

David Dellwo: https://www.iupui.edu/~josotl/index.php

NQLB – Orono 6/23-24/11

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Acknowledgements

 Thanks to Danielle Parent, Aubrie

Dickinson, Ashley Ruggieara, Kerra Gearinger & Shawna Hatfield  Thanks to Susan McKay and Maine RISE Center for the invitation.  Thank you for listening.

NQLB – Orono 6/23-24/11

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Faster and Faster Workshop x(m)

Observables:

Prediction

How does _____ depend on _____ Procedure:

NQLB – Orono 6/23-24/11

0

t(s)

- v(m/s) +

Constants:

t(s)

- a(m/s/s) +

Measureables:

t(s) Page 30

Faster and Faster Workshop Data Table:

x(m)

0

Results

Linearized

t(s)

Math Model:

0

- v(m/s) +

Math Model: t(s)

NQLB – Orono 6/23-24/11

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v(m/s)

Faster and Faster Workshop Linearized

Math Model: ∆x(m)

0

Motion Map: Results Grid:

+x

0

Consensus Math Models:

slope x vs t2 v vs t v2 vs ∆x

NQLB – Orono 6/23-24/11

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