The Problem with Acceleration James Vesenka (
[email protected]) Department of Chemistry and Physics University of New England Physics
Biddeford, ME 04005
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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
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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)
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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/
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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 =
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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
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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
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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
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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.
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Faster and Faster Workshop x(m)
Observables:
Prediction
How does _____ depend on _____ Procedure:
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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)
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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
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