spreadsheets in the physics lab1 spreadsheets for enhancement and engagement in the introductory...

Spreadsheets in the Physics Lab 1

Spreadsheets for Enhancement and Engagement in the Introductory Physics Lab

AAPT Summer National Meeting, 2002

Boise, ID


Introduction

Brian A. Pyper

BYU-Idaho Dept of Physics

Utah State University Advisor: Dr. David Peak


Why Do We Have Physics Labs?

Physics is an empirical science! If we don’t spend time in a lab, there’s no difference between Physics and Mathematics. (Arons, 1993)

There are concepts and skills in Physics we learn best in the lab setting. (Bradley, 1968; Glasson, 1989)

Many types of learning styles improve understanding with ‘hands-on’ instruction. (Gardner, 1993)

Anything we can do to promote the students’ interaction with the material helps. “The best method is whatever one gets the student to spend the time with the material and strive, and strive, and strive for understanding.” (Davis, 2002)


Wish List – or “I’d sure like it if students would…”

Be interested in Physics Be confident in their

understanding Enjoy their Physics

experience


How Spreadsheets Can Help: Graphing and Data analysis

Programming Experience and Numerical Methods

Simulating the Laboratory Setting


Why Spreadsheets?

Spreadsheets are ubiquitous Spreadsheets are simple and

logical Spreadsheets use basic and

universal computer skills useful in the workplace


Three Examples: Graphing Data

Earth Satellites Basic Programming – Numerical

Methods

The Simple Harmonic Oscillator

Euler’s Method Gee-Whiz Modeling

Double-Slit Interference


Graphing Data: Earth Satellites

Satellite Data: (From www.celestrak.com/NORAD/elements)Period (min) apogee (km) perigee (km)

92.51 400.94 394.1590.29 289.5 287.5299.28 729.42 719.1

102.04 863.83 846.15717.99 20483.15 19881.7

1436.11 35810.05 35763.1439312 378622 378622


The Worksheet(From Newton’s second law we derive: T2=4π2(Re+h)3/gRe

2)

Earth Satellite Datak1 Period (min) apogee (km) perigee (km) T' (sec) Period (s) Altitude (m) error9.91 92.51 400.94 394.15 =((4*(PI())^2/$A$3)*$A$5*(1+G3/$A$5) 3̂) (̂1/2) =B3*60 =((C3+D3)/2)*1000 =ABS(F3-E3)k2 90.29 289.5 287.52 =((4*(PI())^2/$A$3)*$A$5*(1+G4/$A$5) 3̂) (̂1/2) =B4*60 =((C4+D4)/2)*1000 =ABS(F4-E4)6380000 99.28 729.42 719.1 =((4*(PI())^2/$A$3)*$A$5*(1+G5/$A$5) 3̂) (̂1/2) =B5*60 =((C5+D5)/2)*1000 =ABS(F5-E5)

102.04 863.83 846.15 =((4*(PI())^2/$A$3)*$A$5*(1+G6/$A$5) 3̂) (̂1/2) =B6*60 =((C6+D6)/2)*1000 =ABS(F6-E6)717.99 20483.15 19881.7 =((4*(PI())^2/$A$3)*$A$5*(1+G7/$A$5) 3̂) (̂1/2) =B7*60 =((C7+D7)/2)*1000 =ABS(F7-E7)1436.11 35810.05 35763.14 =((4*(PI())^2/$A$3)*$A$5*(1+G8/$A$5) 3̂) (̂1/2) =B8*60 =((C8+D8)/2)*1000 =ABS(F8-E8)39312 378622 378622 =((4*(PI())^2/$A$3)*$A$5*(1+G9/$A$5) 3̂) (̂1/2) =B9*60 =((C9+D9)/2)*1000 =ABS(F9-E9)

=SUM(H3:H9) error sum


Earth Satellites

1100

100001000000

10000000010000000000

1 10 100 1000 10000 100000 1000000

1E+07 1E+08 1E+09

Altitude (m)

Period (s)

T' (sec)

Earth Satellites: The Graph


Earth Satellites: The Graph

Earth Satellites (log-log)

1

100

10000

1000000

100000000

1 10 100 1000 10000 100000 1000000

1E+07 1E+08 1E+09

Altitude (m)

Period (s)

T' (sec)


Educational Value

Students can visualize a physical relationship that is far from intuitive

Students ‘discover’ values for physical constants

Entry to discussions about error minimization, log-log plots, appropriate units, etc.


Spreadsheets and Numerical Methods Because of their formatting,

spreadsheets allow very simple access to powerful Numerical Methods applications

Example: The Simple Harmonic Oscillator


The Simple Harmonic Oscillator

kxdt

xdm

2

2

Solution:

k

m

x = Acos(ωt + φ)


Euler’s Method

Use the value of the first derivative at the initial value to evaluate the function at a later point.

SO: if v=Δx/Δt then x(t+Δt)=x(t)+v(t)*Δt

and if a=Δv/Δt then v(t+Δt)=v(t)+a(t)*Δt The Force determines the acceleration,

(a(t)=F(t)/m) and the initial conditions determine x(0) and v(0)

Euler’s Method is unstable for oscillating functions!


Cell Formulasc t x v a E exactdt= 0 =$A$9 =$A$11 =-A7*A9/A5 =0.5*($A$7*(C2)^2+$A$5*(D2)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B2)0.09 =B2+$A$3 =C2+D2*$A$3 =D2+E2*$A$3 =-$A$7*C3/$A$5 =0.5*($A$7*(C3)^2+$A$5*(D3)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B3)m= =B3+$A$3 =C3+D3*$A$3 =D3+E3*$A$3 =-$A$7*C4/$A$5 =0.5*($A$7*(C4)^2+$A$5*(D4)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B4)1 =B4+$A$3 =C4+D4*$A$3 =D4+E4*$A$3 =-$A$7*C5/$A$5 =0.5*($A$7*(C5)^2+$A$5*(D5)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B5)k= =B5+$A$3 =C5+D5*$A$3 =D5+E5*$A$3 =-$A$7*C6/$A$5 =0.5*($A$7*(C6)^2+$A$5*(D6)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B6)10 =B6+$A$3 =C6+D6*$A$3 =D6+E6*$A$3 =-$A$7*C7/$A$5 =0.5*($A$7*(C7)^2+$A$5*(D7)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B7)Xo= =B7+$A$3 =C7+D7*$A$3 =D7+E7*$A$3 =-$A$7*C8/$A$5 =0.5*($A$7*(C8)^2+$A$5*(D8)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B8)0.1 =B8+$A$3 =C8+D8*$A$3 =D8+E8*$A$3 =-$A$7*C9/$A$5 =0.5*($A$7*(C9)^2+$A$5*(D9)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B9)Vo= =B9+$A$3 =C9+D9*$A$3 =D9+E9*$A$3 =-$A$7*C10/$A$5 =0.5*($A$7*(C10)^2+$A$5*(D10)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B10)0 =B10+$A$3 =C10+D10*$A$3 =D10+E10*$A$3 =-$A$7*C11/$A$5 =0.5*($A$7*(C11)^2+$A$5*(D11)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B11)

=B11+$A$3 =C11+D11*$A$3 =D11+E11*$A$3 =-$A$7*C12/$A$5 =0.5*($A$7*(C12)^2+$A$5*(D12)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B12)=B12+$A$3 =C12+D12*$A$3 =D12+E12*$A$3 =-$A$7*C13/$A$5 =0.5*($A$7*(C13)^2+$A$5*(D13)^2) =$A$9*COS((($A$7/$A$5)^0.5)*B13)


Euler’s SHOconstants: t x v a E exact errordt= 0 0.1 0 -1 0.05 0.1 0

0.09 0.09 0.1 -0.09 -1 0.05405 0.095977 0.004023m= 0.18 0.0919 -0.18 -0.919 0.058428 0.084233 0.007667

1 0.27 0.0757 -0.26271 -0.757 0.063161 0.065711 0.009989k= 0.36 0.052056 -0.33084 -0.52056 0.068277 0.041903 0.010153

10 0.45 0.022281 -0.37769 -0.22281 0.073807 0.014723 0.007557Xo= 0.54 -0.01171 -0.39774 0.117116 0.079786 -0.01364 0.001929

0.1 0.63 -0.04751 -0.3872 0.475085 0.086248 -0.04091 0.006601Vo= 0.72 -0.08236 -0.34444 0.823567 0.093234 -0.06488 0.017474

0 0.81 -0.11336 -0.27032 1.133568 0.100786 -0.08364 0.0297190.9 -0.13769 -0.1683 1.376859 0.10895 -0.09566 0.042021

0.99 -0.15283 -0.04439 1.528331 0.117775 -0.09999 0.052839


GraphEuler SHO

-5-4-3-2-1012345

0 2 4 6 8 10

time (s)

x

v

a

E

exact


Educational Value

Numerical methods and ‘best approximations’ (vs. Runge-Kutta or other methods)

Why is calculus important to Physics? Well, how small is a differential? (How small does Euler’s Δt have to be to get a certain degree of allowable error?)


Gee-Whiz Modeling: Double-Slit Interference

Two-slit intensity (see Dykstra & Fuller, Wondering About Physics, Wiley, 1988 p. 109-110)

I/I0=4sin2(Ф/2)cos2(δ/2)/Φ2

where

Φ=2πasinφ/ , δ=2πdsin φ/ and =wavelength, a=slit width, d=slit

separation, φ=diffraction angle.


Interference Worksheetconstants: angle phase diff 2phase diff Intensity (I/Io)wavelength: -90 -5.71E-02 -5.71E+01 3.68E+00

5.50E-07 -89 -5.71E-02 -5.71E+01 3.69E+00slit width: -88 -5.71E-02 -5.71E+01 3.72E+00

5.00E-09 -87 -5.70E-02 -5.70E+01 3.76E+00slit separation: -86 -5.70E-02 -5.70E+01 3.82E+00

5.00E-06 -85 -5.69E-02 -5.69E+01 3.88E+00-84 -5.68E-02 -5.68E+01 3.93E+00-83 -5.67E-02 -5.67E+01 3.98E+00-82 -5.66E-02 -5.66E+01 4.00E+00-81 -5.64E-02 -5.64E+01 3.98E+00-80 -5.63E-02 -5.63E+01 3.91E+00-79 -5.61E-02 -5.61E+01 3.77E+00-78 -5.59E-02 -5.59E+01 3.56E+00-77 -5.57E-02 -5.57E+01 3.25E+00-76 -5.54E-02 -5.54E+01 2.86E+00-75 -5.52E-02 -5.52E+01 2.39E+00-74 -5.49E-02 -5.49E+01 1.86E+00-73 -5.46E-02 -5.46E+01 1.31E+00-72 -5.43E-02 -5.43E+01 7.84E-01-71 -5.40E-02 -5.40E+01 3.50E-01-70 -5.37E-02 -5.37E+01 7.14E-02-69 -5.33E-02 -5.33E+01 6.57E-03


Interference GraphDouble-Slit Interference

-100 -80 -60 -40 -20 0 20 40 60 80 100

angle

Inte

nsity

(I/I

o)


With Macros!

Record a macro changing the values of the wavelength, slit width, and slit separation.

Assign these macros to scroll buttons from the forms toolbox in the visual basic editor, and

Voila! You have an instantly changing graph of intensity vs. diffraction angle!


Example Macros 1


The Power of Visual Basic Code Visual Basic Code can be used to

generate cell data, and plotted simply using the spreadsheet’s chart functions


Example Macros 2


Implications for Further Research Write a full set of Spreadsheet

simulations for supplementary use in introductory-level labs

Pre-post test, compare common exam grades and course grades and survey student groups with/without the spreadsheet component for understanding and general enjoyment

Defend August 2003


Additional Resources

Wondering About Physics, Dykstra & Fuller, Wiley 1988

Spreadsheet Physics, Misner and Cooney, Addison Wesley 1991

Dynamic Models in Physics Vol. 1: A Workbook of Computer Simulations Using Electronic Spreadsheets, Potter & Peck, David Barkley ed., N. Simonson & Co. 1989

Numerical Methods for Physics, Garcia, Prentice Hall 2000

Computational Physics, Giordano, Prentice Hall 1997


References A. Arons, “Guiding Insight and Inquiry in the

Introductory Physics Laboratory,” The Physics Teacher 31, p. 278-282 (May 1993)

R.L. Bradley, “Is the Science Laboratory Necessary for General Education Science Courses?” Science Ed. 52(1) p. 58-66 (Feb. 1968)

D. Davis, "Re: Planning for a PhD in Engineering Education,” Chemed-L post 9 Feb 2002

H. Gardner, Multiple Intelligences, Basic Books (1993) G.E. Glasson, The Effects of Hands-on and Teacher

Demonstration Laboratory Methods on Science Achievement in Relation to Reasoning Ability and Prior Knowledge,” J. Res. Sci. Teach. 26(2) p. 121-131 (1989)


Acknowledgements

Dr. David Peak, Utah State University Dept. of Physics

My wife Heidi My BYUI W02 PH150 lab Partial funding through the Thomas

E. Ricks Memorial Fund

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