Free Fall of a Ruler_Lesson Plan

Pontifícia Universidade Católica de São PauloJunior Scientific initiation at PUC/SP and the development of experimental activities in Physics

using the Classmate PC

FREE FALL OF A RULER ANALYSIS USING AFREE FALL OF A RULER ANALYSIS USING A

PHOTOTRANSISTORPHOTOTRANSISTOR

Lesson plan

Prof. Roger Willians Corrêa

12th grade students from E.E. Profa. Alayde Domingues Couto

Macedo

Danillo L. S. de Carvalho

Irisnelda Alves de Matos

Sarah Rocksone Santos Silva de Araújo

Supervision Prof. Marisa Almeida Cavalcante (PUC/SP) e Prof.

Cristiane R. C. Tavolaro (PUC/SP)



July 2009

Objectives

To understand the characteristics of accelerated motion. Measure the value of the acceleration of the local gravity. Understand the operation of some electronic components.

Content

Free fall of a body subjected to gravity. Kinematic characteristics of a body in accelerated straight motion: variation of its position over time and graph, variation of its speed over time and graph. Electricity and electronic components.

Competences and abilities

Representation and communication Use and understand tables, graphs and graphic mathematical relationships to express

physics knowledge. Express themselves correctly using the appropriate physics language and elements of its

symbolic representation. Investigation and understanding

Know and use physics concepts. Relate magnitudes, quantify and identify relevant parameters. Understand and use physics laws and theories.

Build and investigate problem situations, identify the physics situation, use physics models, generalize from another situation, foresee, evaluate, and analyze predictions.

Sociocultural and historical perception Recognize Physics as human construction, aspects of its history and relationships with the

cultural, social, political and economical contexts.

Materials

An electric circuit in series using: a resistor, a phototransistor, a 9V battery and a LED. A transparent ruler with opaque adhesive tape, a laser pointer, two alligator clamps, wires, sound plug for the entrance of sound board of the Classmate PC, software for data analysis (we used Audacity, a free edition and sound analysis software and calculation spreadsheet).



Assembly

First we will set up the circuit in series, according to the illustration below:

You have to be careful with the correct polarity of the phototransistor and of the LED, so that if the phototransistor is illuminated with the laser pointer the LED turns on.

We will connect the two alligator clamps to the connections of the microphone plug. These claws will be connected to the resistor's terminals. The picture below shows the assembly of the experiment:

resistorLED

phototransistor

battery



Following we see details of the resistor connected to the LED, the connection of the plug to the microphone entrance of the Classmate PC, the phototransistor and the laser pointer in their respective stands.



Operation

When the laser pointer illuminates the phototransistor, it starts the electric current. When the light incidence decreases or ceases, the current also decreases or ceases. When the current travels the circuit there will be a proportional DDP in the resistor's terminals, that information will be sent to the sound board of the Classmate PC.



Once the laser pointer is on, we make its light illuminate the phototransistor. We left the ruler fall freely, interrupting the light that arrives on the phototransistor, varying the current in the circuit. This variation will cause tension variations, which will be captured through the software. The time where the alternations between clear and dark parts of the ruler will be recorded when the ruler passes between the laser and the phototransistor. Observe the illustration to bellow:



Record button



The data collection is made by taking the positions of the transition points dark / clear, clear / dark and the respective values of time, using the time scale in the software.

table of these values is set up and a position over time graph is made:

1.0800 1.1000 1.1200 1.1400 1.1600 1.1800 1.2000 1.2200 1.2400 1.26000.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00Queda da régua

Tempo (s)

Posi

ção

(cm

)

Time scale

Signal obtained

time



tempo (s)posição (cm)

1,0933 0,00

1,1054 1,49

1,1170 2,99

1,1267 4,48

1,1371 5,97

1,1457 7,46

1,1549 8,96

1,1626 10,45

1,1711 11,94

1,1783 13,44

1,1861 14,93

1,1927 16,42

1,2000 17,91

1,2064 19,41

1,2133 20,90

1,2192 22,39

1,2257 23,89

1,2313 25,38

1,2377 26,87

1,2431 28,36

1,2489 29,86

1,2541 31,35

A spreadsheet of calculations is used to do a quadratic regression, based on the graph, to obtain the value of the acceleration of gravity. The following values were obtained:

Equation of the curve: y = 489,23x2 - 953,78x + 457,99 As the position function of accelerated motion is S = S0 + V0.t + (a/2). t2, the number that accompanies the quadratic term in the equation

of the curve is equal to half the value of acceleration due to gravity. Multiplying 489,23 by 2 and dividing it by 100 (to adjust the metric unit to m/s2), we found

g = 9,78 m/s2.

Suggestion for dividing the experiment in classes

Fall of the ruler



Class 1: Revision: Free fall of a body; assembly of the circuit and brief explanation on its components. Class 2: Data collection Class 3: Making of the graph and calculating the value of the acceleration of gravity. Final

considerations.

Final Considerations

To measure the value of the acceleration of gravity of a free falling body fall demands the collection of time intervals. Using a stopwatch is not very accurate. In this experiment we used the computer and electronic components of low cost to find this value. The appeal that the use of computers have on teenagers favors the students' interest for the accomplishment of the experiment and a more attractive learning of the Physics concepts.

Another way to find the value of the acceleration of gravity is to make a speed over time graph. As the function equation of speed in accelerated motion is V = V0 + a.t, the slope of the straight line obtained in this graph results in the value of gravity. For more information, check "Physics Experiments with a PC sound recorder", in links.

Links

Blog with more information about the experiment http://www.picintel-profroger.blogspot.com/ Text about analogical-digital conversion

http://xviiisnefnovastecnologias.blogspot.com/2009/01/texto-de-orientao-para-oficina-de-novas.html

“Physics Experiments with a PC tape recorder ", Carlos Eduardo Aguiar - UFRJhttp://omnis.if.ufrj.br/~carlos/palestras/fisicaGravador/fisicaGravadorLimc.pdf

"Variação da aceleração da Gravidade com a Latitude e Altitude" (Variation of the acceleration of gravity due to latitude and altitude), Wilson Lopes – Physics Department, Guarulhos University.http://www.periodicos.ufsc.br/index.php/fisica/article/viewFile/9106/8450

Latitude e longitude of Brazilian Citieshttp://www.apolo11.com/latlon.php

Latitude, longitude, altitude and other geographic data from all around the planethttp://www.earthtools.org/

Script to calculare the local gravity from the latitude and altitudehttp://www.picintel-profroger.blogspot.com/#calc

http://www.picintel-profroger.blogspot.com/%23calc

http://www.earthtools.org/

http://www.periodicos.ufsc.br/index.php/fisica/article/viewFile/9106/8450

http://omnis.if.ufrj.br/~carlos/palestras/fisicaGravador/fisicaGravadorLimc.pdf



http://picintelproforivaldo.blogspot.com/2009_07_01_archive.html

Free Fall of a Ruler_Lesson Plan

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