Free Fall of a ruler

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

FREE FALL OF A RULER ANALYSIS USING A PHOTOTRANSISTOR

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

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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).

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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

resistor

phototransistor

battery 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:

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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.

PontifĂ­cia Universidade CatĂłlica de SĂŁo Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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.

PontifĂ­cia Universidade CatĂłlica de SĂŁo Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using 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:

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Record button

Time scale

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.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

Signal obtained

time

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

Fall of da the régua ruler Queda 35,00 30,00

Posição (cm)

25,00 20,00 15,00 10,00 5,00 0,00 1,0800

1,1000

1,1200

1,1400

1,1600

1,1800

Tempo (s)

1,2000

1,2200

1,2400

1,2600

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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 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.

Pontifícia Universidade Católica de São Paulo Junior Scientific initiation at PUC/SP and the development of experimental activities in Physics using the Classmate PC

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-paraoficina-de-novas.html • “Physics Experiments with a PC tape recorder ", Carlos Eduardo Aguiar - UFRJ http://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 Cities http://www.apolo11.com/latlon.php • Latitude, longitude, altitude and other geographic data from all around the planet http://www.earthtools.org/ • Script to calculare the local gravity from the latitude and altitude http://www.picintel-profroger.blogspot.com/#calc