Experiment: Determining the Acceleration Due to Gravity


Experiment Determining

The acceleration due to gravity is the rate at which velocity increases as an object falls, neglecting buoyancy or frictional forces such as air resistance. This acceleration is the result of the force of gravitation between the falling object and Earth. The value of this acceleration is about 9.8 m/s/s, or equivalently, about 32 ft/s/s. Thus, for each second that an object falls, its speed increases by 9.8 m/s or 32 ft/s.

The acceleration due to gravity depends upon altitude, latitude, and local density characteristics of the earth crust. It is a little less at the equator than at the poles because the earth is not a perfect sphere, but rather somewhat bulged at the equator. It is a little less at the top of Pikes Peak than at sea level. But the variation across the earth surface typically ranges from a low of about 9.78 m/s/s to a high of about 9.83 m/s/s at the North and South Poles. The value of this acceleration is independent of the mass of the falling object–a bowling ball will fall at the same rate as a marble.

In this experiment you will use a littleBits circuit, including the Arduino at Heart module and a light sensor, to determine the acceleration due to gravity. You will drop a picket fence between the light sensor and an LED. A sketch (program) running on the Arduino will capture information of times when the pickets block the light. From this data and knowing the distance between pickets, you will use Excel to determine the acceleration due to gravity.

Duration: 1 45-minute class

GRADE LEVEL
High School (ages 14-17)
College/University (age 18+)

DIFFICULTY
Intermediate

SUBJECT
Math
Science

MODULES & ACCESSORIES USED (10)
light sensor (1)
power (2)
bright led (1)
mounting boards (2)
Arduino (1)
number (1)
battery + cable (2)

OTHER MATERIALS USED (5)
clear Plexiglass about 2.5″ x 18″ long 1
Black Electrical Tape 1
velcro 1
small wood block 1
ruler 1

LESSON GUIDE

STEP 1 : Prepare the Picket Fence

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Use a piece of clear Plexiglass about 2.5″ x 18″ long. With black electrician’s tape, alternate clear and black regions from one end of the Plexiglass to the other end. Each clear region should be 2.5 cm wide, and each black region should be 2.5 cm wide. The picture below shows what the completed picket fence should look like. You will probably need to overlap two strips of electrician’s tape for each black region of the picket fence. Note that the distance from the start of one black picket to the start of the next black picket is 5 cm.

You will be dropping this picket fence between a light sensor and a bright LED, during which time an Arduino sketch will be taking continuous time and brightness readings as the picket fence falls. When this data is imported into an Excel program, you will be able to analyze the data to determine the acceleration due to gravity.

STEP 2 : Prepare the Circuit

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The circuit consists of the following modules in the order given:

power>bright led>wire>light sensor>wire>number>Arduino

See the photo below.

The power and bright led are on one mounting board. The sensor is on another mounting board. Velcro is used to stick the two mounting boards to a small wood block to keep the boards stable and upright. The light sensor must be set to light (not dark) and set to maximum sensitivity (fully clockwise). The number module should then read quite close to 99 with the bright led on and the other room lights darkened or off. The picket fence will be dropped in the opening shown, with a towel or throw rug on the floor to protect it when it hits the floor. When dropped, the picket fence should have the pickets running horizontally, and the bottom of the picket fence should be about an inch above the sensor and bright led.

You should cover the red led on the power module with black electrician’s tape so that it will not interfere with brightness readings during the experiment. The number module must be connected to the Arduino a0 input. You will also need to power the Arduino–you can use either the d0 or the a1 input to provide this power. Also, the Arduino must be connected to your computer via the micro-USB cable provided with the Arduino.

STEP 3 : Ready the Arduino Module for Data Collection

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Note that the Arduino module’s micro-USB cable must be connected to your computer, and the computer must have the Arduino IDE software installed. THE ARDUINO SWITHCES SHOULD BOTH BE SET TO ANALOG.

Power up the Arduino module. Start the Arduino IDE software. Select Tools>Board>Arduino Leonardo. Then select Tools>Serial Port and select the serial port that the Arduino will use for communication. This will depend upon whether you are using a Windows, Mac, or Linux machine. Open the sketch file called PicketFence.ino. Upload the sketch to the Arduino module. You will see the yellow rx/tx LEDs blink on the Arduino module while the sketch is uploaded. After the blinking stops, you will then have 15 seconds to start the serial monitor by selecting Tools>Serial Monitor from the IDE. After the 15 seconds have elapsed you should see the line “Time Brightness” at the top of the serial monitor’s data area. Everything is now ready for you to drop the picket fence. The bottom of the picket fence should be about a centimeter or so above the gap between the light sensor and bright led

The Arduino Sketch (program) on the Arduino module will automatically collect time and brightness readings for you while the picket fence is falling. The Serial Monitor will look similar to that in the image below.

STEP 4 : Transfer the Data to the Excel File

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When you are done collecting data, then you can transfer the data from the serial monitor to Excel. Here is how to do that. First, uncheck Autoscroll in the bottom left corner of the serial monitor. Use your mouse to drag and select all of the data beginning with the data line containing the column headers “Time Brightness”. Open the attached Excel .xlsx file called Picket_Fence_Template.xlsx, right-click on cell A1 in the Raw Data worksheet and select Paste. (Excel worksheets are named and selected in the bottom left corner of the Excel window.)

You should see the data in the Excel workbook on the far left. In addition you will see a chart displaying a graph of brightness versus time. A portion of a similar chart is shown in the figure below. Your chart should look similar to the chart displayed below. Note that the time axis is in microseconds seconds. The red data points on the chart show relative brightness decreasing as the corresponding black pickets block the light from the bright led. You are interested in where the brightness is at a minimum (bottom red data point) for each of the black pickets.

Starting with the leftmost minimum, cursor over the bottom data point. You will see a tooltip pop up that displays ordered pairs (time, brightness). Note the time and type this time into cell A2 on the TimeAndDistanceData worksheet. Continue this with the remaining minimums, typing the times in the cells to the left of the distances (which are already entered for you in column B). Notice that the distance go up by .05 meters, as the black pickets are 5 cm apart

STEP 5 : Determine the Value for Acceleration Due to Gravity

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After you have keyed in all of the times associated with the minimum brightness for each of the pickets, study the chart of Distance vs. Time on the TimeAndDistanceData worksheet.

Excel has automatically drawn a curve of best fit for your data. Excel was instructed to fit your data to a parabola (a second-order polynomial), as physics tells us that the position of a falling object is given by the equation shown in the figure below. The equation-of-best-fit is seen in the upper-left corner of the chart. In this equation y is position and x is time (since the horizontal x-axis of the chart represents time).

The equation tells us that the coefficient of t-squared is half the acceleration. Voila! The acceleration due to gravity is then twice the value of the coefficient of t-squared.

How does your value compare to the accepted value of 9.8 m/s/s? What do you think may be some sources of error in this experiment?