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Contents 1 Free Fall Lab 2 Objective 3 Materials 4 Directions 5 Analysis 5.1 Method #1 5.2 Method #2 5.3 Method #3 6 Going Further 7 Circuit 8 g versus latitude 9 Inova

Free Fall Lab

Tara Newman and Joseph Sundermier

Objective

To determine the acceleration due to gravity of a freely falling blinking LED by using a digital camera to analyze its path.

Materials

• Completed circuit board with a 9 volt battery
• Digital camera
• Tripod
• Meter stick, 2 red LED’s, 9 volt battery and wires

Directions

Attach a red LED to both ends of a meter stick and connect the wires to a 9 volt battery. Secure the LED’s and the battery to the meter stick with tape. The meter stick will be used to calibrate the distance the blinking LED has fallen. It is important that the meter stick is held in the same plane (same distance from the camera) as the falling circuit board.

Attach the completed circuit board to a 9 volt battery with double sided tape or Velcro. Attach the circuit so that the battery hangs a little lower than the board on the side near the LED. The board should be dropped so that the LED is facing the camera, the side of the circuit board with the LED is towards the bottom, and part of the battery hangs lower than the board. The battery hanging lower will help to prevent the circuit board from turning on the flight down.

Attach a digital camera to a tripod. You should adjust the timer and f-stop of the camera according to the amount of light in the room. We did our experiments in a room with two windows with blinds and two doors which had windows to the hallway and found an exposure of 2 seconds at f 5.6 produced good results. We also found that the optimum distance between the tripod and the dropper was about 4 to 5 meters. Smaller distances produced greater parallax effects with the camera lens, giving poorer results.

Before beginning the experiment, the person who is going to drop the circuit should practice dropping it. The dropper must be careful not to give the circuit any horizontal velocity component or else the path will not be straight, and the board may turn on the way down. The dropper must also be careful not to instill any downward momentum into the circuit. The best technique that we found was to pinch the battery between the thumb and pointer fingers and try to just release the fingers without moving the arm.

With the camera on the tripod, one person should hold the meter stick next to where the circuit is going to be dropped, which should be about 4 to 5 meters from the camera. Take the photo, print it out, and analyze it to get g.

Analysis

From your photo, measure the distance between the two LED’s on the meter stick. This is the conversion factor that you will use when you measure the distances from your photo. Use a digital multi-meter to measure the frequency of the LED, this can easily be converted to the period using the formula T=1/f. If you intend to use method one, you will need to use an oscilloscope to measure the time on and time off of the blinking LED. Below are our measurements for the LED we used:

• Period 33.2 ms
• Time on 8 ms
• Time off 25.2 ms
• Rise time 92 ns

For each photo, there are a few ways in which the data can be analyzed, depending upon the skill of your students.

Method #1

We measure the distance the LED falls during a time-off period to calculate the instantaneous velocity at that point. From two different velocities, we calculate the acceleration.

1. Measure the length between two pulses (the darkness between the bright lines), which is the time off. Divide your measured distance by the conversion factor that you previously determined from the meter stick.
2. Use the time-off time for the LED to calculate the instantaneous velocity of the LED. Repeat for another position. Choose two locations that are far apart.
3. Count the number of cycles between the two locations that you used. Multiply the number of cycles with the period of the LED to determine the total difference in time between those two velocities.
4. Use a = ∆v/∆t to determine the acceleration due to gravity.

Method #2

This method is similar to the previous one, except that we measure the distance over two periods to determine the instantaneous velocity, this works well if you do not have access to an oscilloscope.

1. Measure the distance from one bright line to the line that is two bright lines away (2 periods away). Convert this distance by using the meter stick conversion.
2. Divide this distance by twice the period to find the instantaneous velocity of the middle bright line. Repeat for another position. Choose two locations that are far apart.
3. Count the number of cycles between the two locations that you used. Multiply the number of cycles with the period of the LED to determine the total difference in time between those two velocities.
4. Use a = ∆v/∆t to determine the acceleration due to gravity.

Methods 1 and 2 are not as accurate as method 3, but do not require knowledge or skill of EXCEL. The best results were obtained when the selected points were farther apart. Students could take many measurements and find the average. Students may also find the instantaneous velocities of all the points and make a plot of velocity vs time to find the acceleration from the slope of the line.

Method #3

Students measure the distance to every bright line, plot distance vs time on EXCEL, and use the Solver function to determine the best fit and hence the acceleration.

1. Measure the distances from the first bright line to all other bright lines.
2. Use EXCEL to create a column for distance. Enter the distance measured. Create another column which converts these distances to the converted values.
3. Create a column with the line number and create another column which converts this into time by using the period of the LED.
4. Create a plot of distance versus time.
5. Use the formula ∆x = vit +1/2at2 to do a least square fit to obtain the values for the initial velocity and acceleration.

Going Further

• Another experiment that could be done with the circuit board and camera includes setting up a pendulum to calculate the acceleration due to gravity by means of energy conservation.

• A parachute can also be attached to the circuit board, and the resulting trajectory analyzed and discussed.

Circuit

Circuit for Flashing LED.

List of Materials

• 555 oscillator
• R1 = 10 kOhm
• LED from Superbright LED
• D3 is a common diode
• Battery is a 9V battery, or 6 V
• VR1 is a small trimpot

g versus latitude

The accepted value for the acceleration of gravity as function of latitude is

g = 9.7803185(1 + (5.278895x10 ^{− 3})sin²(L) + (23.462x10 ^{− 6})sin⁴(L)

for a latitude of L = 45^o, g=9.806 m / s²

Inova

INOVA sells a flashlight (Microlight) that pulses at 100 Hz. They sell microlight in different colors. The LED stays on for about a millisecond.

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