Introduction: More Open Source Science - Determine the Acceleration Due to Gravity
I will go through a process that will allow you to determine the acceleration due to gravity. I use this activity with my high school physics students. In the past we've done a similar activity using a commercially available photo gate and device for interfacing the photo gate with a computer. In this instructable I'll show how to do it with a free program and cheap DIY photo gate.
Step 1: Stuff You Need
1. Computer with a microphone input
2. small flashlight
3. Strip of scrap Plexiglas (I get mine free from the local hardware store)
4. Electrical tape
5. An audio recording program. I recommend Audacity. It's free and open source. http://audacity.sourceforge.net/
6. Home made photo gate - (see one of my previous Instructables)
Step 2: Make the Picket Fence
Peel off the protective plastic and start putting on the electrical tape. You're shooting for a regular spacing. Typical picket fences have a 5 cm spacing, so that's what I typically use. You could get higher resolution data by decreasing your spacing. The more precise you are here the better your final data will be.
Note: When measuring be sure to measure from the start of one band to the start of the next!!! Do not measure the space between the bands.
How long you make your fence depends on you. The one I bought from Vernier is about 30 cm long (1 ft). I typically make them longer. The box I store them in will accommodates fences that are 60 cm easily.
When you've reached the desired length just score the plexi with a knife or razor. The plexiglas will break easily at this point. I just use the edge of a table and snap off the excess.
Step 3: Collect Your Data
1. Load up Audacity and plug in the DIY solar probe.
2. Set up the Solar cell and point the flashlight at it.
3. Hit record in Audacity.
4. Drop the Picket Fence (length wise) in between the solarcell and the light
5. Stop recording
6. Click and drag over the series of peaks representing the drop and then click "Zoom to Fit"
Step 4: Record Your Data
Each peak represents one band. Simply record the time each band happened. The easiest way to get precise numbers is to click on each peak. Audacity tells you where your cursor is in the bottom of your window.
Step 5: Analyze Your Data
Open your Spread Sheet of choice. It has to be capable of graphing and analyzing the data to determine slope, so you can't use Google Docs.
1. Put the following labels at the top of each column. A - Time. B - Time Between Bands. C - Instantaneous Velocity
2. Put your time data in Column A
3. In Column B Cell 3 type the following formula: =A3-A2 (note: you must leave B2 empty)
4. Copy your formula (Copy from the Edit Menu) and paste it into the remaining cells in Column B
5. In Column C Cell 3 type the following formula: =0.05/B3 (0.05 is our band spacing in meters. We're just doing distance divided by time here)
6. Copy your formula and paste in the remaining cells in Column C
7. Graph Time vs. Instantaneous Velocity (Column A vs. Column C). Chose X-Y Scatter or X-Y Graph, NOT Line Graph.
8. Find the Slope of your line (add trend line).
The slope of a velocity time graph is acceleration. Here we see a value of 10.323 m/s/s. The true value is 9.8 m/s/s. That's just a hair over a 5% error. I can live with that.
I've always assumed that most of the error in this experiment comes from a sloppy picket fence or sloppy point selection in Audacity. One of my colleagues points out another potential source of error is a poor drop (he thinks this is the most significant source of error). If the picket fence is not precisely true when you drop it then the band spacing will be less then 5 cm when it passes the photo gate.
Step 6: Why Go to All This Trouble?
Now, I have a full class set of Vernier LabPros and I also have photo gates, so why bother with making my own? Vernier makes it all too easy. Students just drop the picket fence through the photogate and the velocity time graph appears instantly on their screen. The students click one button and they have the slope. They spend all of about 30 seconds collecting and analyzing their data. They write the answer in their lab notebooks and move on to the next activity. If that's all I wanted I could just give them the answer or show a quick demo.
With the DIY solution the students get to calculate everything. My usual approach is to have the students tell me how to get the velocity data. Typically they proceed to do the data analysis on their graphing calculators. Most will calculate each velocity by hand (a few will let their calculators do the work for them or will remember they have a perfectly good computer sitting in front of them, these ones already "get it" and I'm not too worried about them).
The students get to see the instantaneous velocity increasing for each band. They see the nice straight line on their graphs and already know they'll need to find the slope (we always find the slope of straight lines). They walk away with a much better understanding of what they did and what it means.
Step 7: Extension
1. You can drop the picket fence from a greater distance above the photogate to show acceleration is the same regardless of how fast it's falling.
2. You can attach a mass to the end of the picket fence to show there is no change in acceleration.
3. You could do The Gallileo Lab. Mount the fence on a cart and run it down a ramp. Vary the angle and find the relationship. Then you make them use vectors and free body diagrams to explain it.
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