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The purpose of this lab is to show you some data analysis techniques that IB is going to want to see when you do your IA next year. They even ask test questions about data linearization, so try to wrap your mind around that. Here we have a glider accelerating down an airtrack.
We think its position is given by:
s = ut + 1/2at2 or just 1/2at2 if the initial velocity is zero
You will gather position data from the video and we will do a number of things with it.
On the complicated steps there are videos that show you how to do the step. Watch those videos.
1. Watch this video of an air track glider coasting from rest down a slight incline. The left side of the airtrack is up on a book, and the aluminum glider floats on a thin cushion of air so there is essentially zero friction.
2. Take a blank sheet of paper, and make a qualitative (no numbers) velocity vs time graph (Label the vertical axis velocity, and the horizontal, time) for this glider. Don't worry about numbers on the axes - just try to get the shape. You know it starts at zero, and at the end it is moving in the positive direction, so it ends above zero. Try to guess what connects those two points. Draw a graph and take a picture of it and put it in the Google Doc you are going to turn in.
3. Draw a picture of what you think the shape of the position vs time graph will be for this glider. This is a bit trickier, so let me give you some clues. You know it just moves to the right. It starts at zero, goes away from zero in the positive direction, but this line is a different shape. On a position graph, the slope is the velocity, so how do you draw a line with a changing slope? In this case the slope starts out zero, and increases. Try to draw that. If you can't, no worries, I just want you to try. Draw a graph and take a picture of it, and put it in the Google Doc you are going to turn in.
Steps 2 and 3:
4. Create a Folder in your Physics class folder? titled "Moving Plots lab" Move the Doc from Canvas into that Folder, and make a new Google Sheets in that folder.
5. Now pick one of these videos to analyze. It doesn't matter which one you pick - Low medium and high refer to the height I raised the airtrack to, so high will accelerate faster than low. Click on the link, and save the file to your Gooooooogle Drive.
High1-720p
Med1-720p
Med2-720p
Low1-720p
Low2-720p
6. Go to this document <Here> and go to the link in the document. This will run the Vernier Video Analysis web App. (You must be signed in to your ttsdstudents.org account)
Steps 5 and 6:
7. Use the Video Analysis App to analyze from the first frame after I release the glider to the last frame before it stops. You will want to skip about 5 frames per click. Copy the data into your Goooooogle Sheets.
8. In your Google Sheets, calculate the instantaneous velocity at every interval and put it in another column. Put your data table and calculations into your Google Doc
9. Make a smooth line Position vs Time graph from the data in Google Sheets, add a tangent line, and screenshot it into your Google Doc. Be sure you have included minor gridlines so that you can read every 0.1 of a second on the horizontal axis, and every 0.05 m on the vertical axis.
Screen shots to clipboard:
Chromebook: ctl-shift-screenshot (The key above the 6) This brings up a window, then click "copy to clipboard", and paste it into your doc with ctl-v
Mac: ctl-shift-command 4 - paste with command-v into your doc
PC: shift-windows-s, paste with ctl-v into your doc
Step 9:
10. Look at your position vs time graph. Answer these three questions:
Is it the shape you predicted in step 3?
What is happening to the slope of your graph as time goes on?
The slope is the velocity. What is happening to the velocity as time goes on? Why does this make sense?
11. Read the (x,y) coordinates of where the tangent line enters and exits the plot frame and use these to calculate the slope. Show what points you used, and your calculations of the slope. Figure out the time that your tangent line touches the position graph, and write a sentence comparing the slope of your line to the instantaneous velocity you calculated in step 7.
Steps 10 and 11:
12. Make a nice scatter graph of Velocity vs Time with a best fit line, and screenshot it into your Google Doc. Be sure it has appropriate Gridlines. Calculate the slope using the endpoints. Show your endpoints and your calculation.
13. Look at your Velocity vs Time graph. Answer these two questions:
Is it the shape you predicted in step 2?
Is your line more curved, or is it maybe just straight with some experimental error? (The slope is the acceleration of the glider)
Steps 12 and 13:
14. So now we have actually calculated the slope of the velocity. This slope is the acceleration of the glider. Now let's find the acceleration a different way using graph linearization. (This is a more robust way...)
We think the equation should be
s = 1/2at2
where s is the position, and t is the time. (This is just the suvat equation s = ut + 1/2at2 where u = 0)
This means if we graph s vs. t2, then we should get a straight line with a slope of 1/2a or half the acceleration.
So copy just your position vs. time data to another new tab in your google sheet, add a column just to the right of "Time (s)" and label it "Time Squared (s^2)" and make that column equal to the time column squared. Put a linear trendline on that graph, and label it with the equation. Put this graph into your Google Doc that you are submitting.
Answer these questions
Does your graph look linear? (If it does, then we guessed the exponent, 2, correctly)
What is the acceleration you calculate from the slope of the linearized graph?
How does that compare to what you got from the slope of the velocity graph?
Step 14:
15. And finally, let's just totally cheat, and use a polynomial model in our graph. Go back in your google sheet to your position vs. time graph you originally made. Add a second order polynomial trendline to it, and display the equation. Look for the coefficient of the x^2 term. That should be equal to the 1/2a. Paste the graph with its model into your google doc.
Answer this question:
How does the acceleration from the polynomial model compare to the other two accelerations you got? (Cite what all three were)
Step 15:
16. Review your completed document and make sure it has:
Your Two Predicted Graphs
Data Table (if you tweak the font size you can get it to fit on one page)
Position vs Time Graph
Gridlines
Tangent Line
Answers to the three questions
Endpoints/Slope Calculation
Comparison of slope to velocity in the data table
Velocity vs Time graph
Gridlines
Best Fit Line
Endpoints/Slope Calculation
Answers to the two questions
Linearization Graph
Linear Trendline with equation displayed
Answers to the three questions
Polynomial Model Graph
Linear Trendline with equation displayed
Answer to the question
Then turn it in. Jump up and down suddenly and say loudly "Woo Hoo!"
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