Lab1.docx
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College of DuPage *
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2111
Subject
Mathematics
Date
Feb 20, 2024
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6
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Lab 01
Introduction to Graphing using Tracker and Excel
In this lab we will learn how to make motion diagrams and kinematic plots using the Tracker and Excel
software packages. We will use both of these packages later on in our lab.
The Tracker software take advantage of the fact that a digital motion picture camera takes data at a rate
of 30 frames per second. So by determining the position of an object in each frame, you can determine
the object motion over time.
Activity 1 – Video Analysis
1)
Download the file that is contained in our Blackboard page titled “Tracker Input Files”. Unzip the
two video files contained in it.
2)
Download the Tracker video analysis tool from:
https://physlets.org/tracker/
.
It is available for
Windows, Mac and Linux and is free.
3)
Start the Tracker software. Under the “File” drop-down menu on the left side, open the video
file titled “Cart01.avi” by selecting “Open File”.
4)
If you click the small green arrow at the bottom of the screen (
), it will play the short video
clip. There is a rewind button (
)) just to the left of this play button.
5)
We need to set the scale so the software knows what one meter is. Select
the Scale Tool as shown to the right and select “New” -> “Calibration Stick”.
Place the cursor on one end of the meter stick taped to the front of the table
and click while holding down the <SHIFT> key. Repeat this for the other end
of the meter stick. When a small pop-upbox appears, fill in a “1” to tell the
computer this distance is 1 meter.
6)
Just to the right of the calibration tool is the coordinates tool. Click on this tool
and drag the origin to roughly where the front wheel of the cart is. Notice the
axis with the small vertical bar on it represents the direction for the positive
x-axis.
7)
Advance the video one frame at a time by pressing on the frame-advance button on the
bottom right portion of the screen. Continue to advance the video until the person’s
hand is no longer touching the cart.
8)
Note red frame number in the lower left corner where you stopped in step 7.
Click on the “Clip Setting” icon just to the left of the Scale Tool and type this
number is as the “Starting Frame”.
9)
To the right of the coordinates tool is the position-marking tool titled “Create”. Click on
this tool and when a drop down menu appears, select “Point Mass”.
10) Now pick a specific point on the cart (e.g. the front wheel) and
while holding the
<SHIFT> key down
, put your cursor on that point and click. Tracker will record
the position of the wheel and advance the video one frame. Continue to do this
until the cart has moved all the way across the track. (~80 frames)
11) Now go to “File -> Export” . Select “Data File”. In the pop-up menu, select “Comma”
and the “Delimited” and hit “Save As”. You can pick any file name you want
but the
extension of the file name must be “.csv”
12) You now have a data file with the carts position and time recorded.
Activity 2 – Motion Analysis and Graphing
Note: These instructions are assuming you are using the free version of Excel available to COD
student. If for some reason you decide to use another spreadsheet software (e.g. Googlesheets), the
instructions will be similar.
1)
Select the file you saved in Activity 1. You will see your data set with the time recorded
in column A, the x position recorded in column B and the y position in column C.
2)
We want to determine the average velocity of the cart
over time. Average velocity is
Δ
x/
Δ
t.
In this case, Dt
is the time between frames which is always a 1/30 of
second. We need to use Excel to calculate Dx during
in each frame. In cell D4 type
=(B4-B3)*30
. Here,
(B4-B3) is the change in x position and 30 is 1/
Δ
t.
3)
Select Cell D4 again and a small solid square will appear in
the lower right corner of the cell. Select this square by
clicking on it with your cursor and drag the square
downwards until you have reached the last row where you
have data.
4)
You now have a column that has the average velocity for every
1/30 of a second while your cart was moving. Let’s actually
calculate that average velocity.
Click on the cell just below the
last average velocity value and type =average(D4:D22) where
D22 is the last cell that has a velocity value in it.
5)
Now let’s graph the position and the velocity.
Use your
cursor to select all the time values in column A. Then
holding the control key down (or the command key for a
mac) select all the x-position values in column B. Now
select the “Insert” menu and then the “Charts” sub menu.
Now click on the “Scatter Plot” that has lines connecting
the dots. (See right).
You should now have a plot of
position vs time.
6)
Click anywhere on the graph and you should get a little “+” symbol to the right of the
graph.
Click on it and select “Add axis labels”. Label both your axis with both titles and
units. For example, your horizontal axis should be label “Time (seconds)”. Add a title to
your graphs describing what you have plots. For example, “Position vs time for cart 1”.
All graphs should have the axes labeled and include a title.
7)
Right click on any data point (or hold down the control key
while clicking on a data point for a mac). A pop-up menu will
appear and select “Add Trend Line”.
A menu will appear on
your right-hand side. Select the option “Display Equation on
Chart” near the bottom.
8)
Now repeat steps (5) and (6) except of selecting column B while holding the control key down,
select column D which had the velocity in it. You should now have a plot of velocity vs time.
Note: you do not hold the control key down when selecting Column A, only when selecting
Column D.
9)
Instructor Check:
Write your name in large letters on the spread sheet above the plot you just
created in step 7.
With your log into the lab’s zoom meeting and share your screen so the
instructor can see your plot and name. Wait for the instructor will tell you to continue.
Activity 3 – Changing Velocity
1)
Repeat activities 1 and 2 except now load the video file titled “Cart02.avi”.
You do not need to
find the trend line position graph in this case.
Collect enough data so that the cart to return to
its starting point.
Activity 4 – Discussion
These first four questions near with activity 2 where the cart moved in a straight line.
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1)
In Activity 2, the cart was moving at a constant velocity. For this situation, what does the
position vs time graph look like?
Straight Positive Slope.
2)
Unless you were very precise with your position selecting in Activity 1, your velocity vs time
graph from Activity 2 may look a little ragged. But, in general, what does the velocity vs. time
graph look like for an object moving at a constant velocity?
Shows a trend of a straight line (no slope) that is positive (slight downward slope but most likely
due to human error)
3)
What was the average velocity you found in step 4 of Activity 2 where you found the average of
all the values in column D?
.928 or (9.28E-01)
4)
How does this average velocity found in step 4 of Activity 2 compare with the slope of the
position graph found in step 6 of Activity 2?
Close, should be exact but human error. .9205 for the slope and average velocity was .928.
These next two questions deal with Activity 3 where the cart returned to its starting position.
5)
In activity 3, the cart was moving at a changing velocity. In fact, it reversed directions. For this
situation, what does the position vs time graph look like?
The trend line looks like a parabola. (Open downwards)
6)
Unless you were very precise with your position selecting in Activity 1, your velocity vs time
graph from Activity 3 may look a little ragged. But, in general, what does the velocity vs. time
graph look like for an object moving at a constantly changing velocity?
The trend line for the velocity of cart 2 is a downward slope (negative slope that goes in the negative
the moment the cart went in the opposite direction).
7)
Paste copy of your velocity vs time graph and your position vs time graphs for Activity 2 below.
Be sure to label the graphs so I can tell what you’re plotting.
8)
Paste your position vs time and your velocity vs time graphs here from Activity 3. Be sure to label
the graphs so I can tell what you’re plotting.
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