Juggling Stacked Graphs Part 2
Part II: Vertical Ball Toss Lab- Comparing Throws
Part 1 can be found here, but is not required to complete before part 2.
Background
Looking at graphs of motion can tell us exactly what is happening in the physical world. Just one graph can be helpful, but evaluating distance, velocity, and acceleration graphs for the same moment in time can tell us so much more.
When it comes to perfecting the ball toss, jugglers spend hours trying to get identical throws. Only when they are perfectly comfortable with throwing one object can they move onto practicing with two, three, or more!
This dataset records a person practicing the first step of juggling - a ball tossed in the air and then caught. Jugglers must practice this simple step over and over to be able to get a feel for how far up they are tossing their objects and the timing of the catch.
You will be looking at data from two tosses, and comparing them. Do they reach the same heights? How do their velocities and accelerations compare? Does this person need some more practice or are they ready to juggle multiple objects?
Dataset
“With this dataset, patterns can be analyzed and jugglers can be compared. The tracking data, source video, graphs, and animations are stored in this Google Drive folder and described in the links above. [The goal of this data is to] develop a model that watches a video of juggling and outputs details like trick name and number of catches.” - Stephen Meschke on his website.
This specific data was taken by using the Vernier video analysis app. View the first two tosses of the pink ball at this link: “trick_tower_id_996.mov” created by Stephen Meschke.
Variables
Time - This numeric variable describes the moment in time that data was taken, every .03 seconds. Zero is when data collection began. Measured in seconds.
Position - This numeric variable describes vertical height (not any horizontal movement). The value of zero represents the ground. Measured in meters.
Velocity - This numeric variable describes the speed and direction the object was moving. Measured in meters per second.
Throw - This categoric variable describes if it is data from the first throw, or the second. This data is defined as beginning once the juggler has let go of the ball, and ends just before he catches the ball again. Observations where the ball was in the juggler’s hand (before or after a throw) were left blank.
Activity
Part 1 - Predict:
Before we look at the data, make predictions as to what you would expect to see if the two tosses were identical:
Part 2: Compare
2. Make a scatter plot so you can see the vertical path the ball took over time:
3. Look at the tosses only by selecting Throw as your z-axis. Paste the graph below:
4. Do these tosses look consistent? Provide evidence for “yes!” or “nope!”.
5. Create a scatterplot of Velocity vs. Time and paste it below. Keep Throw as your z-axis:
6. Add a regression line to this graph. Paste your new graph below, and include the equations of your lines.
7. Do these tosses look consistent? Provide evidence for “yes!” or “nope!”.
8. Remove Throw as your z-axis so you can look at the velocity graph in its entirety. Paste that graph below (you will need this graph for the next section):
Final Findings:
9. Copy/Paste your graph from #2 (position), #7 (velocity). Note: Resize the images so the x axis all lines up
10. What is happening to the velocity between the approximate times of t=10 -> t=11 s? What is physically happening to the ball?
11. Looking at our stacked graphs, fill in the following summary table: NOTE: not all boxes may be filled.
12. We do not have acceleration data from this juggling experiment. Looking at just the velocity graph, what would you expect an idealized acceleration graph to look like? Select the best answer below and JUSTIFY your choice with a sentence or two.
The best match for acceleration is:
13. We have not put any values on the y-axis to describe the actual value for acceleration. What value should that be?
14. Looking at your data from all your graphs, would you conclude this student is ready to move on to the next phase of juggling? Have they created a consistent enough throw pattern?
*Teachers can request an answer key through the form below.