The Analysis
of a 2-Dimensional Trajectory |
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Introduction
The following lab is intended to
give you practical experience with 2-D motion and how we can model this motion
mathematically. To help, you will use a LoggerPro/VideoLab clip that shows the motion
of a small rubber ball. You will analyze this motion using LoggerPro/VideoLab and try
to reproduce it using the "trajectory diagram" approach developed
in N4.6 of your text. Finally, you will use EXCEL to model the motion.
Reminder: Distance Time Formulae
Uniform Motion |
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Uniform Accelerated Motion |
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How to get Started
There are three main steps:
- run LoggerPro/VideoLab and from this get
all information you will need to use both the trajectory diagram technique
and the EXCEL analysis. This should include all relevant velocities, time
of flight, height etc (Be sure to set the scale correctly for the video. If you need a refresher on how to do this refer to the previous lab where you measured the motion of the CM in a collision. In this video the frame size is 0.80 m wide by 0.55 m tall).
- prepare a carefully constructed
trajectory diagram. It would be a good idea to put some of the information
used to prepare this diagram in a table much as we did in a previous lecture
period.
- model the motion mathematically
using EXCEL. How well can you make your model fit the actual data that you
analyzed in part 1?
Part 1: LoggerPro/VideoLab (Week One)
This lab is intended to be "group
driven" - you should discuss how best to do the following:
- prepare x-t and y-t graphs and
fit the appropriate trendlines to these graphs - you can do this in either LoggerPro or Excel
- determine the acceleration of
gravity implied by this data - Be sure to explain how you did this.
- find the velocity (magnitude and
direction) of the ball at launch
- explain the significance of the
terms in your trendline equations
Have this information completed and ready for next week's lab
Part 2: Using EXCEL or VPYthon to Model the
Motion (Week Two)
How can you simulate the
motion of the ball? It is surprisingly simple!
The basic equations are:
These are general equations that
we will use next week when we encounter a variable acceleration (the effects
of air resistance). For today's lab you can safely let a = g!
Your lab instructor will decide on whether you will do this either VPYTHON or EXCEL. Even though these are very different programs the underlying physics is the same!
- Prepare a simple flow chart that
shows how these equations work together and also explain in your own words
what each equation means.
- Next, using the values that you
found in Part 1, set up a spreadsheet that uses these equations. Be sure to
understand how to go from vector notation to component form in the spreadsheet!
- Set up a table in EXCEL that allows
you to determine x and y coordinates (as well as vx and vy ) and prepare graphs
of x-t, y-t and any others that you think would help demonstrate that your
model works!
- You may use the file 2DTrajectory.xlsx to assist you but you will need to spend some time understanding how this file reproduces the equations given above.
What to Hand In
I would like the following from
each lab group:
- neatly and appropriately labeled
x-t and y-t tables and graphs with accompanying trendlines and equations clearly
shown for Parts 1 and 3
- calculation showing how you found
the initial velocity of the ball
- the value that your group found
for "g" , a brief discussion of how you determined this and an estimate
for the percentage error in this result.
- Discussion of how well your model
worked and what factors influence its accuracy.
Date Due: One week from today |