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 VideoLab clip that shows the motion
of a small rubber ball. You will analyse this motion using 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.
How to get Started
There are three main steps:
- run 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.
- prepare a carefully constructed
trajectory diagram. It would be a good idea to put some fo the infromation
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 you model fit the actual data that you
analyzed in part 1?
Part 1: VideoLab
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
- 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
Part 2: Trajectory Diagram
Use information gathered in Part
1 to enable you to prepare a trajctory diagram. Follow the steps outlined in
your text. Include a table of relevant information with the diagram. You may
wish to use Newton2.2
to do this part. If so, you can include a print version of Newton's output.
Part 3: Using EXCEL to Model the
Motion
How does Newton 2.2 simulate the
motion of the ball? It is surpisingly 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!
- 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!
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
