Conservation Lab 5

Conservation
Figure 1: Overview of the setup for the Conservation Lab, after you mass your carts, make sure you keep track
of which one is which.
Lab Objectives
• Data collection
• Data Analysis
• Propagation of Error
• Conclusions
Lab Equipment
• 2 Vernier Motion Detector
• 2 Vernier Dynamics Cart
• Flat Cart Track
• Mass Balance
1
Overview
Today we will look at the energy and momentum in two different collisions. The main goal will be to calculate
if Kinetic Energy (K ) and Momentum (P~ ) are conserved during the collisions. If momentum is conserved, that
will mean that the total momentum of the system before the collision (P~
1 ) will be equal to the total momentum if
the system after the collision (P~
2 ), within your uncertainties. Where ~pa is the momentum for cart a and ~pb is the
momentum for cart b or
P~
1 = ~pa1 + ~pb1 = ma1
~va1 + mb1
~vb1
(1)
and
P~
2 = ~pa2 + ~pb2 = ma2
~va2 + mb2
~vb2
(2)
We can use a similar format for Kinetic Energy (K ),
K1 = ka1 + kb1 =
1
2
ma1
v
2
a1 +
1
2
mb1
v
2
b1
(3)
and
K1 = ka2 + kb2 =
1
2
ma2
v
2
a2 +
1
2
mb2
v
2
b2
(4)
Procedure
Data Collection
You will be collecting data from two different collisions with the carts. One collision will have the plunger on the
cart extended so that the carts collide and they bounce away from each other. The other collision will have the
velcro facing each other so that when the carts collide, the carts will stay together. It is recommended that one
cart starts stationary and the other collides with it, however, the experiment can be done with both carts initially
in motion.
• Adjust the motion sensors so that they pick up the cart motion well for the whole range of motion on the
track.
• Take your data. Your data should be of sufficient quality to perform the analysis on in the next section, if it
is not, you should repeat that trial.
Analysis
Velocity
Use the statistics function to find the velocity of each cart before and after the collision, while the velocity may
not be exactly constant, avoid areas of large change. Make sure your group agrees on how to get the uncertainty
in the mass of your cart.
Propagation of Uncertainties
Propagate the uncertainties for your momentums and energies, you should have uncertainties for your velocities
and masses. There is a quick review of the propagation of uncertainty equations at the bottom of this lab.
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Writing
Based on the data that you took today, write and answer the questions in the following sections. Remember
that even though you will have the same data as your partner, the writing in these sections should be done
individually.
Experimental Method
• In paragraph form, communicate the steps that you took when collecting and analyzing your data. Pretend you are writing this so a fellow student that missed this lab could take and analyze the data using
only this section. For example, you do not need to tell them to press start in Logger Pro or open the
program, but you would want to tell them what sensors you used to collect data and if there are any
special settings that you used.
Results
• Report the results of your experiment in complete sentences using your calculated numbers, you should
also include you numbers in table. You should place your graphs with captions in this section as well.
At minimum, your table should have the following columns: mass for each cart, velocities before and
after collision, momentum before and after, kinetic energy before and after. Don’t forget to include units,
significant figures and uncertainties.
• Compare the initial and final K and P for both collisions, including your propagated error in the comparison.
Conclusion
• What conclusions are you able to make based on the data you collected for this lab? Back up your
conclusions with evidence, use equations, measurements, references to figures, etc when appropriate. If
you are not sure where to start, you will want to use the words inelastic and/or elastic and conserved
and/or not conserved in your conclusion.
Graph and Data Checklist You should have 2 graphs with complete captions, answered all of the questions
highlighted by the gray boxes and written an experimental methods, results, and conclusions section.
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Review
The Figures and Captions
There are a few very important aspects to creating a proper figure and caption. If you follow these rules, not only
will you get points on your physics lab grades, you will impress your instructors and peers in the future.
The Caption
• The caption should start with a label so you can reference the figure from other places in your paper/report.
For this course you should use “Figure 1”, “Figure 2”, etc.
• The caption should allow the figure to be standalone, that is to say, by reading the caption and looking at
the figure, it should be clear what the figure is about and why it was included without reading the whole
paper.
• The caption should contain complete sentences and be as brief as possible while still conveying your information clearly (this is not always easy).
The Figure
• Make sure that the resolution is high enough to not be pixelated at its final size.
• Check that any text is readable at the final size (Using a smaller graph in Logger Pro will cause the text to
be larger in relation to the graph when inserted into another program).
• For graphs, ensure that the axes are labeled (including units) and that there is a legend if you have multiple
data sets on the same graphs.
Propagation of Uncertainties
Addition and Subtraction
In the case of addition and subtraction, the equation for combining uncertainties is
δx = δx1 + δx2 + δx3 , (5)
where δx is the total uncertainty of your calculation and δx1, δx2, and δx3 are the uncertainties of your individual measurements.
Multiplication and Division
This method is valid for both multiplication and division of measurements with uncertainties.
δA
|A|
=
δx
|x|
+
δy
|y|
, (6)
where A is the area, x is the length, y is the width, δx and δy are the uncertainties associated with these
measurements, and δA is the propagated uncertainty of the product or quotient.
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Figure 2: Navigate to jupyterhub.wpi.edu and sign in with your WPI email address and password, choose
an instance to spawn (either is fine) and create a new Python 3 file as shown here
Python
Python is a high level programming language that is regularly used by the scientific community for general and
research computation. We will be introducing it and using it in a very limited way in this lab course although we
encourage you to explore it more on your own. We will primarily make use of the Python to calculate statistical
values and propagate uncertainties. We will be using an interface for Python called Jupyter and WPI has set up
a JupyterHub server that you can access from any browser (Figure 2). The files you create on the server will stay
for at least the term, probably much longer.
Jupyter uses a cell based system and evaluated variables carry over to the next cell. There are a few different
types of cells, Figure 4 shows 2 kinds, the code cell, which we will be using most of the time, and the markdown
cell, which you can use to add nicely formatted notes to you file.
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Figure 3: Above is the code that you could use use to propagate uncertainty for values that are added or subtracted. Always remember to comment every line of your code in this class.
Figure 4: Above is the code that you could use use to calculate the mean and standard deviation. Always remember to comment every line of your code in this class.
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