Lab 8: Physics Physics 193
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Lab 8: Forensic Physics
This is the second part of the project that you began work on in recitation this week. Refer to the work you did in recitation as you design and perform your experiment.
LEARNING GOALS OF THIS PROJECT
1. Use your physics knowledge to analyze a complex process by breaking it into a sequence of smaller consecutive processes.
2. Learn to revise a mathematical method so fewer assumptions are made.
I. APPLICATION EXPERIMENT: MODELS AND REALITY
During this week’s recitation you were presented with a problem in which the New York City Police Dept. was contracting you to use the forensic evidence from an accident scene to determine the coefficient of kinetic friction between the tires of a car and the road surface. Your group members each developed a mathematical model of a toy version of this (shown in the video:
http://www.islephysics.net/pt3/experiment.php?topicid=4&exptid=141.) The goal of this application experiment is to determine the coefficient of kinetic friction between the tissue box and the tabletop.
Available equipment: Ring stand + accessories, tissue box, soft pendulum, 2 meter sticks used as guide rails for the box, tape, force probe, motion sensor, digital scale, stopwatch app (on your phone, the web, the lab computers, etc.) Constructing the mathematical model
First, come to a consensus with your group members about the mathematical model you will use to represent the situation. Write up the results of your consensus. Include the following:
a) Start by making a rough plan for how you will solve the problem. In particular, divide the problem into two or more smaller problems that each involves one central physics idea. Write a brief outline of your mathematical procedure. Include a labeled sketch of your setup.
b) Identify which physics ideas you will use for each part. Describe how you will model the objects, interactions and processes you will use in your mathematical model.
c) Construct force diagrams, energy bar charts, and momentum bar charts as appropriate. d) Identify the physical quantities you will need to measure in order to solve the problem.
e) Put together the complete mathematical method you will use to solve the problem. Do not plug any numbers; express the method as an equation for the coefficient of kinetic friction written in terms of the physical quantities you will measure experimentally.
f) What assumptions did you make in your mathematical model? Specifically the effect making each of them will have on the result produced by your mathematical model (will it make the calculated value smaller, larger, or randomly different than the real-world value). Explain your reasoning.
Designing and performing the experiment
Now, design and perform an experiment that uses your mathematical model to determine the coefficient of kinetic friction between the box and the tabletop. Include the following in your writeup:
g) A detailed description of the experimental procedure. Include a labeled sketch of your setup.
Rubrics you’re being scored on in this experiment:
D5, D7, D8, D9, G2
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h) Identify the physical quantities you will measure. Describe how you will measure each quantity. What steps will you take to minimize the uncertainty in your measurements?
i) Perform the experiment and record the data. Estimate the uncertainty in each measurement.
j) Use the mathematical procedure you devised to determine the coefficient of kinetic friction. Estimate the uncertainty in your result.
k) Design and use an independent method to determine the coefficient of kinetic friction. Hint: It can be a very simple experiment, but make sure you deal with assumptions and uncertainties properly and completely.
l) Decide if the results of the 2 experiments are consistent or not. What is your judgment about the model you used to represent the situation shown in the video?
Improving the mathematical model
m) Think about assumptions you made in your mathematical procedure. Which of your assumptions is least likely to be valid? Describe how you will revise part of your mathematical procedure to deal with this. What additional
measurements will you need to make? Symposium
Discuss your experimental design and mathematical method with other groups. Ask other groups to explain their methods when they differ from your group’s. Be sure to discuss with them the assumptions you made, how they affected your value of the kinetic friction coefficient, and whether or not you think they are reasonable. Finally, discuss your ideas about how you could improve your method, and ask other groups what improvements they are considering for theirs. Then, return to your table and incorporate all of those improvements.
n) Construct force diagrams, and energy and/or momentum bar charts for your revised mathematical method. o) Come up with a new equation for the coefficient of kinetic friction that incorporates your revisions. Again, do not
plug in numbers.
p) Make any additional measurements you need, and then use your new equation to determine a revised value of the coefficient of kinetic friction.
q) Now are the results of the 2 independent methods consistent? Now what is your judgment about the mathematical model?
r) Are any of the other assumptions in your revised mathematical model questionable? How could you revise your mathematical procedure further to deal with these?
II. WHY DID WE DO THIS LAB?
1. Explain how knowing the coefficient of friction between the tire and the road helps the police department to determine the speed of a vehicle before the collision using the length of skid marks.
2. What is the reason for improving the mathematical model of a process?
III. HOMEWORK
In the next lab you will need to collect data and find quantitative patterns in them. To do this you will need to represent the data graphically. This is easy when your data can be represented as points. But how do you plot data that includes uncertainty? The following problems will help you learn how to do this.
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smallest increment of 1°. He measured the temperature every 15 sec and recorded values of 35°, 38°, 42°, 44°, 48°, and 50°. Represent this data with a graph that includes:
a. The temperature measurements as a function of the time measurements.
b. The absolute uncertainty of the temperature measurements in the form of error bars. c. The absolute uncertainty of the time measurements on the form of error bars.
Hint: Google “error bars” for some background. You may use Microsoft Excel to create your graph if you wish. Make sure the graph is properly labeled.
2. Then, Jim decided to improve his experiment and use a digital thermometer that could measure temperature with the accuracy of 0.1°. Jim continued to measure the temperature every 15 sec and recorded values of 55.5°, 58.8°, 61.6°, 64.9°, 67.7°, and 71.2°. How will the graph of the new data be different from the previous one? Represent this data with a graph in the same way you did for problem 1.
RUBRICS
RUBRIC D: Ability to design and conduct an application experiment
Scientific Ability Missing Inadequate Needs some
improvement Adequate
D5
Is able to evaluate the results by means of an independent method
No attempt is made to evaluate the consistency of the result using an independent method.
A second independent method is used to evaluate the results.
However there is little or no discussion about the differences in the results due to the two methods.
A second
independent method is used to evaluate the results. The results of the two methods are compared using experimental uncertainties. But there is little or no discussion of the possible reasons for the differences when the results are different.
A second independent method is used to evaluate the results and the evaluation is done with the experimental uncertainties. The discrepancy between the results of the two methods, and possible reasons are discussed.
D7
Is able to choose a productive
mathematical procedure for solving the experimental problem
Mathematical procedure is either missing, or the equations written down are
irrelevant to the design.
A mathematical procedure is described, but is incorrect or incomplete, due to which the final answer cannot be calculated.
Correct and complete mathematical procedure is described but an error is made in the calculations.
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D8
Is able to identify the assumptions made in using the mathematical procedure
No attempt is made to identify any assumptions.
An attempt is made to identify
assumptions, but the assumptions are irrelevant or
incorrect for the situation.
Relevant
assumptions are identified but are not significant for solving the problem.
All relevant assumptions are correctly identified.
D9
Is able to determine specifically the way in which assumptions might affect the results
No attempt is made to determine the effects of assumptions.
The effects of assumptions are mentioned but are described vaguely.
The effects of assumptions are determined, but no attempt is made to validate them.
The effects of the assumptions are determined and the assumptions are validated.
RUBRIC G: Ability to collect and analyze experimental data
Scientific Ability Missing Inadequate Needs some improvement Adequate
G2
Is able to evaluate specifically how identified experimental uncertainties may affect the result
No attempt is made to evaluate experimental uncertainties.
An attempt is made to evaluate experimental uncertainties, but most are missing, described vaguely, or incorrect. Or only absolute
uncertainties are mentioned. Or the final result does not take the uncertainty into the account.
The final result does take the identified uncertainties into account but is not correctly evaluated.
The
