Calculating Air Resistance using the Monte Carlo Method
Summary
Students will use Vernier motion detector and Logger Pro software to first discover if air resistance of an industrial size coffee filter is a vtm or vt2m relationship (vt = terminal velocity). Once this relationship is found it will be used to calculate the air resistance constant with error bars. The error of air resistance constant will be found using the Monte Carlo method.
CollapseLearning Goals
Determine how terminal velocity of a falling object is affected by air resistance and mass (from Physics with Vernier, experiment 13).
Calculate air resistance constant for a falling coffee filter.
Evaluate air resistance constant using Monte Carlo method.
Calculate air resistance constant for a falling coffee filter.
Evaluate air resistance constant using Monte Carlo method.
Context for Use
This activity is for a 9-12 physics classroom. Class size depends on computer hardware (vernier motion detector, and computer with loggerpro and Internet access). This could be accomplished as a class lab if only one computer setup is available.
Description and Teaching Materials
The following schedule is for a 50 minute class.
Day 1: It is suggested that the first day you review free body diagrams, velocity, and acceleration. This can be done using a class-starting question. Then review how to use motion detector and loggerpro. Have students collect data using loggerpro and motion detector to find terminal velocity.
Day 2: Review the relationship between mass of coffee filter and terminal velocity. What did they observe yesterday? Did the heavier coffee filter fall faster than the lighter coffee filter? Then have students determine which relationship between mass and velocity is vtm or vt2m is correct.
Day 3: Review which relationship between mass and velocity is correct. Have students draw a free body diagram of a falling coffee filter at terminal velocity. What is the net force on the coffee filter? What will acceleration of the coffee filter be at terminal velocity? Using the sum of forces equation, have the students calculate the air resistance constant for each mass of the coffee filter. Use the Monte Carlo method to determine the errors of the air resistance. Then curve fit the air resistance data to a straight line to get the most accurate result.
See example Monte Carlo excel sheet
Use website, http://www.hamline.edu/~arundquist/webMMA/utility/curvefit/ for curve fitting the data to a straight line.
The student handout was modified from the Physics with Vernier by Gastineau, J. Apple, K. Bakken, C. Sorensen, R. & Vernier, D. Published by Vernier Software & Technology in Beaverton, OR in 2007. Student handout (Microsoft Word 37kB Aug15 08) Monte Carlo excel spreadsheet (Excel 8kB Aug15 08)
Day 1: It is suggested that the first day you review free body diagrams, velocity, and acceleration. This can be done using a class-starting question. Then review how to use motion detector and loggerpro. Have students collect data using loggerpro and motion detector to find terminal velocity.
Day 2: Review the relationship between mass of coffee filter and terminal velocity. What did they observe yesterday? Did the heavier coffee filter fall faster than the lighter coffee filter? Then have students determine which relationship between mass and velocity is vtm or vt2m is correct.
Day 3: Review which relationship between mass and velocity is correct. Have students draw a free body diagram of a falling coffee filter at terminal velocity. What is the net force on the coffee filter? What will acceleration of the coffee filter be at terminal velocity? Using the sum of forces equation, have the students calculate the air resistance constant for each mass of the coffee filter. Use the Monte Carlo method to determine the errors of the air resistance. Then curve fit the air resistance data to a straight line to get the most accurate result.
See example Monte Carlo excel sheet
Use website, http://www.hamline.edu/~arundquist/webMMA/utility/curvefit/ for curve fitting the data to a straight line.
The student handout was modified from the Physics with Vernier by Gastineau, J. Apple, K. Bakken, C. Sorensen, R. & Vernier, D. Published by Vernier Software & Technology in Beaverton, OR in 2007. Student handout (Microsoft Word 37kB Aug15 08) Monte Carlo excel spreadsheet (Excel 8kB Aug15 08)
Teaching Notes and Tips
Some common areas of confusion is the coffee filter is falling towards the motion detector so its distance will be getting smaller. It will have a negative slope. Have students practice using the setup and Logger Pro before the lab so they know how to use and read the equipment. Also, practice using Excel and the graphing website before hand as a class with a different problem so that students use the resources instead of following a step by step process.
Assessment
Students will complete a full lab report that will include the answer to the lab (What is the Air resistance constant?). It should also include an analysis of their answer. How accurate is their answer and what could they do differently next time.
Standards
Grade 9-12
I.B.2;I.B.3;I.B.4;I.B.6 - Scientific Inquiry
II.D.1;II.D.2 - Motion
II.E.1;II.E.2 - Forces of Nature
I.B.2;I.B.3;I.B.4;I.B.6 - Scientific Inquiry
II.D.1;II.D.2 - Motion
II.E.1;II.E.2 - Forces of Nature