The Research Experience for Teachers Program /

Activity Title: “Studying circular motion with image processing”

Summary:

In this activity students will use image processing tools and spreadsheet software to study the motion of an object moving in a circle. It will also review vector concepts.

Introduction/Motivation:

Image processing is key in studying the characteristics of moving objects. Computer scientists are called into study professional athletes (e.g. Sport Science on ESPN) and learn ways to maximize performance. Car manufacturers and insurance companies also use image processing to study the safety issues during automobile collisions to improve upon designs.

Background

This activity requires prior knowledge of forces, vectors, and speed. It is also assumed that the student has some prior experience using ImageJ, spreadsheet software, and Movie Maker.

Procedure

Materials

glass tube with protective cover, 20 washers (or some other form of hanging mass), rubber stopper, paper clips, ~1.5 m string, meter stick, balance

Lab Activity:

*Note: Videos can be pre-recorded by the instructor for time purposes.

  • Thread the string through the glass tube and attach the rubber stopper to one end.
  • Thread one hanging mass (be sure to record the mass) on the end of the string, leaving several centimeters to attach the paper clip.
  • Pull enough string through the tube to allow a radius of about one meter, and then attach a paperclip to the string a few centimeters below the tube. This paperclip should NEVER touch the tube during the lab.
  • Run a few trial runs to be sure you can swing the stopper by grasping the glass tube and slowly move the top of the tube in small circles above your head. Adjust speed until the paperclip under the tube remains at a fixed distance below the tube. Once you get a feel for this move to the next step. See picture below for reference.
  • Place the video camera in a position above the incline so that the entire motion of the stopper can be seen.
  • Begin recording and begin rotating the rubber stopper in a circular motion as described above for at least 30 revolutions. When completed, slowly decrease the speed of the stopper by placing your finger on the string at the point where it comes out of the top of the tube. DO NOT LET GO OF THIS!
  • When the stopper has stopped swinging, measure the radius of your circle by measuring from where you held the string to stop it (i.e. top of the tube) to the rubber stopper. Record this data.
  • Stop recording.
  • Repeat this process for at least 5 additional amounts of washers/mass at the end of the string, being sure to keep track of the amount of mass being used.
  • Connect the camera to the computer and save the video to the computer. Rename the file so that they can easily be found later.
  • Open your video in Windows Movie maker or other video editing software.
  • For each trial, use the video software to count the revolutions and amount of total time for the revolutions.
  • For each trial, take a snapshot from the video when the stopper is in a location that will allow the angle of the string to be easily measured.
  • Save the image as a .PNG file and name it in a way that lets you know which trial it is from.
  • Open your first image in ImageJ.
  • Using the angle function on ImageJ to determine the angle of the string with respect to the horizontal direction and choose “Measure” under the “Analyze” menu.
  • Repeat the process for all of your snapshots and then save your data table as a .csv file (name the file something memorable and add .csv at the end)
  • Open the .csv file in the spreadsheet software.
  • Add the time, radius, and mass data for each trial in columns beside the angle data.
  • Add columns for circumference, speed, speed squared, and weight. Use the spreadsheet software to calculate these values for each trial.
  • Add another column, and using the angle measurements, the weight, and knowledge of vectors, calculate the centripetal force for each trial. Use picture on previous page for a reference.
  • Plot a scatterplot, using the spreadsheet software, of speed vs. centripetal force. Add a trendline of polynomial order 2.
  • Plot a scatterplot, using the spreadsheet software, of speed squared vs. centripetal force. Add a linear trendline.
  • Save the data table and graphs and submit the files to the instructor as instructed. Answer the questions in the analysis section.

Analysis

1.) How do we know to use the weight of the washers to determine our centripetal force?

2.) Do EACH of the graphs verify the formula for centripetal force? Explain your reasoning.

3.) What factors may have played a role in any deviation from the predicted relationship between centripetal force and speed?

4.) How could you find the centripetal acceleration for each trial?

5.) How would change this lab in order to test the effects of the mass of the object in motion on the speed, rather than the centripetal force? How about the effects of the radius on the speed of the object in motion?