Physics in the Mathematics Curriculum Summary
Wednesday, July 3, 2002
Discussed inclusion of variety in teaching (give enough background as topics are introduced : history, greek alphabet, etc.)
We will come back to bean and tube tone activity during next week. Steve to bring sewer pipe and vacuum hose.
PVC and White Board Marker Cannon
We demonstrated the PVC cannon with 5 people blowing into pipe (projectile is white board marker). What is the mathematics involved?
Bouncing Ball and Time to Complete Three Bounces
- Calculation of muzzle velocity using different length tubes. Relate muzzle velocity to length of tube. Use photo gate to measure muzzle velocity. We could also do length of pipe versus distance covered by projectile. We expect that relationship between tube length and distance traveled (measure length by doing activity on football field) to show a maximum because there is a length at which the student blowing into the tube does not have enough air to fill the length of the tube.
- Give enough background on physics involved (air resistance, volume of tube, etc.)
- Calculate the volume of each tube. The length which produces a maximum distance corresponds to lung capacity of the blower.
- Drop a super ball from different heights (100cm, 90 cm, 80 cm, 70 cm, ..., 10cm). Use a stop watch to time from when the ball first hits the table to the the third bounce. Do three at each height and find average.
- Enter heights in L1 and times in L2.
- Plot this data.
- What kind of relationship exists between height and time for three bounces?
- Try to find a functional model for this relationship (regression, etc.)
Our data collection indicates a power function model, square root as a best fit.
Thus, the time should be a function of square root of s, where s is the distance the ball travels.
Since the ball bounces back at a constant proportion of its original height.
Therefore, although the actual distance traveled is not the height h which we plotted in our graph, this distance s is proportionally related to h. The constant of proportionality p is the fraction of original height the ball bounces back.
- Suppose you mistimed each of the times for three bounces by 0.01 sec, for which height is this error the greatest? (percantage error)
- Why doesn't the ball bounce back to the original height?
Note: Start timing when ball hits the table, and end when the ball hits the table on the third bounce.
Back to Journal Index
PCMI@MathForum Home || IAS/PCMI Home
© 2001 - 2015 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King
With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.