Mechanics Projects - Physics - 210

There are many projects which relate mechanics concepts to real physical systems. Each individual student should choose such a system to investigate in some detail. You should read about the system (see the black notebook in RI-261), design an experiment, do some theoretical calculations before starting, carry out the experiment, apply the appropriate mathematics, carry out an error analysis, and make conclusions. Each student should write his/her own written report (due November 23) and make an oral report to the class (November 30). The actual experiment should take about two hours. The report is like an individual lab report.

The report should include:

• A. Objectives, clearly stated. Background information on the historical motivation.
• B. Equipment, listed, described, and sketched.
• C. Procedure, described so that it could be replicated.
• D. Data, original data sheets and well-organized tables of the same data.
• E. Analysis of the data, statistical, graphical, and error propagation of experimental uncertainties.
• F. Conclusions, discussion of the results, comparison with expected values if appropriate.
• G. Suggestion for future work in this field and for improving the experiment.

Topics for projects:
Many systems involve energy distributed among modes.
How much energy is there in each state?
How quickly does the energy move back and forth?
How quickly does it decay away?
Can you decrease the frictional losses?
Does the system ever become chaotic? Under what conditions?
Does the system display resonnance when driven? Under what conditions?

It is recommended that you consult me about the feasibility of a possible project and about borrowing books and equipment from the physics stockroom. Remember that SAFETY is a prime concern.

Some generally useful equipment we have at hand: Universal Lab Interface with LoggerPro and various probes and sensors (motion detectors, photogates, probes for temperature, force, magnetic field, sound, pressure, etc.), GLXplorer hand-held unit with DataStudio and various probes and sensors (motion detector, thermometer, voltage, etc.), strobe light, function generator, mechanical vibrator, oscilloscope, microphone, Kundt tube, airtrack, air table, magnets, solenoid.

Ideas can be found listed below and also in the American Journal of Physics, and in The Physics Teacher magazine. Photocopies of instructions and of the articles listed below are in the black notebook in RI-261.

References:
Enns, Richard H., and McGuire, George C., Lab Manual for Nonlinear Physics with Maple for Scientists and Engineers, Birkhauser Publishing, Boston, 1997
Kutscher, Eugene, Physics Research Activities, Alpha Publishing, Annapolis, MD, 1988

Here are a few ideas.

• 1. Torsional vibrations of a mass on a spring.
• 2. Standing waves in a closed tube and hanging string (Kutscher, #29)
• 3. Standing waves in flat plates (Chladni plates)
• 4. Standing waves in some particular musical instrument.
• 5. Musical beats, harmonies, discordances (Kutscher, #30)
• 6. Falling objects with air resistance.
• 7. Nonlinear damping of air drag on sails (Enns and McGuire, #2)
• 8. Objects falling or rising in viscous liquids (Shafer, Zare, Physics Today, Oct 1991, p 48)
• 9. Damped oscillations in a viscous liquid (Enns and McGuire, #3)
• 10. Three-body gravitational interactions, Lagrangian points, Trojan asteroids
• 11. Brownian motion (Kutscher, #26)
• 12. Loop-the-loop circular path
• 13. Spin toy pendulum (Enns and McGuire, #1)
• 14. Driven spin toy (Enns and McGuire, #27)
• 15. Anharmonic potential, magnetism vs. gravity (Enns and McGuire, #3)
• 16. Inverted pendulum, forced Duffing equation (Enns and McGuire, #8)
• 17. Drinking bird's relaxation oscillations (Enns and McGuire, #14)
• 18. Nonlinear hard spring on air track (Enns and McGuire, #16)
• 19. Mechanical nonlinear resonance curve on air track (Enns and McGuire, #17-18)
• 20. Magnetic nonlinear resonance curve (Enns and McGuire, #19)
• 21. Subharmonic magnetic response and period doubling (Enns and McGuire, #20)
• 22. Magnetic power spectrum (Enns and McGuire, #22)
• 23. Magnetic route to chaos (Enns and McGuire, #26)
• 24. Mapping chaotic toys (Enns and McGuire, #28)
• 25. Water flow up trees and cavitation (Dr. Vanderklein, Biology Dept.)
• 26. Physics of somersaulting (Frohlich, Scientific American, March 1980, videos of MSU diving team, 2003)
• 27. Moment of inertia and velocity of objects rolling down inclines.
• 28. Torque on a spinning top (Walker, Amateur Scientist, Sci Am, March, 1981, p 182)
• 29. Cloud chamber to view cosmic rays (Kutscher, #48)
• 30. The Brachistochrone
• 31. Physics of skateboarding, or another sport
• 32. Vibrations of a thin rod
• 33. Velocity vs. time in a binary star system observed from an arbitrary angle
• 34. Making internal thermal energy visible (Zou, The Physics Teacher, Sep 04, p 343)
• 35. Motion of a sand-filled funnel (Sullivan, McLoon, The Physics Teacher, Nov 2000, p 500)
• 36. Rattleback (celt) (Walker, Amateur Scientist, Sci Am, Oct 1979, p 172)
• 37. Energy in a yo-yo
• 38. Swinging spring (www.maths.tcd.ie/~plynch/SwingingSpring/System.html)
• 39. Fit extrasolar planet velocity curves (Laughlin, G.P., Sky and Telescope, October, 2006, p 39)
• 40. Stability of a bicycle (Jones, D.E. H., Physics Today, September, 2006, p 51)
• 41. Some experiment of your own (Please have it approved by the instructor before you start.)

• 1. Torsional vibrations of a mass on a spring - Bill P.
• 8. Objects falling in viscous fluids (terminal velocity) - Brian R.
• 10. Lagrangian points - Joe C.
• 11. Brownian motion - Alex C.
• 13. Spin toy pendulum - Victor S.
• 17. Drinking bird's relaxation oscillations - Tim R.
• 24. Mapping chaotic toy - Ryan C.
• 28. Torque on a spinning top - Matt H.
• 37. Energy in a yo-yo - Kaitlyn M.
• 31. Physics of Darts - Mike C.
• 31. Physics of Baseball - Patrick C.
• 41. Folding of rock layers - Deepa S.
• 41. Work and muscle strain in lifting loads - Ivan S.
• 41. Sine-Gordon wave - Garrett N.