courses > lab
Source code in LaTeX format -- students don't need this.
Other lab-related stuff
Quite a few of the labs involve verifying the principles stated in the textbook, which is not much like what you would do in a real scientific experiment. For students who would like to do more real experiments, I have a few ideas listed here for alternative labs. If you want to do one of these, you should start talking to me about ideas either verbally or by email about a week before. You can also come up with your own ideas. Here is a catalog of the apparatus available in the physics stockroom.
friction involving wetted surfaces (first of three alternatives to "Newton's second law")
The standard model of friction given in the text is usually fairly accurate for dry surfaces, but may not work as well for wetted ones. There are various fancy mathematical models of friction that you can find out about by googling for names like Stribeck, Karnopp, Armstrong, Bliman, and Sorine. What I have not seen on the web is much practical information on how friction behaves for specific wetted surfaces of interest, such as rubber on asphalt wetted with water, steel on steel lubricated with oil, sweaty human skin (which is of interest to rock climbers), etc. Can you formulate and test an interesting hypothesis on, e.g., how the frictional properties of a particular wetted surface compare with its properties when dry?
testing models of knots (second of three alternatives to "Newton's second law")
The following papers build up a theory of why friction makes knots hold or not hold:
- Bayman, Am J Phys, 45 (1977) 185
- Jearl Walker (Amateur Scientist column), "In which simple equations show whether a knot will hold or slip," Sci Am 249:2, p. 120, August 1983.
- Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185-1200.
As far as I know, nobody has published any high-quality experimental tests of the theory. As an example of a test, one could determine the maximum radius of a post that allows a clove hitch to hold. If you want to work on this project, I can give you copies of the papers.
logically rigorous tests of Newton's third law (third of three alternatives to "Newton's second law")
Lab 1, interactions, is meant to lead students to construct Newton's third law based on their own observations. This lab has a logical loophole in common with virtually all experimental tests of Newton's third law, from the ones done in Newton's time down to high-precision tests in the present day. Consider a version of lab 1 in which magnet A interacts with a stack of the two magnets B and C. Since A, B, and C are all identical, and they all have their axes aligned, it is guaranteed by symmetry that A's force on B equals B's on A, and A's force on C also equals C's on A; this holds even if Newton's third law is false! If we also assume that forces add linearly, then the total force of A on BC is also guaranteed to equal the force of BC on A. We run into a similar issue in other tests as well. For example, Newton's third law has been verified to extremely high precision for the earth's force on the moon and the moon's force on the earth. But the earth and moon contain many of the same minerals, so the good agreement with theory could be at least partly due to symmetry. E.g., the force of 9 nickel atoms in the earth on 42 nickel atoms in the moon is guaranteed by symmetry to be the same as the force of the 42 on the 9. Can you come up with an experimental test of Newton's third law that doesn't risk being a tautology in this way?
systematic errors in a pendulum (alternative to "resonance")
Back in the 90's, a colleague, whom I'm no longer in touch with, bragged about having done a student lab in which they measured the earth's gravitational field to pretty high precision (better than we usually achieve in my lab 4), using only a stopwatch plus a pendulum made out of an index card and a pin. Recently I've put a little effort effort into figuring out how this would be done. The period should theoretically be related to g by g=(4π2L/T2)[1+(1/12)(d/L)2], in the case of negligible friction and small amplitude, where d is the length of the card's diagonal and L is the distance of the pinhole from the center. (This can be proved using the equation for the angular momentum of a rectangle and the parallel axis theorem.) An advantage of the technique, compared to historically important ones like Kater's pendulum, is that d and L are the only physical properties of the pendulum that need to be measured, and they can both be found very accurately using Vernier calipers. When there is negligible friction but the amplitude isn't small, there is a correction factor for T given here. When there is nonnegligible friction but the friction is proportional to velocity (as assumed in the text), there is a further correction of (1-1/4Q2)-1/2. However, the friction between the card and the pin is friction between two dry surfaces, so it's probably independent of velocity, and the air friction is probably proportional to the square of the velocity. Depending on the detailed behavior of these forces, the period might either increase or decrease as the amplitude falls away. If a pendulum measurement of this type is to succeed, one would have to figure out this behavior using a photogate. A related difficulty is that there will probably be some tendency for the card wiggle rather than rotating uniformly. It might make sense to vary the relative importance of air friction and friction at the axle by studying rectangles of different thicknesses.
lore about "the air that vibrates beyond the end of the tube" (alternative to "resonances of sound")
Labs like my lab 13, in which one measures the resonances of an air column, are a worldwide staple of the freshman physics lab curriculum, and every lab manual, including mine, says to add a certain correction for "the air that vibrates beyond the end of the tube," so that the length of the tube is effectively increased from L to L+X. X is typically given as something like X=cd (for one open end) or 2cd (for two open ends), where d is the diameter of the tube and c is a unitless constant. There is not universal agreement on c; it seems to be something that is just passed on as lore. Fletcher and Rossing, in The Physics of Musical Instruments, p. 182, reproduce a graph from Levine and Schwinger, "On the radiation of sound from an unflanged pipe," Phys Rev 73 (1948) 383, which is a theoretical prediction showing c as depending on the unitless number d/λ. The value of c is shown as falling off from about 0.3 for small d/λ to about 0.1 for d/λ≈1. I don't know whether it actually works as predicted in real life. One possible way to test this would be to compare the effective length of a tube when one of its ends was open to the case where that end was closed off. If this is done by listening for resonances as in lab 20, then a graph of f versus N should show a staggering effect like a sawtooth. It might be easier to do by making a click and observing both the original click and its time-delayed echo as pulses on an oscillscope.