🚀 go-pugleaf

Another "low cost" activity.

Take a hand saw and firmly mount its tip in a vise so that the handle is up.
Tap the handle and it will oscillate at low frequency. Ask students to
measure the time, t, for ten cycles and to calculate frequency (f=10/t). Let
them discover that for small displacements the frequency does not depend on
amplitude. (As you probably did for a pendulum.) Then ask for the following
predictions, test predictions and discuss topics.

1. What happens to the frequency, f, when the oscillating blade is shortened
   (by pushing the saw deeper into the jaws of the vise)?

2. Where is the center of mass? Make a chalk mark there.

3. How will f be affected if an additional mass (say 0.5 kg) is taped at the
   center of mass position?

4. Is the dependence of f on mass linear? You may ask them to plot f versus
   the square root of M (where M is the mass of the oscillating part of the
   saw plus the extra mass added).

5. Remove the added mass and show how f depends on the distance of the center
   of mass from the clamp point. (It is the CM of the sticking part of the
   saw that counts here.) Demonstrate that f is directly proportional to the
   square root of this length, L. A way of estimating L must be "invented".

6. Reorient the oscillator so that the saw handle points down rather then
   up. What should happen to f? Will it go up, down or ramain the same? It
   goes up, doubles in my case, because the restoring force is increased.
   (The net restoring force is due to elasticity and to gravity. For the
   handle-down saw the gravity component adds to the elastic force; for the
   handle-up saw the two forces tend to cancel.)

7. The frequency of the clamped saw can be numerically predicted from the
   harmonic oscillator formula if k, the Hooke's law constant, is already
   known. You can calculate k as F/x, where F is a static force with which
   the saw is pulled at the center of mass and x is the resulting CM
   displacent. In my demonstrations F was produced by a loop of thread wound
   around the center of mass with the saw mounted horizontally. The loop was
   pulled sideways by a known weight (over a low friction pulley) while x was
   measured with a ruler. A frequency calculated by f=2*Pi*sqr(k/M) differed
   from the actually measured f (horizontal mounting) by about 3%.

8. To reach audible frequencies clamp the saw with the blade up (the handle
   is not vibrating); only about 10 cm of the blade should be allowed to
   oscillate. Hit the blade as if it were a prong of a tuning fork and listen.
   Then show how the pitch is affected by the length of the "prong".

Trivial? Yes. Useful? I hope so. Let me know. And ask for help if necessary.
Good physics can be extracted from nearly everything, even from an old rusted
saw. The teeth of my saw are covered by a tape to prevent injury.

          ---------------------------------------------IIIIIIIII
          I                                           III      III
           ******-_                                    III      III
                    -******-_                           III      III
                              -******-_                 III       III
                                       -******-_        III        III
                                                -******* III        III
P.S.                                                      IIIIIIIIIIIIII

Would you guess that I am trying to send a picture of a saw with the handle
on the right side? Very awkward! It would be nice if pictures could be sent,
received and printed as easily as text. How far are we from that luxury?
Can somebody summarize the status of the "picture transfer technologies" on
internet?

                          Ludwik Kowalski   kowalski@apollo.montclair.edu