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Re: CONSERVATION OF ENERGY, experiment



A good experiment is worth sharing, even with those who think that the
debate degenerated into discussing words instead of discussing simple
situations. What is described here is a crude experiment whose purpose
was to verify the expectation of teacher B. You know the story, it was
repeated so many times that even I hesitate to tell it again.

The bottom line is that K and R*x are not significantly different. The
experimental uncertainties, however, were significant and a difference
between K and R*x would have to be larger than about 10% of K in order
to be detectable. Please note that K is the initial kinetic energy of the
sliding block, R is the force of kinetic friction and x is the distance
traveled. To put it differently, I decided to compare x with K/R
experimentally. The conclusion was that the difference, if any, was too
small to be measured. Do not miss the P.S. question at the end.

Details
*******

1) In preparation for the experiment I made an inclined plane from a thick
plexiglass board (22*90*0.5 cm^3). The board was washed and used as a slide
for a plastic block. The block consistently accelerated when the angle of
inclination was larger than 22 degrees and consistently decelerated when
the angle was less than 21 degrees. Knowing that the coefficient of kinetic
friction, mu, is equal to the tangent of the inclination angle (when v is
constant) I know that it is between 0.38 and 0.40 (The nature of plastic
materials is not known to me. The board, probably plexiglass, was
transparent; the block was opaque and blue.)

2) Assuming that mu=0.39, and knowing the mass of the block (0.0865 kg), I
was able to calculate the frictional force (R=0.331 N) on the horizontal
surface. I pushed the block and saw it slide to rest. Then I recorded
the sliding motion with a camcorder (30 frames per second) and digitized
the frames. The screen resolution was 640 by 480 pixels. One frame was
selected as initial (showing my hand already away from the block)
and the distance traveled after t=o was found to be 0.368 m.

The initial velocity was also determined [v=0.5*(v1+v2)=1.65 m/s, where
v1 is the mean speed between t=-1/30 and t=0 while v2 is the mean speed
between t=0 and t=+1/30 s.] The initial kinetic energy of the block,
K=0.118 J was calculated from v=1.65 m/s. It was then used to calculate
the maximum possible sliding distance xmax=K/R=0.118/0.331=0.356 m. This
value is practically identical with what was actually measured (0.368 m).

The non-significant digits were retained to eliminate rounding errors.
The experiment shows that the fraction of K which was converted to thermal
energy was too small to be detected. A fraction larger than 10% would be
measurable in this crude experiment.

3) Actually I did a little more. "Instantaneous" velocities were measured
for all pairs of consecutive frames. The data were as shown below:
............................................................................
Average v (m/s) for consecutive pairs of frames (each step is 1/30 sec):

1.65 1.50 1.38 1.25 1.14 1.02 0.90 0.77 0.61 0.51 0.42 0.28 0.19 0.09 0.04
............................................................................

The first v corresponds to t=0, the second to t=1/30 s, next to 2/30 s,
etc. The rate at which the sliding speed decreases is practically linear
and I identified the slope with a constant frictional deceleration of
3.6 m/s^2. Multiplying this deceleration by the mass of my block I found
that the frictional force
R = m*a = 0.0865*3.65=0.315 N.

This is practically the same as what was found in the preliminary (inclined
plane) experiment. It is nice to see that all is self-consistent. If I had
to start again I would probably use a much larger block and an ultrasonic
motion detector.
Ludwik Kowalski
P.S. Can you answer this question?

Suppose a large meteor hits the moon and penetrates its surface to a
certain depth. The material from which the meteor is made is infinitely
strong and perfectly rigid. Its melting temperature is infinitely high.
Yes, I am trying to simplify the situation.

The meteor penetrates to a certain depth x (distance traveled by its
center of mass under the influence of a "constant friction" force R.
Given K, the initial kinetic energy of the meteor, and R, calculate x.
Would you say that x=K/R? Or would you say that x should be smaller than
K/R because part of the initial K is used to heat and melt and evaporate
and push away some lunar material? You know what teacher B said.

And PLEASE, PLEASE, PLEASE do not forget that the problem was formulated
by a real high school teacher from the Chicago area. Forget about entropy,
and hamiltonians, and virtual displacement, ... I am an university professor
and some of the introduced words were new to me, or partially forgotten.
We do not solve problems with lagrangians and chemical potentials in the
introductory courses which I teach. Even entropy is a term which I have
no time to discuss.

I do not know why our debate degenerated into a cacophony of arguments
about meaning of words from formal thermodynamics. Don't we have enough
weapons, in the arsenal of an introductory physics course, to deal with
this problem? Perhaps not. In that case let us say that this problem is
not appropriate and stop wasting time trying to solve it. I would
disagree, initially, with such position. Even a partial solution in
semi-quantitive terms is worth seeking; perhaps in a discussion, perhaps
through an experiment. What do you think?