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Re: oscillations test question



Robert Cohen asked:

If the 200 grams is then stretched a distance x from the new equilibr=
ium point, the potential energy relative to the new equilibrium point=
is equal to 1/2 kx^2. What do you call the quantity 1/2 kx^2? The =
difference in the elastic-gravitational potential energy?

I generally call it the total PE. Of course that assumes there are no
other potential energies of interest.

A favorite Mazur question of mine is:

"An object hangs motionless from a spring. When the object is pulled
down, the sum of the elastic PE of the spring and the gravitational
PE of the object and Earth:
1. increases
2. stays the same
3. decreases."

Herb wrote:

The change in gravitational energy over a vertical distance of a meter or
two is very close to zero.

And following in this vein, there are always several groups of
students arguing among themselves about this Mazur question and
actually trying to calculate and compare the two kinds of PE. When
pressed, it always turns out that they assumed m=1 and k=1 and
anything else they felt like ("units? what units?" they tell me,
BTW). Of course, it *is* possible to substitute in some convenient
values and get an answer, but of course they are not careful to
choose a self-consistent set of values nor have they thought about
the issue of the zero point.

While for gravitational PE, the change in PE is the same regardless
of where you put the zero level, the same is not true for elastic PE
unless you exercise some care. (I believe this issue was discussed on
the list earlier this year.)

This Mazur question certainly reveals IMHO the utility of combining
the two forms of PE together to get 0.5kx^2 with x measured relative
to the *equilibrium* position not to the *unstretched* position of
the spring. By expressing things this way, we can use the same energy
formulas for either horizontal or vertical springs and otherwise
ignore gravity. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.