Re: test problem

[Rick Tarara <rtarara@SAINTMARYS.EDU>]

It seems that both you and John M have taken the displacement of the spring
from the totally unstretched position.  I'm not sure that is correct.  The
equilibrium position is with the spring stretched 5 cm and therefore at the
extreme, the spring is stretched 20 cm from the equilibrium.  Isn't that
what should go in the 1/2kx^2 term?   That is, the energy equation would be:

mg(-.25m) + 1/2k(.20m)^2 = mg(-.125m) + 1/2k(.075m)^2 +1/2mv^2

This yields a lower value for v than your 2.6 m/s.  This seems related to
problem 10-10 in Hecht's Calculus text (which I had my class do and is the
only reason I question this--being immersed in papers right now).

Rick

**********************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

FREE PHYSICS INSTRUCTIONAL SOFTWARE
www.saintmarys.edu/~rtarara/
PC and MAC software
NEW! SIMLAB2001--DYNAMIC CARTS now available.
CD-ROMs now available
******************************************************


----- Original Message -----
From: "Justin Parke" <FIZIX29@AOL.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, December 04, 2001 2:36 PM
Subject: test problem


> I recently did a conservation of energy lab with my high school gifted and
talented physics students.  The lab involved a mass oscillating on a spring,
locating the top and bottom displacements for a vertical oscillation, and
comparing the potential energies (elastic and gravitational) at these
points.
> Part of the analysis was to compute the potential energies for the
midpoint of the oscillation and find the difference between this value and
the value at the top of the oscillation, and then to use energy conservation
to find the speed of the mass as  it passed through the midpoint.  Only a
few diligent students have asked me any questions about this and I suspect
the rest just made up some numbers.  These diligent students found that the
total potential energy was greater at the midpoint than at the top, which
would lead to negative kinetic energy.  I trust that they took reasonably
accurate measurements.  Did I miss something in my writing of the lab?
> Along the same line, I wrote the following question for a test on energy
and momentum, related to the lab.  I get 2.6 m/s.  In your (plural) opinion,
is this a reasonable test question?
> Thanks as always for your (plural) input.
>
>
> Test question:
>
> "This question is related to the conservation of energy lab:  a 1.0 kg
mass is hung from a spring which is then observed to stretch 5 cm.  The mass
is then pulled down 25 cm from the unstretched length of the spring and
released from rest.
>     a)  find the spring constant of the spring
>     b)  find the total potential energy (spring and gravitational) of the
system after it is stretched down.  (Define the origin to be the bottom of
the unstretched spring.)
>     c)  Use conservation of energy to find the speed of the mass as it
passes through the midpoint (i.e. 12.5 cm from the origin)"