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)"