The underlying concept like the Ek lab will be conservation of energy. However there are numerous ways to do this since we already have mathematical models for Eel and Ek. We chose to use a vertical spring to shoot a ball bearing into the air. The system our case was the ball, earth, and the spring. Our assumption was that energy storage right before the ball shot was Eel and the storage at the top of the ball’s path was Egmax. This gave a direct relationship between Eg and height. The slope of this graph was 0.32 N and the mass of the ball was 0.016-kg. This assumed that Eelmax was a trapezoidal region given by the product of the average force and the displacement of the spring. When the more traditional method of using Eel = ½ k∆x2 the Eg vs. height graph was linear with a slope of 0.27 N.
Physics teachers know the slope should be the weight of the ball. Since the slope was significantly more than the weight this would imply that ball should have gone significantly higher than it did go. Since the ball did not go higher a significant amount of energy must have been stored as Eint when the ball was at its highest point. We do not have a mathematical model to determine this Eint so this method should be abandoned.
This was my exact experience this past year. I even tried having the students let the cart explode upward from the backstop of an inclined dynamics track. First I had them let the cart roll down the ramp and then bounce off the backstop again ascending the inclined track. The cart didn’t go as far back up as it started. Students used this ratio to determine the percent initial Eel that was stored in Eg at the top of the cart’s motion as it exploded upward from the backstop.
It worked but was very contrived and I feel that I lost a lot of students in the process. The thing that I learned from today’s activity is that students need to be directed to develop a lab that will minimize ∆Eint. I will illicit from students what are some ways in which you can cause a greater ∆Eint. Hopefully they will say to somehow increase the effects of friction or to cause some sort of radiative process (sound, light, etc.). I will then lead them to the point that they need to choose a procedure which “eliminates” these effects and suggest that they develop energy pie charts and play with their lab equipment to see if in fact these have been “eliminated”. I really wish I had flip cameras to open up the possibilities of quickly gathering data.