ESTM Challenge Problem

ESTM Challenge Problem

     Our group's goal for this challenge was to predict where to compress two different springs so that two carts of equal mass come off with the exact same velocity. Below is a diagram of what our setup looked like, with the corresponding masses and spring constants for each cart/ spring. 

     At first glance, our group got a little bit confused as to which spring constant went with each cart, as our velocity sensors were hooked up to the opposite carts. Once we got through that small hiccup, we began working in ernest. 

     We reasoned that because we were working on a surface track with negligible friction, we could simply say that E (Elastic) = E (kinetic). We decided on setting a distance for one cart, the red spring cart, and working to find a distance for the second cart this way. Here is our work.

     All of our masses were taken using the scale. We have now found both of the starting points (x) to pull our carts back to get to the final velocity of .49 m/s. Once we had this prediction, we pulled our carts back and tested what the real velocity would be. Turns out, it was .55 m/s, which was definitely within ten percent error of our prediction. Overall, this was a very successful challenge problem that pulled together everything that we knew about the ESTM model so far.