Lab 11: Conservation of Energy - Mass-Spring System

Physics Lab #11 started on 4/08/15
Conservation of Energy - Mass-Spring System
Annemarie Branks
Professor Wolf

Objective: Unlike most of the physics problem we have been doing, we want to prove the Law for Conservation of Energy with a non-negligible mass for the spring.

Procedure:
     1.  Set up a system so you have a spring attached to a hanging mass over a motion sensor. Downward will end up being the positive direction and the top will be the origin. In our experiment H=1.457m, y=0.857m, and L=0.6m for an unstretched spring.

     2. Find a spring constant by either using a force sensor like we have done in previous labs, or by weighing masses on the spring and measuring its stretch. We chose the second option which in hindsight probably wasn't the best option because we didn't get consistent k values for different masses. They were relatively close of each other so we just averaged them and got 8.92 k/m.

     3.  Put 250 grams on the end of the spring and create a Position vs Time graph and a Velocity vs. Time graph.

     4.  Since we want to include the mass of the spring, the gravitational potential energy and the kinetic energy are different from the typical equations we use; however, elastic potential energy stays the same since that equation does not include mass. This is how we came up with our new equations for gravitational potential energy and kinetic energy:

     5.  With our known masses and the known unstretched position of the spring, we can plug in these equation into a new calculated column and generate graphs. So for the "y" in the GPE equation we are going to use the "position" column to replace it. Use the "velocity" column to replace v-end in the KE equation. Finally, for the elastic PE's delta y, use (unstretched - "position").

   For our experiment the mass of the spring was 0.085 kg and the unstretched position was 0.857 m..

     6.  After plugging in our equations, we generated a graph. We also included a Total Energy line which was achieved by simply adding KE, EPE, and GPE together. The Conservation of Energy Law tells us that the Total Energy line should be straight.

You can see that wherever one energy rises another will fall and this proves the Work-Energy theorem. The reason the Total Energy line is not straight it because of some variations and errors as listed below; however, this is fairly good data to prove the Total Energy Theorem in a classroom.

Errors:

• An assumption we made in the lab was that the spring was uniform. So elastic energy of the spring would not be the equation we used for it 0.5k(x)^2.
• There was uncertainty in where "zero" should begin on the spring.
• There are some uncertainties in the measurements we took which is typically +/- 0.001m, but it was difficult to measure a hanging object that moved easily so the uncertainty is probably slightly more that 0.001 meters. 
• Vibrations and heat are also forms of energy, which could have some from the spring making contact with the bar from which it was hanging from, or even the spring wire hitting against itself and making a noise.
• I also mentioned earlier that there was uncertainty in our k value because we were not getting the same answer every time, just something that was close. If we had found the k value using the force sensor then there would be uncertainty from the force sensor. Better, more expensive equipment would reduce the uncertainty. This is typically the case for all devices like the motion detector and LoggerPro itself.