4/8 Conservation of Energy-- Mass-Spring System

Purpose: To prove the Conservation of Energy Theorem in an oscillating mass-spring system.

Procedure:

FIGURE (1)

We started off by setting up the apparatus in FIGURE (1). We hung a spring attached to a force sensor from a rod a few meters off the ground. Under the spring, we set up a force sensor. For this lab, we needed to figure out the spring constant of our spring. To to this we slowly pulled down on a 50 gram mass while the motion sensor was taking data. This gave us a Force v. Time graph and a Stretch v. Time graph, from which we determined our spring constant to be 16.35 N/m. We then hung a 200 gram mass from the spring and recorded the position using the motion detector which gave us a value of .610 m. This was our in initial position and in LoggerPro, we created a new calculated column, "stretched" where we had the equation: stretch= .610-"position", where "position" was the current position the motion sensor was measuring. We then set up calculated columns to measure kinetic energy (.5mv^2), gravitational potential energy (mgh), elastic potential energy (.5kx^2), and a sum of all the energies.

Once we had the columns set up, we attached a 250 gram mass to the spring, pulled the mass down about 10 cm, and then let go as we recorded our data (FIGURE (2)).

FIGURE (2)

Conclusion:
Our total energy line should have been flat, not wavy, since energy was conserved. Possible sources our error could be a miscalculation of the spring constant, not pulling the spring down enough or too much and using a non-uniform spring.