October 5, 2016: Conservation of energy for an oscillating mass/spring system

Anthony Betancourt
Lab Partner: Josh Fofrich
Professor Wolf

Lab #12: Oscillating Mass/Spring System

Purpose:

The purpose of this experiment is to provide a representation for the conservation of energy in a oscillating mass/spring system.  The experiment can show how a spring conserves energy in the form of elastic potential energy and kinetic energy while the mass oscillates.   The logger pro software can visually represent the energy graph as the mass moves up and down.

Procedure:

1. Mount a able clamp and long metal rod to the lab table.
2. Place 90 degree clamp and short metal rod near the top of the vertical metal rod.
3. Place force sensor on the end of the horizontal rod. Be sure to zero force sensor after placing spring on it.  
4. Place motion sensor on floor directly underneath the spring facing up.
5. Hang 50 gram mass hanger on the spring and zero the motion sensor.
6. Verify operation of motion sensor by collecting data and pulling hanging mass down ward and letting it oscillate and making sure graph shows appropriate shape.  

Theory:

We must be able to relate the ideas of kinetic and potential energy to the use of a oscillating mass/spring system.  This experiment is a simple and effective way of combing both concepts into  easily obtainable data.  The use of the hanging mass on the end of the spring can give us the spring constant, change in position from unstretched with the stretched length after hanging the 50 gram mass.  The kinetic energy of the system can be collected from using the motion sensor to track the oscillating mass and getting a graphical representation of its movement.  This graph can be further analyzed using logger pro's features.  

Measured Data:

(Diagram depicting set up for oscillating mass/ spring system)

(Graph showing position vs. time, velocity vs. time, KE vs. time)

(graphs of Kinetic, Elastic, and Gravitational Energies, all vs. time)

(graph depicting GPE, EPE, KE vs velocity)

(graphs of GPE, KE, EPE vs positions and vs. time; Also included is Energy Sum)

Analysis:

The first screen shot is of the mass oscillating back and forth in front of the motion sensor. The graph must be nice and smooth in order to be best utilize to derive energy graphs.  The third graph on that slide is a derived calculation of kinetic energy using "1/2 MV^2".  Second screen shot is of the three energies derived in logger pro: Elastic Potential Energy, Kinetic Energy, and Gravitational Potential Energy.  Same technique used to derive the kinetic energy graph was utilized for elastic and gravitational potential energy.  The graphs of EPE and GPE are opposite of one another since the EPE of the system is transferred into GPE when the spring is unstreched and vice versa when GPE is less and EPE is greater due to the stretch in the spring.  Third screen shot shows the graphs of each energy vs velocity.  The graphs look as such due to the oscillation of the mass and alternate from positive to negative.  The last screenshot has all three energy graphs vs. position and vs. time including the Energy sum.  The energies vs. position graph is to visually represent the conservation of energy in each one over the entirety of the system.  The energy sum graph should be a straight line with little to no slope depicting all the energies canceling each other out.  

Conclusion:

This experiment has a simple yet effective out come to derive the various energies and utilizing the logger pro software to analyze the graphs.  Where someone might have some difficulty is in the setup of the experiment.  It takes several trial runs to position the motion detector in the correct spot under the mass in order for the data collection to result a smooth graph.  Any other difficulty might be due to certain uncertainties in the lab equipment and procedural faults.  The spring utilized in this experiment was not a uniformed shape, possibly effecting the EPE due to skewed change in position from stretching.  In order to achieve a smooth graph, we had to place a larger mass on the end of the spring to help alleviate the shakiness and bouncing around from the spring oscillating.  Also with the heavier mass, the bar bent at 90 degrees near the top of the long metal bar starts to bend when oscillating possibly effecting the change in position for the spring.  Lastly, not properly securing the force sensor on the 90 degree bar can result in faulty force reading.