Apparatus: We used a spring, a mass, a motion sensor and logger pro.
Our set up
What we did: We grabbed a mass that was attached to a hook which was a total of .5kg. Next we grabbed a spring and weighed it which gave us .1kg. We set up by hanging the spring with out the mass stretching it and measured the height from the floor to the bottom of the mass.(76cm) Next we measured the stretch of the spring by getting the distance to the floor to the bottom of the mass.(55cm) This gave us a delta x of 21 cm. We Then we found the K in the PEe=.5kx^2 formula by using the formula Mg/Delta x which gave us 23.53 After we set up our motion sensor and activated it onto logger pro. We let the mass start to oscillate and then we began to record the movement of the mass/spring system for ten seconds. This gave us two graphs on logger pro which consisted of a position vs time chart and a velocity over time chart.
What we did with this information: With this information we added 5 new calculated columns. These included gravitational potential energy(GPE), Kinetic energy (KE), Elastic potential energy(PE elastic),gravitational potential energy of the spring(GPE RED), Kinetic energy of the spring(KE spring) and a final column for the Total Energy(Total. we set up a formula of each column as followed.
GPE: Mass*gravity*position
KE:.5*mass*velocity^2
GPE RED: (Mass of spring/2) *gravity*postion
KE Spring: .5*(mass of spring/3)*Velocity^2
PE elastic: .5*K*Delta Position
Total: Sum of all forms of energy
We finally graphed all of our new calculated columns together in out position over time chart which gave us multiple graphs that looked as followed.
Conclusion: The image above proves that energy is conserved. The yellow line above is the total energy of the spring as it oscillates up and down with the mass. As you can see, the total energy is relatively constant between .6 and .7 J.
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