Graphs of Kinetic Energy vs. Time, Gravitational Potential Energy vs. TIme, and Total MEchanical Energy vs. TIme
This Kinetic Energy vs. Time Graph is only for one motion of oscillation of the object, as opposed to the one at the end of this page. The energy increases as the mass springs upwards and downwards, but then the certain points at which there is no kinetic energy in the system displays where it was, for a brief moment, either at the top of the top of string, or at the bottom of the bottom of the string, and this is where the kinetic energy is at it's lowest point in the graph, and zero kinetic energy is found when the mass has not yet been set in motion and when it finishes springing.
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This graph of Gravitational Potential Energy vs. Time may look familiar, and that is not a mere coincidence. In the Kinematics section of this lab, the Position vs. Time Graph also looked like this, and goes back to their formulas. They each have the 'mass' and 'force of gravity' constants, so they end up producing clone-like graphs. No gravitational potential energy is found in the exact same positions where there was no kinetic energy. Gravitational potential energy begins with zero energy before the system begin work, but increases when going up, and decreases when it moves down. |
The Graph of Total Mechanical Energy vs. Time is actually made from two other types of energies: potential and kinetic. This is strikingly apparent of our former Potential and GPE vs. Time Graphs, but it has fuller curvatures due to addition of kinetic energy. As mentioned, the energy in this system will increase and decrease in a similar way to the two graphs mentioned. Also, many believe that the only total mechanical energy graph is a straight horizontal line, however, this is not always the case. If the kinetic and potential energies are at their max values, a straight line will appear. But, if there happens to be varying amounts of each energy, then the graph will produce curves such as the ones in this graph.
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Entire motion of the Spring; Kinetic Energy vs. Time Graph
Evidently the most jumbled graph of this whole lab is this Kinetic Energy vs. Time Graph that maps out the entire oscillatory action of the 500g mass. As the other KE vs. Time Graph displayed, energy increases when the object rises and falls, and decreases at the summit and the base of the spring. Over time, the kinetic energy will actually lower as the system begins to slow down, despite Tracker lapses displaying the contrary. So really, energy in this system is conserved, as it is transferred to potential energy form from kinetic, though not clearly obvious, and the TME graph supports this.
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