Purpose: We looked at the work-energy theorem which equates the area under a kinetic energy graph to total work being done.
To set up the experiment, a cart was attached to a metal spring and placed on a metal track. The cart was positioned to be at rest with the spring at a neutral length, where it is at rest and neither stretched or unstretched. This was the zero position that was used to calibrate a motion sensor attached to the end of the track. Once calibrated and setting a positive axis on loggerpro, the cart was pulled back a small length to measure a positive distance. The cart was then released and loggerpro was used to measure the force vs time and plot it in a graph.
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| Cart and mass at rest while spring is unstretched |
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| Cart and mass after moved a distance x so that spring is stretched and containing potential energy. |
Once the data was collected, a new calculated column was created for kinetic energy using the formula K=(1/2)mv^2. Kinetic force vs time and kinetic energy vs time were both graphed. The integral of kinetic force vs time was equivalent to the total kinetic energy over the same interval of time.
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| As seen in the figure above, the total area under the graph is the integral of kinetic force. The integral is equal to the calculated kinetic energy for the region. |
The three points are three different intervals that correlate with kinetic energy intervals with a % error of less than 1%.
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