Calculating Force-Distance Equations for Elastic Band Lab | Homework Help

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The discussion focuses on deriving a theoretical equation that relates force and distance for an experiment involving an elastic band. The user has already formulated an equation based on their experimental data but seeks a comparative equation to analyze experimental error. Key inquiries include the relationship between the distance traveled by a block and the kinetic energy provided by the elastic band, as well as the equations for tension in the elastic band and the potential energy stored in it. Understanding these relationships is crucial for accurately interpreting the results of the lab experiment. The conversation emphasizes the need for clarity on the connections between force, energy, and distance in the context of elastic potential energy.
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Homework Statement


I am soo lost and I need a theoretical equation for force in relation with distance. My lab is about how the force used to pull an elastic band back affect the distance a block travels after the elasticband is released. I got my results and made graphs and everything and came up with an equation. : D = (0.3489 ± 0.0999) F^2 + (5.5097 ± 1.6253). I need another equation to compare this equation with and calculate my experimental error. Can someone help me with a equation for force-distance or an equation where force^2 is = to distance? Someone just lead me in the right direction
 
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If we assume the block is slowed by a constant frictional force, how does the distance the block moves relate to the kinetic energy supplied by the elastic band? (What equation connects force, energy and distance? Why can you apply it here?)
What is the equation for the tension in an elastic band of given modulus pulled back some distance x? What is the equation for the potential energy stored in such a band?
 
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