Work vs Position: Force-Displacement Relationship

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SUMMARY

The discussion centers on the relationship between work and position as represented by the linear trendline equation y = 3.75 x + 0.135, where y denotes work in Joules and x denotes position in meters. The area under the force versus position graph directly correlates to the work done, with the derivative of the work-position graph yielding the applied force. Participants express confusion regarding the interpretation of the area under the curve and its implications for deriving the physics equation.

PREREQUISITES
  • Understanding of basic physics concepts, specifically work and force.
  • Familiarity with graph interpretation in physics.
  • Knowledge of calculus, particularly derivatives.
  • Ability to apply linear equations in physical contexts.
NEXT STEPS
  • Study the relationship between force and position in the context of work-energy principles.
  • Learn about the graphical representation of work in physics, focusing on area under the curve.
  • Explore the concept of derivatives in physics, particularly how they relate to force.
  • Investigate the differences between work, power, and their respective equations.
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding the work versus position relationship in physical systems.

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Homework Statement


1. You create a plot and the linear trend is y = 3.75 x + 0.135.
The plot is titled "Work [Joule] versus Position [meter]".
Write the "physics" translation for this plot's trendline.


Homework Equations



y = 3.75 x + 0.135.
Find physics equation.


The Attempt at a Solution



My understanding is that the area under a graph of force vs. position is work. However, I have no idea what a work versus position graph represents in terms of area underneath the curve and thus am unsure how to write the physics equation for this. Any ideas?
 
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The derivative of the graph with respect to position would be the applied force, correct? I can't really think of anything else that it would be representative of. Maybe it could somehow relate to power, but that's work versus time.
 

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