Which one of these 3 graphs represents Hooke's law?

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SUMMARY

The discussion centers on identifying which graph represents Hooke's Law among three options, specifically analyzing the behavior of a rubber band and two springs. The consensus is that Spring 2 closely follows Hooke's Law due to its linear relationship, while the other graphs deviate significantly. To calculate the spring constant (k), participants confirm the use of the formula F=-k(x) for each data point, suggesting averaging the results for accuracy. The fitted value obtained from Excel is recommended for better precision in determining the spring constant.

PREREQUISITES
  • Understanding of Hooke's Law and its linear relationship
  • Familiarity with the formula F=-k(x)
  • Basic knowledge of graph interpretation and data fitting
  • Proficiency in using Excel for data analysis
NEXT STEPS
  • Calculate the spring constant using F=-k(x) for multiple data points
  • Learn about linear regression techniques in Excel for data fitting
  • Explore the concept of elasticity and its applications in materials science
  • Investigate the limitations and deviations from Hooke's Law in real-world materials
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and material properties, as well as educators seeking to enhance their understanding of Hooke's Law and its practical applications.

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Homework Statement


Which one obeys Hooke’s Law and why?

For the material(s) that did obey Hooke’s Law, calculate the spring constant, k. SHOW ALL WORK: listed variables, units, equations without substitutions, equations with substitutions, final answer with units!

The Green line on the graph represents the Rubberband, Blue and Red represent Spring 1 and 2 respectively.

Homework Equations


F=-k(x)


The Attempt at a Solution



From what I can tell, Hooke's law has a linear relationship, so the line would be perfectly straight. Spring 2 is almost the same as its perfect fit line, so I think it does follow the law (it's a little different due to human errors, I am thinking). Does any other graph represent Hooke's Law? They seem to deviate from their perfect fit line a lot more than spring 2. Also, to calculate the spring constant, would I have to use F=-k(x) for each of the points I gathered than find the average (I have a force/weight and displacement table as well)? The slope of the line shown is for the perfect fit so I am not sure. Thank you for your time!
 

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From what I can tell, Hooke's law has a linear relationship, so the line would be perfectly straight. Spring 2 is almost the same as its perfect fit line, so I think it does follow the law (it's a little different due to human errors, I am thinking).
Right.
They seem to deviate from their perfect fit line a lot more than spring 2.
Right
Also, to calculate the spring constant, would I have to use F=-k(x) for each of the points I gathered than find the average (I have a force/weight and displacement table as well)?
The fitted value from excel is better.
 

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