Is My Professor Wrong? Understanding the Work-Energy Principle

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SUMMARY

The discussion centers on the Work-Energy Principle, specifically addressing a student's misunderstanding regarding the relationship between work done by a spring and the work done by a weight. The professor's assertion that the work done must account for variable forces, as described by Hooke's Law, is confirmed. The student's calculation of the spring constant (k) was incorrect due to the assumption of a constant force, leading to an overestimation by a factor of two. Additionally, the student failed to show all steps in the integral calculation, which is essential for accurate problem-solving in physics.

PREREQUISITES
  • Understanding of Hooke's Law and its implications on variable forces
  • Knowledge of integral calculus and its application in physics
  • Familiarity with the Work-Energy Principle in classical mechanics
  • Ability to perform dimensional analysis to verify calculations
NEXT STEPS
  • Study the derivation and applications of Hooke's Law in mechanical systems
  • Learn how to perform integrals in the context of physics problems
  • Explore the Work-Energy Theorem and its implications for variable forces
  • Practice problem-solving techniques that require showing all steps in calculations
USEFUL FOR

Students of physics, educators teaching classical mechanics, and anyone looking to deepen their understanding of the Work-Energy Principle and its applications in real-world scenarios.

Frederick Wittman
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See attached file. I believe my professor is incorrect. Work in must equal work out. We can imagine the work done by the mass as being a separate issue. Then, we recognize that the work done by the spring must be the same. Am I right? If not, why?


 

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Your professor's comment is correct. Your calculation of the work done by the weight assumes a constant force, independent of compression x. However, the force law given (Hookes law) is variable and depends on the compression x. Because of the incorrect assumption, this led to you calculation of k being incorrect (too high) by a factor of two. After obtaining k, it is not clear that you performed the integral correctly in any case. You jumped from integral to answer. (Maybe your calculator allows this). Many problems require you to show all work and supply the missing step.
 

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