The potential corresponding to the motion of particle.
Answer to Problem 4.1P
The potential corresponding to the motion of particle is
Explanation of Solution
Consider the figure below.
Unstretched length is
Here, F is the force on the mass.
Potential is given by,
Here, U is the potential.
From the diagram,
The unstretched length is given by,
Replace
Using Binomial theorem and expressing up to first two terms,
Conclusion:
Substitute for F in the expression for U and integrating,
Therefore, potential corresponding to the motion of particle is
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Chapter 4 Solutions
CLASSICAL DYNAMICS OF PARTICLES AND SYST
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- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University