Finding the Speed of a Mass Attached to a Spring Returning to its Relaxed Length

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SUMMARY

The discussion centers on calculating the speed of a mass attached to a spring as it returns to its relaxed length. The spring has a stiffness of 0.6 N/m and a relaxed length of 0.18 m, while the mass is 0.023 kg. The relevant energy conservation equation is applied: Kf + Uf = Ki + Ui, where the final potential energy (Uf) is zero at the relaxed length. The user seeks clarification on how to correctly apply the velocities in the equation to find the speed at the moment the spring reaches its relaxed length.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with kinetic and potential energy equations
  • Basic knowledge of energy conservation principles
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the application of Hooke's Law in spring-mass systems
  • Learn about energy conservation in mechanical systems
  • Explore the derivation of the kinetic energy formula
  • Investigate the effects of mass and spring constant on oscillation speed
USEFUL FOR

This discussion is beneficial for students in introductory physics, particularly those studying mechanics, as well as educators looking for examples of energy conservation in spring systems.

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Homework Statement



A horizontal spring with stiffness 0.6 N/m has a relaxed length of 18 cm (0.18 m). A mass of 23 grams (0.023 kg) is attached and you stretch the spring to a total length of 25 cm (0.25 m). The mass is then released from rest. What is the speed of the mass at the moment when the spring returns to its relaxed length of 18 cm (0.18 m)?


Homework Equations



Kf + Uf = Ki + Ui
((1/2)mv^2)_{f} + ((1/2)KsS^2)_{f}=((1/2)mv^2)_{i} + ((1/2)KsS^2)_{i}

The Attempt at a Solution



I know that the final Uf should be zero since the final length of the spring would be zero. I am confused on what I should plug in for the velocities, one of them should be left as a variable and the other perhaps set to zero?
Please let me know what I'm doing wrong, and set me on the right track!
 
Physics news on Phys.org
A good tactic to start any physics problem is to come up with an answer you expect. What kind of answer are you expecting?

(Also note: this probably belongs in introductory physics.)
 

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