How can I determine the instant the block overcomes static friction?

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SUMMARY

The discussion centers on determining the moment a block overcomes static friction when connected to a spring and subjected to a force. The critical condition for movement is established as the elastic force (Fs) exceeding the static friction force (Fs,f), leading to the equation Fs > μs mb g. The participants suggest using energy balance equations to analyze the system, specifically the work done by the applied force (F = 20 N) and the spring's potential energy. The final conclusion indicates that the displacement of the spring (x) must exceed 0.0491 m for the block to start moving.

PREREQUISITES
  • Understanding of static friction and its coefficient (μs = 0.5)
  • Knowledge of Hooke's Law and spring constant (k = 200 N/m)
  • Familiarity with energy conservation principles in mechanics
  • Ability to formulate and solve equations of motion for connected systems
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  • Learn how to apply Work-Energy principles in mechanical systems
  • Study the dynamics of rolling motion and its implications on connected bodies
  • Explore the relationship between force, displacement, and friction in mechanical systems
  • Investigate the effects of varying coefficients of friction on system behavior
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Students and professionals in physics, mechanical engineering, and applied mechanics, particularly those interested in dynamics and friction analysis in connected systems.

  • #61
Thanks, well done.
 
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  • #62
Thermofox said:
##\sqrt {\frac {2~20~0.0491 - 200~(0.0491)^2} { \frac {21} 5 (0.3)^2}}## ##≈ 1,252~rad/s##
Check the evaluation. (Maybe you already caught this.)
 

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