Static friction and fraction of mass of rope that can hang.

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SUMMARY

The discussion centers on determining the fraction of a rope that can hang over the edge of a table before slipping occurs, given the coefficient of static friction (μ) between the rope and the table. The solution involves analyzing the forces acting on the rope and applying static friction principles. The conclusion is that the fraction of the rope that can hang is directly proportional to the coefficient of static friction, expressed mathematically as a function of μ.

PREREQUISITES
  • Understanding of static friction and its coefficient (μ).
  • Basic knowledge of forces and equilibrium in physics.
  • Ability to decompose forces into x and y components.
  • Familiarity with algebraic manipulation to isolate variables.
NEXT STEPS
  • Study the principles of static friction in detail, focusing on real-world applications.
  • Explore force decomposition techniques in physics problems.
  • Learn about the dynamics of objects in equilibrium.
  • Review algebraic methods for isolating variables in equations.
USEFUL FOR

Students in physics courses, particularly those tackling mechanics and static equilibrium problems, as well as educators seeking to clarify concepts related to friction and force analysis.

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Homework Statement



The coefficient of static friction between a rope and the table on which it rests is μ.
Find the fraction of the rope that can hang over the edge of the table before it begins to slip.
Express your answer in terms of μ.


Homework Equations





The Attempt at a Solution



i have tried to break all the equations i know into their parts like x and y components using just variables since no numbers are given but i just can't seem to isolate for something multiplied to μ. For some reason i think it is just μ but i do not truly understand why this would be if anyone could help it would be really appreciated as it is the last question in an online assignment and i have been working at it for quite some time. Thanks in advance.
 
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