Minimum Turns for Equilibrium: Rope Winding on Cylinder with Belt Friction

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SUMMARY

The discussion focuses on determining the minimum number of turns required to maintain equilibrium when winding a rope around a cylinder, given a coefficient of friction of 0.20, mass1 of 80 kg, and mass2 of 2 kg. The key equation utilized is T2 = T1 e^(μB), where μ represents the coefficient of friction and B is the angle of the rope in radians. Participants seek guidance on solving for B and applying the equation effectively to achieve equilibrium.

PREREQUISITES
  • Understanding of basic physics concepts related to tension and equilibrium
  • Familiarity with exponential equations and logarithmic functions
  • Knowledge of friction coefficients and their implications in mechanical systems
  • Ability to manipulate algebraic equations to isolate variables
NEXT STEPS
  • Study the derivation and application of the equation T2 = T1 e^(μB)
  • Learn how to solve exponential equations, specifically e^x = 2
  • Explore the principles of static equilibrium in mechanical systems
  • Investigate the effects of varying coefficients of friction on tension in ropes
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone involved in solving problems related to tension and equilibrium in mechanical systems.

maine0504
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Homework Statement




find the minimum number of turns the rope should be wound around the cylinder to maintain equilibrium of the weights the coefficient of friction is 0.20 and the mass1= 80kg and mass2-2kg.
 
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You must attempt the problem for anyone to help. What are the applicable equations?
 
by using this formula how can i get the angle/B?

T2=T1 e^(mu*B)
 
by using this formula how can i get the angle/B?

T2=T1 e^(mu*B)
 
Solve the equation for B.
 
LawrenceC said:
Solve the equation for B.
how?

can u please teach me..?
 
Try this:



How would you solve e^x = 2?
 

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