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

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To find the minimum number of turns for a rope wound around a cylinder to maintain equilibrium with given weights, the relevant equation is T2 = T1 e^(μB), where μ is the coefficient of friction and B is the angle in radians. The problem specifies a coefficient of friction of 0.20, a mass of 80 kg for mass1, and 2 kg for mass2. To solve for B, one can rearrange the equation to isolate B, typically requiring logarithmic manipulation. Understanding how to apply logarithms to solve equations like e^x = 2 can provide insight into finding the angle B in this context. Mastery of these principles is essential for effectively tackling the problem.
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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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