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20A rope is wrapped around a pole of radius R = 3 cm. If the tension on one end of the rope is T = 1000 N, and the coefficient of static friction between the rope and pole is µ = 0.2, what is the minimum number of times the rope must be wrapped around the pole so that it doesn’t slip off?Assume that the minimum number of times the rope must be wrapped around the pole corresponds to a tension of 1 N on the other end of the rope.

Vicki Sharma , 11 Years ago
Grade 12
anser 1 Answers
Ankur Sachan

Last Activity: 6 Years ago

Here we have to use CAPSTAN equation
It says
(loading tension)=(holding tension)*e(u*a) 
 u=friction coefficient
a=turn angle
let there will be minimum “n” turns then a=2(pi)n
u=0.2
then 
  1000=1*e0.2*2(pi)n 
taking natural log and solving
ln(1000)=0.2*2(pi)n
n=5.4970
[minimum no. of turnes= 6]
 

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