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20 A 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.

20

A 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.

Grade:12

1 Answers

Ankur Sachan
26 Points
3 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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