Rope on a pulley

JEE Advanced Forum › Mechanics questions › Rope on a pulley

A rope with length L and mass density Ïƒ kg/m hangs over a massless
pulley. Initially, the ends of the rope are a distance x₀ above and below
their average position. The rope is given an initial speed. If you want
the rope to not eventually fall off the pulley, what should this initial
speed be?

#Physics #Mechanics

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3 Answers

1

Philip Calvert ·2010-01-15 10:11:27

anyone with full sol. ??

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niteen9128 ·2010-01-15 18:11:50

is the answer v=x₀√2g/L

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Jagaran Chowdhury ·2010-01-16 05:55:40

let the length of rope on one side be i and on other side be l-x₀

mass of string on one side =lÏƒ

mass of string on other side =(l-x₀

for string to remain on pulley,the length must be equal on both side i.e one side go up by x₀/2

and oter side come down by x₀/2.

accln. of string as it moves from l-x₀ to l-x₀+dl

lÏƒg-T=lÏƒa

T-(l-x₀)Ïƒg=(l-x₀)Ïƒa

solving a=x₀Ïƒg/(2lÏƒ-x₀Ïƒ)

final vel=0

u²=2as

=2âˆ«x₀Ïƒg/(2lÏƒ-x₀Ïƒ)

integrating betn limits 0 and x₀/2 ,u can be calculated

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