M1 Help needed

I need help with this question: -

Two small rings, A and B, each of mass 2m are threaded on a rough horizontal pole. The coeffiecient of friction between rignt and pole is mu. The rings are attached to the ends of a light inextensible string. A smooth ring C, of mass 3m, is threaded on the string and hangs in equilibrium below the pole. The rings A and B are in limiting equilibrium on the bole, with angle BAC = ABC = x, where tan x = 3/4.

a) find the tension in the string in terms of m and g

b) find value of mu.

Thanks :biggrin:

Reply 1

Magician

.......... please...!

Reply 2

Fermat

ok, back soon :smile:

Reply 3

Fermat

Resolving forces at C,

2Tsinx = 3mg
2T(3/5) = 3mg (using tanx = 3/4 -> sinx = 3/5, cosx = 4/5)
T = 2.5mg
=======

Resolving forces at B,

Vertical forces

Tsinx + 2mg = R (R is the reaction of the pole against the ring at B)
2.5mg*(3/5) + 2mg + R
3.5mg = R
========

Horizontal forces

Tcosx = Fr
2.5mg*(4/5) = Fr
2mg = Fr
======

µ = Fr/R
µ = 2mg/3.5mg
µ = 4/7
=====

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