Tension? knowing friction. I have the answer but need explaination :(

1. The problem statement, all variables and given/known data

A ring of mass 4 kg is attached to one end of a light string. The ring is threaded on a fixed horizontal rod and the string is pulled at an angle of 25◦ below the horizontal (see diagram). With a tension in the string of T N the ring is in equilibrium. (first image)

(i) Find, in terms of T, the horizontal and vertical components of the force exerted on the ring by
the rod.

The coefficient of friction between the ring and the rod is 0.4.

(ii) Given that the equilibrium is limiting, find the value of T.

=> Summary:
m = 4kg
angle = 25◦

2. Relevant equations


3. The attempt at a solution (second image)

(i) R (→) Tcos25
R (up) Tsin25 + 40
(ii) The answer says Tcos25 = μR + 0.196T
Why? What is 0.196? My first thought was Tcos25 = μR but it appears to be wrong. Help please D:

Attached Images
File Type: png Screenshot (124).png (48.6 KB)
File Type: png Screenshot (125).png (34.2 KB)


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