Feedback on the concepts surrounding pulley, ropes, friction

[goodOrBad]

Homework Statement

Having been working on problems that included weight, ropes, pulley and friction I wanted to make a sort of reminder. But I need to know if and what changes if F2 > F1

Relevant Equations

Fx=0
Fy=0

 

[Lnewqban]

Revisit the angles for the two first cases.
From first diagram, β<90°.
From second diagram, β>90°.

 

[goodOrBad]

really? Because I thought it goes like this

 

[Lnewqban]

You are correct for the angle of contact.

What if F1>F2?
The idea is to use friction as a way to reduce the pulling resisting force respect to the greater load.

Please, see:
https://en.wikipedia.org/wiki/Capstan_equation

 

[haruspex]

if and what changes if F2 > F1

Friction acts to oppose relative motion of the surfaces in contact. It will aid whichever of the two forces is weaker.
In the usual linear arrangement, $|F_1-F_2|<\mu_sN$ for static friction; in these capstan arrangements, $|\ln(F_1)-\ln(F_2)|<\mu_s\theta$.
(I'm assuming each force is measured with pulling away from the frictional contact as positive.)