A small mass m is set on the surface of a sphere. If the coefficient of static friction is µs = 0.8?

Question

A small mass m is set on the surface of a sphere. If the coefficient of static friction is µs = 0.86, at what angle would the mass start sliding?
I have no idea how to approach this...please help
and thank you in advance

Answer 1

Let theta be the angle from the top.
The force normal to the sphere
Fn = mgcos(theta)
The force tangential to the sphere
Ft = mgsin(theta)
When the mass starts to slide,
Ft = µs * Fn
µs = Ft/Fn = tan(theta)
theta = arctan(µs)