Please help with finding the angle at which an object will slide off a surface.

Nov 2019
Queens, NY
If given the coefficient of friction and the mass of an object, one should be able to find the angle at which the object will begin to slide off an inclined plane right?
1) I thought it would be F=mg to find weight
2) Set the weight equal to normal force as if it were on a flat surface
3) Calculate the frictional force using Ff = uFn
4) Set that frictional force equal to the force parallel to the inclined plane and then use Sin (x) = Ff/Weight

It seems that I am missing something though as every time I put it in the simulator it comes out wrong.

Also, I know that the coefficient of friction is tied to molecular level phenomena, but can it also be described as the relationship between two forces that are perpendicular to each other for an object on a surface?
Jan 2019
to begin sliding, the object's weight component parallel to the incline has to exceed the maximum force of static friction acting in the opposite direction

if $\theta$ is the angle of inclination to the horizontal, $mg$ is the weight of the object, and $\mu_s$ is the coefficient of static friction,

$mg\sin{\theta} \ge f_{s \, max} = \mu_s \cdot F_N = \mu_s \cdot mg\cos{\theta} \implies \sin{\theta} \ge \mu_s \cos{\theta} \implies \tan{\theta} \ge \mu_s \implies \theta \ge \arctan(\mu_s)$

check out the link for a good explanation of friction

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