How to calculate angle given coefficent of friction

[Eats Dirt]

Homework Statement

two objects are suspended on a platform one weighs 10 kg and the other weighs 20 kg, the coefficient of static friction is 0.4

Homework Equations

how to find angle each of the objects start to slide

The Attempt at a Solution

OK so Us=Fs/Fn
0.4= Fs/Fn
Fg=9.8(10) for the 10 kg object
using the vertical and horizontal components of the fg vector i get
Fn= ma cos(theta)
Fs= ma sin(theta)
U=fs/fn
0.4=sin(theta)
cos(theta) mass and acceleration cancel out
this is where i get stuck because i have theta over theta they should cancel out and i will be left with a broken equation :( any help would be appreciated.

Also if mass cancels out how am i supposed to get different angles for each of the boxes which weigh different amounts?

 

[rock.freak667]

You should have for motion that F_s≥μF_n

so you have mgsinθ ≥ μmgcosθ. (the minimum angle of theta would be when they are equal)

Which gives you a simple relation with θ and μ.

 

[Eats Dirt]

You should have for motion that F_s≥μF_n

so you have mgsinθ ≥ μmgcosθ. (the minimum angle of theta would be when they are equal)

Which gives you a simple relation with θ and μ.

i don't understand how you would isolate theta without it canceling out or being 1

 

[rock.freak667]

i don't understand how you would isolate theta without it canceling out or being 1

Remember the identity tanθ = sinθ /cosθ ?