Solving Dynamics-Friction for Max θ w/ μ_s=0.25

[hsphysics2]

Homework Statement

A box is halfway up a ramp. The ramp makes an angle, θ with the ground. What is the maximum value of θ before the mass will slip? μ$_{s}$=0.25

Homework Equations

F$_{x}$=ma$_{x}$

The Attempt at a Solution

I drew a free body diagram to show the forces affecting the box

η-mgcos=0
η=mgcosθ (eq'n 1)
F$_{x}$=ma$_{x}$
μ$_{s}$η-mgsinθ=ma$_{x}$ (sub eq'n 1 in)
μ$_{s}$(mgcosθ)-mgsinθ=ma$_{x}$
mg(μ$_{s}$cosθ-sinθ)=ma$_{x}$


I'm not sure where to go from here, or even if this is the correct path for me to take

 

[NihalSh]

Your equations are correct.

The question has essentially asked you to calculate max value of (theta), so the block does not slip. What does that tell you?...Acceleration is 0. Now you know what to do.