Dynamics and Friction: Solving for Maximum Angle on a Ramp with 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

 

[PhanthomJay]

You have correctly identified the forces acting, but just as the box is on the verge of slipping, is it accelerating?

 

[hsphysics2]

the box wouldn't be accelerating, so would it be

mg(μ_{s}cosθ-sinθ)=0
mgμ_{s}cosθ=mgsinθ
μ_{s}cosθ=sinθ
μ_{s}=tanθ
θ=14.036

 

[PhanthomJay]

the box wouldn't be accelerating, so would it be

mg(μ_{s}cosθ-sinθ)=0
mgμ_{s}cosθ=mgsinθ
μ_{s}cosθ=sinθ
μ_{s}=tanθ
θ=14.036

Yes, good, in degrees (don't forget units), but you should round your answer to 14 degrees ( 2 significant figures).