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).