# Dynamics- Friction

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

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
Homework Helper
Gold Member
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).